Situations in Natural Language Semantics

First published Mon Feb 12, 2007; substantive revision Wed Oct 13, 2021

Situation semantics was developed as an alternative to possible worldssemantics. In situation semantics, linguistic expressions areevaluated with respect to partial, rather than complete, worlds. Thereis no consensus about what situations are, just as there is noconsensus about what possible worlds or events are. According to some,situations are structured entities consisting of relations andindividuals standing in those relations. According to others,situations are particulars. In spite of unresolved foundationalissues, the partiality provided by situation semantics has led to somegenuinely new approaches to a variety of phenomena in natural languagesemantics. In the way of illustration, this article includesrelatively detailed overviews of a few selected areas where situationsemantics has been successful: implicit quantifier domainrestrictions, donkey pronouns, and exhaustive interpretations. Itmoreover addresses the question of how Davidsonian event semantics canbe embedded in a semantics based on situations. Other areas where asituation semantics perspective has led to progress include attitudeascriptions, questions, tense, aspect, nominalizations, implicitarguments, point of view, counterfactual conditionals, and discourserelations.

1. Situations in direct perception reports

Situations entered natural language semantics with Jon Barwise’spaperScenes and Other Situations (Barwise 1981), followed byBarwise and Perry’sSituations and Attitudes (Barwise& Perry 1983).Scenes and Other Situations is about themeaning of direct (or epistemically neutral) perception reports, aconstruction illustrated in (1):

(1): Beryl saw Meryl feed the animals.

Direct perception reports contrast with indirect (or epistemicallypositive) perception reports, which typically have finite embeddedclauses, as in (2):

(2): Beryl saw that Meryl fed the animals.

Both (1) and (2) presuppose that Meryl fed the animals. But (1) and(2) still differ with respect to the interpretation of their embeddedcomplements: the embedded complement in (1) can only be interpreted astransparent, and this is not so for the embedded complement in (2).The transparency of the embedded complement in (1) is shown by thevalidity of inferences like that in (3), for example:

(3)

Beryl saw Meryl sprinkle the white powder on Cheryl’sdinner.

The white powder was the most deadly poison.

Beryl saw Meryl sprinkle the most deadly poison onCheryl’s dinner.

In contrast to (3), the first sentence in (4) has an interpretationthat renders the inference in (4) invalid.

(4)

Beryl saw that Meryl sprinkled the white powder onCheryl’s dinner.

The white powder was the most deadly poison.

Beryl saw that Meryl sprinkled the most deadly poison onCheryl’s dinner.

A semantic analysis of direct perception reports has to explain whatit is that forces their complements to be transparent. Barwise 1981proposes to analyze direct perception reports like (1) along the linesof (5):

(5): There is an actual past situations that Beryl saw, ands supports the truth ofMeryl feed the animals.

The virtues of Barwise’s analysis can be appreciated evenwithout seeing the exact details of how situations might support thetruth of sentences. In (5) the verbsee semantically selectssituations rather than propositions as its first argument, and thishas the desirable effect that the truth value of those sentences doesnot change when the description of the perceived situation is replacedby an extensionally equivalent one. If Meryl fed the animals just oncein the actual world, and she fed them hay, then the set of actualsituations that support the truth ofMeryl feed the animalsis expected to be the same as the set of actual situations thatsupport the truth ofMeryl feed the animals hay. But then (5)and (6) must have the same actual truth-value, and Barwise’sanalysis predicts correctly that (1) and (7) must, too.

(6): There is an actual past situations that Beryl saw, ands supports the truth ofMeryl feed the animalshay.
(7): Beryl saw Meryl feed the animals hay.

The publication of Barwise 1981 in theJournal of Philosophywas followed by two papers providing commentary: Higginbotham 1983 inthe same journal, and Vlach 1983 inSynthese. The peerverdict on situations was that they were not needed for the semanticsof direct perception reports: the facts could just as well beexplained by Davidsonian event semantics. (Davidson 1967a, 1980. Seethe entriesDonald Davidson andevents.) In fact, Barwise’s argument showing that direct perceptionsee selects a situation is very much like Davidson’sargument showing that the verbcause expresses a relationbetween events (Davidson 1967b, 1980). Comparison with Davidsonianevent semantics has been an issue for situation semantics throughoutits history. The relation between situation semantics and Davidsonianevent semantics will be taken up in section 9.

2. States of affairs, infons, and information content

Later developments in situation semantics emphasized its role as ageneral theory of information content. The key concept is the notionof a state-of-affair or “infon” (see the entrystates of affairs). State-of-affairs are non-linguistic formal objects that come invarious stages of complexity (see Gawron & Peters 1990 for a briefoverview, Devlin 1991, 2006 for a more detailed exposition, andGinzburg & Sag 2000 for a system based on a richer ontology). Thesimplest kinds of state-of-affairs consist of a relation, individualsrelated by the relation, and a polarity, and might be represented asin (8):

(8)

a.: << bothering, Nina, Stella; no >>
b.: << helping, Stella, Nina; yes >>

Arguments of a relation may be parameterized, as in (9):

(9): << bothering,x, Stella; no >>

Parameterized roles can be anchored to individuals. In (9), theparameterized botherer role may be anchored to Nina, for example, andin that case, the result is the unparameterized state-of-affairs in8(a). Parameterized states-of-affairs can be restricted by otherparameterized state-of-affairs, as in (10), where the subject role forthe property of taking a shower is restricted to individuals who aresinging:

(10): << showering,x_{<< singing,x;yes >>}; no >>

Properties and relations can be produced from parameterizedstates-of-affairs by absorbing parameters:

(11): [x | << bothering,x, Stella; no>>]

Parameter absorption is the situation theory analogue ofλ-abstraction. (11) corresponds to the property of notbothering Stella. There are additional operations that build complexstates-of-affairs from simpler ones, including analogues ofconjunction, disjunction, and existential and universal quantification(see Devlin 1991, 2006, and Ginzburg & Sag 2000). The ultimategoal is to provide the necessary tools for a theory of informationcontent (see the entrysemantic conceptions of information). Barwise 1988 mentions a wide range of applications, including“a theory of information to account for the role informationpickup plays in the life of the frog, how the information it detectsis related to the actions it takes, actions like flicking its tongueand hopping about” (Barwise 1988, 257). Other applicationsmentioned are theories of vision, databases, robot design,mathematical proofs, information exchange between speakers ofparticular language, and cognitive science as a whole. Finally, thetheory should be able “to be turned on itself, and provide anaccount of its own information content, or rather, of the statementsmade by the theorist using the theory” (Barwise 1988, 258).

When Barwise and Perry started their joint work, a new, morefine-grained, notion of information content seemed to be urgentlyneeded in natural language semantics, because of a known challengefacing possible worlds semantics, which, under the influence of Lewis1972 and Montague 1974, was the framework of choice for most formalsemanticists at the time (see the entry onpossible worlds). In possible worlds semantics, propositions are identified with theset of possible worlds where they are true (see the entrypropositions). Consequently, propositions that are true in the same possible worldsare identical, and we seem to predict wrongly that a person whobelieves a propositionp should also believe any propositionthat is true in the same worlds asp (see the entrypropositional attitude reports). To distinguish logically equivalent propositions, we seem to need amore fine-grained notion of what the information content of a sentenceis, and the state-of-affairs or infons of situation semantics weremarketed to provide just that.

The solution that situation semantics offered for the puzzle oflogically equivalents in attitude ascriptions encountered competitionfrom the very start: state-of-affairs and infons looked suspiciouslylike structured propositions (see the entrystructured propositions). Intensional versions of structured propositions had already beenoffered as remedies for the attitude ascription problem by Carnap1947, Lewis 1972, Cresswell & von Stechow 1982, and were alsoappealed to for the analysis of information structure and intonationalmeaning. The structured meanings of Carnap, Lewis, and Cresswell &von Stechow are tree structures whose end nodes are intensions, ratherthan lexical items. They are thus objects that are independent of thevocabularies of particular languages, but are neverthelesshierarchically structured in the way sentences are. Differencesbetween structured propositions in various frameworks and thestate-of-affairs or infons of situation theory seem to largely boildown to foundational matters regarding the status of possibilia (seethe entries onpossible objects and possible worlds) andthe nature of properties and relations (seeproperties).

There is currently no consensus about the semantics of attitudeascriptions, and it is not clear whether situation semantics has aprivileged place in the family of accounts that have been proposed.Perhaps more importantly, for most empirical generalizations inlinguistic semantics, propositions construed as sets of possibleworlds or situations provide the right level of abstraction. Thereseems to be no need to posit unwieldy information contents in areaswhere simpler notions provide more elegant accounts. Since thisarticle is not about theories of information, the concern to provide ageneral theory of information content will now have to be set aside,even though it is central to some areas in situation semantics andsituation theory (Devlin 1991, 2006; Ginzburg and Sag 2000; see alsoBarwise & Seligman 1997). The remainder of this article willreview situation-based accounts of selected topics that are currentlyunder active investigation in linguistics and philosophy: Austiniantopic situations, domain restrictions, donkey sentences, exhaustiveinterpretations, and Davidsonian event predication. None of thosephenomena requires a more fine-grained notion of information content.The discussion will thus be cast within a possibilistic framework(Kratzer 1989, 2002, 2012; Elbourne 2005, 2013). Possibilisticversions of situation semantics are conservative extensions ofpossible worlds semantics that construe propositions as sets of worldparts, rather than complete possible worlds (see Barwise 1988, chapter11, for an overview of the major branch points in situationsemantics). There are many areas that situation semantics hascontributed to that could not be reviewed here for reasons of space,including knowledge ascriptions, questions, discourse relations,counterfactuals, viewpoint aspect, gerunds, and implicit arguments.Stojanovich 2012 and Zucchi 2015 are recent general overviews ofsituation semantics. Additional references to work on variousphenomena within a situation-based semantics are given below under theheadingreferences not mentioned in the text.

3. Austinian topic situations

A core feature of many actual analyses of natural language phenomenawithin situation semantics is the idea attributed to John L. Austin1950 that utterances are about particular situations, with the actualworld being the limiting case (see the entry onJohn Langshaw Austin.) Barwise & Etchemendy 1987 illustrate the idea with an imaginedutterance of sentence (12):

(12): Claire has the three of clubs.

Whether an utterance of (12) is true or false depends, among otherthings, on what situation the utterance is about.

We might imagine, for example, that there are two card games going on,one across town from the other: Max is playing cards with Emily andSophie, and Claire is playing cards with Dana. Suppose someonewatching the former game mistakes Emily for Claire, and claims thatClaire has the three of clubs. She would be wrong on the Austinianaccount, even if Claire had the three of clubs across town. (Barwiseand Etchemendy 1987, p. 122)

If assertions are about particular situations, reports of assertionsmight not be accurate unless they take into account the situations theassertions were about. And there are more repercussions of Austinianreasoning: if assertions are about particular situations, beliefsshould be, too, and this means that our belief ascriptions might notbe accurate unless they take into account the situations the beliefsare about. That those situations do indeed matter for beliefascriptions is illustrated by the story of the Butler and the Judgefrom Kratzer 1998 (see Ogihara 1996, Kratzer 1990 (Other InternetResources), 2002, 2012; Portner 1992, Récanati 2000, forrelevant work on the role of topic situations in attitude ascriptionsand other embedded constructions):

The judge was in financial trouble. He told his butler that he hadbeen ready to commit suicide, when a wealthy man, who chose to remainanonymous, offered to pay off his debts. The butler suspected thatMilford was the man who saved his master’s life by protectinghim from financial ruin and suicide. While the butler was away on ashort vacation, the judge fell into a ditch, drunk. Unconscious andclose to death, he was pulled out by a stranger and taken to the localhospital, where he recovered. When the butler returned to the village,he ran into a group of women who were speculating about the identityof the stranger who saved the judge’s life by taking him to thehospital. One of the women said she thought that Milford saved thejudge’s life. The butler, who hadn’t yet heard about theaccident and thought the women were talking about the judge’sfinancial traumas, reacted with (13):

(13): I agree. I, too, suspect that Milford saved the judge’slife.

The next day, when discussion of the judge’s accident continued,somebody said:

(14): The butler suspects that Milford saved the judge’slife.

Given that the butler’s suspicion is not about the accident,there is a sense in which this belief attribution is not true. Itseems infelicitous, if not outright false. This suggests that ourimagined assertion of (14) makes a claim about a particular situationthat the suspicion is about. In the context of the story, thatsituation is the one everyone was talking about, and where the judgewas rescued from the ditch. Since the butler has no suspicion aboutsuch a situation, the person who uttered (14) said somethinginfelicitous or false. If (14) simply said that the butler suspectedthat there was a situation where Milford saved the judge’s life,the assertion would be true. There is support for the Austinianperspective on assertions and attitude ascriptions, then.

Austinian topic situations (also referred to as “focussituations”, “described situations”, or“reference situations” in the literature) are oftennon-overt, but the tense of a sentence might give them away. A closelook at tenses tells us that topic situations do not always coincidewith the situations described by the main predication of a sentence.Klein (1994, 4) imagines a witness who is asked by a judge what shenoticed when she looked into the room. The witness answered with(15):

(15): There was a book on the table. It was in Russian.

It is surprising that there is a past tense in the second sentence,even though the book must have still been in Russian when the witnesswas called for testimony. Even more surprising is the fact that thewitness could not have said (16) instead of (15).

(16): # There was a book on the table. It is in Russian.

Translated into a situation semantics (Klein himself talks about topictimes, rather than topic situations), Klein’s explanation isthat tense relates utterance situations to topic situations, which donot necessarily coincide with the situations described by the mainpredication of a sentence. In Klein’s scenario, the topicsituation for the second part of the witness’s answer was thepast situation that she saw when she looked into the room. Since thetopic situation was past, tense marking in the second sentence of (16)has to be past, too. Via their temporal locations, topic situationsplay an important role in the semantics of both tense and aspect (seethe entry ontense and aspect; also Smith 1991, Kamp & Reyle 1993, and Cipria & Roberts2000).

If Austinian topic situations play a role in the grammars of naturallanguages, there should be grammatical devices in at least somelanguages that track them. Recent work by Andrew McKenzie (McKenzie2012, 2015) has suggested that certain Switch Reference systems in anumber of genetically unrelated languages seem to track Austiniantopic situations. For example, the North American language Kiowa(Tanoan, spoken in Oklahoma) uses different forms for certainsentential connectives (including conjunction), depending on whetherthe topic situations of the conjoined conjuncts changes or stays thesame.

4. Situation semantics and implicit domain restrictions

Among the most innovative ideas in Barwise & Perry 1983 is theproposal to exploit the Austinian perspective on utterances to accountfor implicit quantifier restrictions and so-called“incomplete” definite descriptions (see the entrydescriptions):

Suppose that I am in a room full of people, some of whom are sleeping,some of whom are wide awake. If I say, “no one issleeping,” have I told the truth or not? Again, it depends onwhich situation I am referring to. If I am referring to the wholesituation including all the people in the room, then what I have saidis false. However, one can well imagine situations where I am clearlyreferring only to a part of that situation. Imagine, for example, thatI am conducting an experiment which requires an assistant to monitorsleeping people, and I look around the sleep lab to see if all of myassistants are awake and ready to go. Surely, then I may truly andinformatively say, “No one is asleep. Let’s begin.”…. The crucial insight needed goes back to Austin … AsAustin put it, a statement is true when the actual situation to whichit refers is of the type described by the statement. (Barwise &Perry 1983, 160)

A similar example discusses incomplete definite descriptions:

Suppose my wife and I collaborate on cooking for a party. And supposethat at a certain point in the party I say, “I am thecook,” referring tol. Is what I said true or not?

The answer is, “It depends on which situation I amdescribing.” First, suppose someone comes up to me and says,“The food at this party is delicious! Who is the cook?” IfI say “I am the cook,” I have clearly not described thingsaccurately. I have claimed to bethe person who did thecooking for the party. But suppose instead someone comes up to meeating a piece of my famous cheesecake pastry and says, “Whomade this?” Then I may truly say that I am the cook. (Barwise& Perry 1983, 159)

On the Austinian perspective, at least certain kinds of implicitrestrictions for quantification domains are a direct consequence ofthe fact that assertions are about particular actual situations, andthat those situations can be smaller or bigger parts of the actualworld.

The Austinian answer to implicit domain restrictions was endorsed anddeveloped in Récanati (1986/87, 1996, 2004a) and Cooper 1996.An influential attack on the situation semantics approach to“incomplete” definite descriptions came from Soames 1986,who concluded that “the analysis of definite descriptions is notfacilitated by the kind of partiality that situation semanticsprovides” (Soames 1986, 368). Soames’ reservations againstthe Austinian approach to domain restrictions come from two majorpotential counterarguments, both of which are directed againstparticular implementations of the approach. One of the potentialproblems discussed by Soames concerns attributive readings of definitedescriptions. However, as Soames is careful to note (Soames 1986,359), this problem does not necessarily affect possibilistic versionsof situation semantics. Since Soames’ qualification is notelaborated in his article, it might be useful to look at a concreteexample illustrating his point. Suppose the two of us observe a bearcrossing the road one night in Glacier National Park. Since it isdark, we can’t see the bear very well, and I say to you:

(17): The bear might be a grizzly.

I am aware that the bear we see is not the only bear in the world, somy assertion relies on an implicit domain restriction. On theAustinian view, my assertion is about a particular situation locatedsomewhere in Glacier National Park at a particular time in August2006. Call that situation “Bear Sighting”. Bear Sightinghas a particular bear in it, the bear we see. Call that bear“Bruno”. On the intended attributive reading, what I wantto get across to you is not that Bruno may be a grizzly, but that ourevidence about Bear Sighting is compatible with the assumption thatthe bear there—whoever he is—is a grizzly. There is alegitimate question whether we can get that reading on the Austinianapproach to domain restrictions. If Bear Sighting has to give us therestriction forbear, it seems that all it can do is restrictthe bears we are talking about to Bruno. But that wouldn’tproduce the attributive reading we are after. For that reading, so itmight seem, domain restrictions must be properties.

The above conclusion might look inevitable, but it is not. It is truethat on the Austinian view, my utterance of (17) is interpreted as aclaim about Bear Sighting. To see that we can nevertheless get thedesired interpretation, we need to look at technical details. 18(a)gives a plausible interpretation of the possibility modal in (17)within a possibilistic situation semantics. 18(b) is theinterpretation of the whole sentence (17) before the Austiniancomponent comes into play:

(18)

a.	[[might]]^c	λpλs∃s′[Acc_c(s)(s′)&p(s′)]
b.	[[(17)]]^c	λs ∃s′[Acc_c(s)(s′) &grizzly(ιxbear(x)(s′))(s′)]

(18) assumes an intensional semantics that is based on possiblesituations. In possible situation semantics, propositions are sets ofpossible situations, or characteristic functions of such sets, and allpredicates are evaluated with respect to a possible situation. 18(b)is the proposition expressed by (17) in contextc. Thatproposition is a property that is true of a situations iffthere is a situations′ that is accessible froms and the unique bear ins′ is a grizzly ins′. The modalmight introduces existentialquantification over possible situations that are accessible from theevaluation situations (see the entrymodal logic). The kind of accessibility relation is determined by the lexicalmeaning of the modal in interaction with properties of the utterancecontextc (see the entryindexicals). In our example, the modality is a particular kind of epistemicmodality that relates two situationss ands′in a contextc just in cases ands′are equivalent with respect to the information available inc, that is, whatever evidence abouts is availableinc isn’t specific enough to distinguish betweens ands′ (epistemic contextualism).Evidence that counts as available for epistemic modals might includethe distributed knowledge of the discourse participants (see vonFintel & Gillies 2011), other available sources of informationlike ship’s logs or computer printouts (Hacking 1967, von Fintel& Gillies 2011), but, interestingly, not necessarily informationthat happens to be hidden from sight like test results in sealedenvelopes (de Rose 1991), babies in wombs (Teller 1972), weatherconditions behind drawn curtains (Gillies 2001), or details of animalsobscured by darkness. Suppose the actual bear in Bear Sighting is infact a black bear, and not a grizzly. Since it is night and wecan’t see the bear very well, the evidence we have about BearSighting when I utter (17) cannot distinguish the real situation frommany merely possible ones, including some where the bear is a grizzlyand not a black bear. This is what makes my utterance of (17)true.

When I uttered (17), I claimed that the proposition in 18(b) was trueof Bear Sighting. Applying 18(b) to Bear Sighting yields the desiredattributive interpretation. Bear Sighting is exploited to provideimplicit domain restrictions, but it doesn’t do so directly. Weare considering epistemic alternatives of Bear Sighting. The epistemicalternatives are alternatives of Bear Sighting, hence are partial,just as Bear Sighting itself is. They have no more than a single bearin them. This suggests that the analysis of definite descriptionsis facilitated by the kind of partiality that situationsemantics provides. Austinian topic situations can give us domainrestrictions for attributive definite descriptions.

Soames’ second major objection against the Austinian approach todomain restrictions relates to the fact that there are instances ofdomain restrictions that can’t seem to come from Austinian topicsituations (see also Westerståhl 1985). One of Soames’examples is (19) below (Soames 1986, 357), which is a variation ofBarwise and Perry’s sleep lab example quoted above.

(19): Everyone is asleep and is being monitored by a researchassistant.

If all quantifier domains were provided by Austinian topic situations,(19) would seem to make contradictory demands on such a situation.Assuming that there is just a single topic situation for utterances of(19), we seem to predict that those utterances imply that the researchassistants are among those who are asleep. But there is no suchimplication. Soames is aware that proponents of the Austinian approachare not committed to the assumption thatall domainrestrictions are directly provided by Austinian topic situations(Soames 1986, footnote 17, 371), and he therefore emphasizes that heis only commenting on the particular account of domain restrictionsoffered in Barwise and Perry (1983, 1985). Soames’ objectiondoes not apply to Cooper 1996, for example, who allows quantifierdomains to be determined by different resource situations, which hedistinguishes from the Austinian topic situation (his “describedsituation”). The objection also does not apply to possibilisticversions of situation semantics, where every predicate is necessarilyevaluated with respect to an actual or possible situation. Differentpredicates in one and the same sentence can then be evaluated withrespect to different situations (Heim 1990, Percus 2000, Elbourne2002, 2005, 2013). A possible interpretation for (19) might be(20):

(20): λs ∀x [[person(x)(s′) &s′≤_ps] →[asleep(x)(s) & ∃y[research-assistant(y)(s) &monitoring(x)(y)(s)] ] ]

When the doctor of the sleep lab utters (19), she claims that theproposition in (20) is true of a particular situation, call it“Sleep Lab”. Sleep Lab is the Austinian topic situation,but it is not the situation that picks out the sleepers. The sleepersmight be recruited from a contextually salient (possibly scattered)situations′ that is related to Sleep Lab via the partrelation ≤_p and functions as a resourcesituation for the evaluation of the predicatepersonintroduced by the quantifier phraseeveryone. This situationcould be the sum of the patients in the lab, for example.

Neither topic nor resource situations have to be posited for theexclusive need of domain restriction. In a possibilistic situationsemantics resource situations are the kind of entities that theevaluation of any predicate routinely depends on. Topic situations,too, are independently needed: they are the situations that assertionsand beliefs are about, and they are key players in the semantics oftense and aspect. This means that the contribution of topic andresource situations to domain restriction comes entirely for free.Many instances of domain restrictions can thus be explained withoutpositing any special devices. Some of the remaining cases might alsobe accounted for by independently attested mechanisms includingsyntactic ellipsis, presupposition projection and conversationalimplicatures. But there is also exaggeration, taboo related omissions,and some such. The implicit domain restriction in the followingsentence, which appeared on a note posted in a bathroom in York(England), might very well fall in the last-mentioned category:

(21): Please do not dispose of anything down the toilet, except toiletpaper.

It is hard to see how any theory would want to literally prevent anykind of pragmatic enrichment processes (Récanati 1993, 2002,2004) from contributing to implicit quantifier restrictions, giventhat humans are able to “interpret utterances replete withirony, metaphor, elision, anacoluthon, aposiopesis, and on top of allof this …identify what a speaker isimplying as wellas saying” (Neale 2004, 123). Implicit domain restrictions arelikely to be the byproducts of a number of independently attestedmechanisms, then.

5. Situation variables or unarticulated constituents?

An important question in situation semantics is how exactly situationsenter the semantic interpretation process. Are they articulated viasyntactically represented variables, or are they “unarticulatedconstituents” (Perry 1986, Récanati 2002), possibly mereindices of evaluation? The issue is well explored for times andpossible worlds (see the entry onontological commitment). Kripke’s semantics for modal logic allows quantification overpossible worlds only in the metalanguage (see the entrymodal logic), for example. Likewise, in Prior’s tense logic (see the entryArthur Prior), quantification over times is confined to the metalanguage (see theentrytime).

(22)

a.: [[must α]]^w = 1 iff[[α]]^w′ = 1 for allw′that are accessible fromw.
b.: [[past α]]^t = 1 iff[[α]]^t′ = 1 for somet′that precedest.

Montague’s language of intensional logic (Montague 1974) wasdeveloped in the tradition of Kripke and Prior, and does not havevariables ranging over times or worlds: tense and modal operatorsshift evaluation indices, as illustrated in (22), but do not bindvariables in the object language. Quantification over worlds and timesis treated differently from quantification over individuals, then. Thedistinction was made deliberately because it predicts differences thatwere thought correct at the time. Once an evaluation index is shifted,it is gone for good, and can no longer be used for the evaluation ofother expressions. This constrains temporal and modal anaphora. Untilthe early seventies anaphoric reference to times and worlds in naturallanguages was believed to be constrained in precisely the waypredicted by the evaluation index approach. The belief was challengedby work on temporal anaphora (Kamp 1971, Partee 1973, Vlach 1973, vanBenthem 1977), however. Cresswell 1990 presented parallel argumentsfor modal anaphora, and showed more generally that natural languageshave the full expressive power of object language quantification overworlds and times. Quantification over worlds or times is thus nodifferent from quantification over individuals, and should beaccounted for in the same way.

Exact analogues of Cresswell’s examples can be constructed toshow that natural languages have the full expressive power of objectlanguage quantification over situations. Here is a first taste of thekind of example we have to look at.

(23): If, whenever it snowed, it had snowed much more than it actuallydid, the town plow would have removed the snow for us.

Suppose (23) is uttered to make a claim about the town of Amherstduring the last 20 years. We are looking at the snowfalls during therelevant period. For each of those actual snowfallss, we areconsidering counterfactual situationsr where it snowed muchmore than it did ins. The claim is that each of thosecounterfactual situations is part of a situation where the town plowremoved the snow for us. To formalize what was said, we have to beable to consider for each actual snowfalls a set ofcounterfactual alternatives and compare the amount of snow in each ofthem to the actual amount of snow ins. This means that wehave to be able to “go back” to the actual snowfallsituations after considering corresponding counterfactual situations.To do so we have to keep track of the original situations. Theavailable bookkeeping tools are either evaluation indices, or elsesituation variables and binding relations in the object language. Ifwe want to avoid possibly unpronounced situation variables, we needtwo shiftable evaluation indices for (23). In the long run, even twoindices wouldn’t be enough, though. Here is an example thatrequires three:

(24): Whenever it snowed, some local person dreamed that it snowed morethan it actually did, and that the local weather channel erroneouslyreported that it had snowed less, but still more than it snowed inreality.

It is not hard to see that we can complicate such examplesindefinitely, and that there would be no end to the number ofevaluation indices needed. But that suggests that natural languageshave the full power of object language quantification over situations.Quantification over situations is no different from quantificationover individuals, then, as far as expressive power is concerned. Sincenatural languages have syntactically represented individual variablesand it would be surprising if they used two different equally powerfulquantification mechanisms, it seems to be at least a good bet thatthere are syntactically represented situation variables in naturallanguages (but see Cresswell 1990 and Jacobson 1999 for dissentingopinions). But then the situations quantified over or referred to in(23), (24) and their kin do not necessarily correspond to“unarticulated constituents”. They are syntacticallyrepresented, even though they might happen to be unpronounced. Thesyntactic representation of situation variables is investigated inPercus 2000, Keshet (2008, 2010), and F. Schwarz (2008, 2012).

6. Situations, minimality, and donkey sentences

One of the most frequent uses of situation-based frameworks is in theanalysis of “donkey” pronouns, that is, anaphoric pronounsthat are interpreted as definite descriptions (seedescriptivetheories of anaphora under the entrydescriptions and the entryanaphora).

(25)

a.: Whenever a donkey appeared, it was greeted enthusiastically.
b.: Whenever a donkey appeared, the donkey was greetedenthusiastically.

The pronounit in 25(a) is an instance of a descriptivepronoun that is interpreted like the corresponding definitedescription in 25(b). Suppose I use 25(a) or (b) to talk about aparticular situation, call it “Donkey Parade”. Thesituations thatwhenever quantifies over are then all part ofDonkey Parade. They are precisely those subsituations of Donkey Paradethat are minimal situations in which a donkey appeared. Those mustthen be situations with a single donkey in them. The claim is that allthose situations are part of situations where the donkey was greetedenthusiastically. More formally, my claim about Donkey Parade is(26):

(26): λs ∀s′ [ [s′≤_ps &s′ ∈Min(λs ∃x[donkey(x)(s) &appeared(x)(s)])] → ∃s″[s′ ≤_ps″ &greeted-enthusiastically (ιxdonkey(x)(s′))(s″)] ]

(26) reflects the standard analysis of adverbs of quantification anddescriptive pronouns in a possibilistic situation semantics (Berman1987; Heim 1990; Portner 1992; von Fintel 1994, 2004b; Elbourne 2002,2005, 2013, 2016). All resource situations that are introduced in (26)are directly or indirectly related to the topic situation via the partrelation ≤_p. The topic situation is theultimate anchor for all resource situations. It indirectly restrictsthe donkeys being talked about to those that are present in DonkeyParade. The antecedent of the conditional introduces a furtherrestriction: we are considering only those subsituations of DonkeyParade that are minimal situations in which a donkey appeared. Thosesituations have just one donkey in them, and they can thus be used asresource situations for the definite descriptionthe donkeyor a corresponding descriptive pronoun.

The crucial feature of any analysis of donkey sentences within asituation semantics is that quantification is over minimal situationssatisfying conditions imposed by the antecedent of the conditional.The minimality condition is crucial for the analysis of descriptivepronouns. Without it, we wouldn’t be able to analyze thosepronouns as definite descriptions:

(27): Whenever a man saw a donkey, the man greeted the donkey.

We have to make sure that the situations or events quantified overhave just one man and just one donkey in them, because definitedescriptions have to be unique with respect to their resourcesituations. The minimality condition is a source of potential trouble,however (Reinhart 1986, Dekker 2004; von Fintel 2004a,b). When theantecedent of a conditional contains a mass noun, negativequantifiers, or certain kinds of modified quantifier phrases,quantification over minimal situations or events seems to yieldunwelcome results or isn’t possible at all:

(28)

a.: When snow falls around here, it takes ten volunteers to removeit.
b.: When a cat eats more than one can of Super Supper in a day, itgets sick.
c.: Whenever there are between 20 and 2000 guests at a wedding, asingle waiter can serve them.
d.: Whenever nobody showed up, we canceled the class.

28(a) raises the question whether there ever are minimal situations orevents in which snow falls. But even if there are, we do not quantifyover them in this case. We also do not seem to rely on discrete scalesfor measuring portions of Super Supper. But even if we did, this wouldnot help with 28(b). This sentence does not necessarily quantify oversituations in which a cat eats just a little more than a can of SuperSupper. Minimality also doesn’t seem to play a role for 28(c).If 28(c) quantified over minimal situations that have between 20 and2000 wedding guests, it would quantify over situations or events withexactly 20 wedding guests, and might very well be true. 28(d) is evenmore dramatic. What would a minimal situation or event look like inwhich nobody showed up? If any event- or situation-based analysis ofdonkey sentences is to succeed, then, it must keep the events orsituations that are quantified over small enough to contain just oneman and one donkey in cases like (27), but it has to accomplish thiswithout minimizing the amount of snow, Super Supper, or wedding guestsin cases like 28(a) to (c). And it should not mess with negativeconstructions at all. When we are quantifying over situations indonkey sentences, then, we need to relate possibly very complexsentences to exemplifying situations in a way that is responsive tothe different behavior of different kinds of antecedents illustratedby (27) and 28(a) to (d).

There are several proposals in the literature that elucidate therelation between a sentence and the situations or events thatexemplify it by positing a special recursive mechanism that relatessentences to the set of exemplifying events or situations (see Schein1993, chapters 9 and 10 for discussion of this issue). Possibilisticversions of situation semantics typically start out with a recursivetruth definition that relates utterances of sentences to the sets ofpossible situations in which the utterances are true, the propositionsexpressed. The situations or events that exemplify a proposition canthen be defined as the “minimal” situations in which theproposition is true (see the entries onevents, facts,states of affairs, and truthmakers). Thechallenge presented by sentences (27) and 28(a) to (d) is that theysuggest that a naïve notion of minimality won’t do. A moreflexible notion of minimality seems to be needed. The followingsection will document in some detail how the desired notion ofminimality might emerge from a simple definition of exemplification ininteraction with independently justified sentence denotations. Theissue is under active investigation, however, and cannot be consideredsettled before a wide range of different constructions has been lookedat. Whatever the ultimate outcome may be, the following discussionwill provide the opportunity to illustrate how the shift from possibleworlds to situations affects the denotations we might want to positfor an expression. In a situation semantics, there are often severalways of assigning denotations to an expression that are hard todistinguish on truth-conditional grounds. Looking at the situationsthat exemplify a sentence as well as its truth-conditions helps withthe choice.

7. Minimality and exemplification

In possibilistic versions of situation semantics, possible situationsare parts of possible worlds. Some authors also assume that the partsof a possible worldw form a join semi-lattice with maximalelementw (Bach 1986; Lasersohn 1988, 1990; Portner 1992; seealso the entrymereology). The part relation ≤_p and the sum operation +are then related as usual:s ≤_ps′ iffs +s′ =s′. Propositions are sets of possible situations ortheir characteristic functions (see the entrypropositions). The notion of a situation that exemplifies a proposition might bedefined as in (29), which is a variation of a definition that appearsin Kratzer 1990 (Other Internet Resources), 1998, 2002:

(29): Exemplification
A situations exemplifies a propositionp ifwhenever there is a part ofs in whichp is nottrue, thens is a minimal situation in whichp istrue.

Intuitively, a situation that exemplifies a propositionp isone that does not contain anything that does not contribute to thetruth ofp. The first part of (29) allows two possibilitiesfor a situations to exemplifyp. Eitherpis true in all subsituations ofs ors is a minimalsituation in whichp is true. The notion of minimalityappealed to in (29) is the standard one: A situation is a minimalsituation in which a propositionp is true iff it has noproper parts in whichp is true. The situation Mud (Case Onebelow) gives a first illustration of what (29) does.

Case One: Mud

Mud is a situation that consists of mud and only mud.

Assuming that Mud and all of its parts are mud, Mud and all of itsparts exemplify the proposition in 30(b), since there are no parts ofMud where there is no mud.

(30)

a.: There is mud.
b.: λs ∃xmud(x)(s)

30(b) is not exemplified by Mud & Moss (Case Two below),however:

Case Two: Mud & Moss

Mud & Moss is a situation that consists of some mud and somemoss and nothing else.

Mud & Moss has parts where 30(b) is not true: the parts wherethere is only moss. But Mud & Moss is not a minimal situation inwhich 30(b) is true.

Next, consider (31):

(31)

a.: There are three teapots.
b.: λs ∃x [x≤_ps & |{y:y≤_px &teapot(y)(w_s)}| = 3]

31(b) describes situationss that have at least three teapots(individuals that are teapots in the world ofs) in them. Theproposition in 31(b) seems to be exemplified by the situation Teapots(Case Three below).

Case Three: Teapots

Teapots has three teapots and nothing else in it.

There is no proper subsituation of Teapots in which 31(b) is true.Since Teapots has nothing but three teapots in it, any propersubsituation of Teapots would have to be one where a part of at leastone of the three teapots is missing. But 31(b) is true in Teapotsitself, and Teapots is thus a minimal situation in which 31(b) istrue.

There is a potential glitch in the above piece of reasoning. Itassumes that when an individual is a teapot in a world, no proper partof that individual is also a teapot in that world. This assumption canbe questioned, however. Following Geach 1980 (p. 215; see entriesidentity,problem of many), we might reason as follows: My teapot would remain ateapot if we chipped off a tiny piece. Chipping off pieces fromteapots doesn’t create new teapots, so there must have beensmaller teapots all along. We might feel that there is just a singleteapot sitting on the table, but upon reflection we might have toacknowledge that there are in fact many overlapping entities that allhave legitimate claims to teapothood. The unexpected multitude ofteapots is a source of headaches when it comes to counting. Afundamental principle of counting says that a domain for countingcannot contain non-identical overlapping individuals (Casati &Varzi 1999, 112):

(32): Counting Principle
A counting domain cannot contain non-identical overlappingindividuals.

(32) implies that just one of the many overlapping teapots on thetable over there can be counted, and the question is which one. If weare that liberal with teapothood, we need a counting criterion thattells us which of the many teapots in our overpopulated inventory ofteapots we are allowed to count.

With spatiotemporal objects like teapots, humans seem to rely oncounting criteria that privilege maximal self-connected entities(Spelke 1990, Casati & Varzi 1999). A self-connected teapot is onethat cannot be split into two parts that are not connected. Incontrast to parthood, which is a mereological concept, connectednessis a topological notion (see Casati and Varzi 1999 for discussion ofvarious postulates for a “mereotopology”, a theory thatcombines mereology and topology). The maximality requirement preventscounting teapots that are proper parts of other teapots, and theself-connectedness requirement disqualifies sums of parts fromdifferent teapots. Casati and Varzi point out that not all kinds ofentities, not even all kinds of spatiotemporal entities, come withcounting criteria that involve topological self-connectedness. Obviouscounterexamples include bikinis, three-piece suits, and broken glassesthat are shattered all over the floor. We have to recognize a widerrange of counting criteria, then, that guarantee compliance with (32)in one way or other.

Assuming counting criteria, the proposition expressed by 31(a) wouldstill be exemplified by Teapots, even if we grant that teapots canhave proper parts that are also teapots. The specification ofdenotations for sentences with numerals would now have to makereference to teapots that can be counted, call them “numericalteapots”. Representations like 31(b) and its kin should then beunderstood along the lines of 33(b):

(33)

a.: There are three teapots.
b.: λs ∃x [x≤_ps & |{y:y ≤_px &numerical-teapot(y)(w_s)}| =3]

If Teapots contains nothing but three individuals that are numericalteapots in the actual world, 33(b) is true in Teapots. But then noneof the proper subsituations of Teapots can contain three individualsthat are numerical teapots in the actual world. Any such situationcontains at least one teapot that is a proper part of one of theteapots in Teapots, hence can no longer contain three numericalteapots.

In contrast to Teapots, Teapots & Scissors (Case Four below) doesnot exemplify 31(b). Teapots & Scissors has parts where 31(b) isnot true: take any part that has just the scissors or just a part ofthe scissors in it, for example. But Teapots & Scissors is not aminimal situation in which 31(b) is true.

Case Four: Teapots and Scissors

Teapots & Scissors has three teapots and a pair of scissorsand nothing else in it.

Definition (29) has the consequence that Teapots does not exemplifythe proposition 34(b) below, even though 34(b) is true in Teapots.

(34)

a.: There are two teapots.
b.: λs ∃x [x≤_ps & |{y:y ≤_px &teapot(y)(w_s)}| = 2]

34(b) is true in Teapots, since Teapots contains a plural individualthat contains exactly two teapots. However, 34(b) is not exemplifiedby Teapots. Teapots has parts in which 34(b) is not true without beinga minimal situation in which 34(b) is true. More generally, ifsentences of the formthere are n teapots denote propositionsof the kind illustrated by 34(b), then those propositions can only beexemplified by situations that have exactlyn teapots.Likewise, ifthere is a teapot is interpreted as in 35(b)below, the proposition it expresses can only be exemplified bysituations with exactly one teapot, even though it can be true insituations with more teapots.

(35)

a.: There is a teapot.
b.: λs ∃x [x≤_ps & |{y:y ≤_px &teapot(y)(w_s)}| = 1]

The predicted exemplification properties of sentences with numeralsare welcome, since they suggest that (29) might indeed capture therelation between propositions and situations that we are after: Thesituations exemplifying the proposition expressed bythere is ateapot are all situations that have a single teapot in them,hence are literally minimal situations containing a teapot. Incontrast, the situations exemplifying the proposition expressed bythere is mud are all situations that contain mud and nothingelse, hence do not have to be minimal situations containing mud.

The major consequence of (29) is that if a proposition hasexemplifying situations at all, the set of its exemplifying situationsmust be either homogeneous or quantized in the sense of Krifka 1992. Aset of situations is quantized iff it doesn’t contain both asituations and a proper part ofs. A set ofsituations is homogeneous iff it is closed under the parthoodrelation, that is, whenever it contains a situations, italso contains all parts ofs. As argued in Krifka’swork, algebraic notions like homogeneity and quantization mightcapture linguistically important aspectual distinctions like thatillustrated in (36) (see the entry ontense and aspect).

(36)

a.: Josephine built an airplane.
b.: Josephine flew an airplane.

The proposition expressed by 36(a) seems to be exemplified by minimalpast situations in which Josephine built an airplane, and this set ofsituations is quantized. On the other hand, the proposition expressedby 36(b) seems to be exemplified by all past situations that containairplane flying by Josephine and nothing else, and this set ofsituations is homogeneous. Homogeneous sets cannot be used as countingdomains, however, and this requires adjustments with examples like37(b).

(37)

a.: Josephine built an airplane just once.
b.: Josephine flew an airplane just once.

37(b) cannot quantify over all situations that exemplify thepropositionJosephine flew an airplane, since this would giveus a quantification domain that violates the Counting Principle (32).We have to impose a counting criterion, then, and the topologicalnotion of self-connectedness seems to be relevant here, too (see vonFintel 2004a,b). As a result, 37(b) might quantify over maximalself-connected situations exemplifying the proposition expressed byJosephine flew an airplane.

We are now in a position to see how exemplification can be used forthe analysis of donkey sentences. Look again at (38) and (39):

(38): Whenever a man saw a donkey, the man greeted the donkey.
(39): Whenever snow falls around here, it takes ten volunteers to removeit.

(38) and (39) quantify over parts of a contextually salient topicsituation. The antecedents of the conditionals tell us more about whatthose parts are. In (38) quantification is over situationsexemplifying the proposition expressed bya man saw a donkey,which are all situations that contain a single man and a singledonkey. Those situations can then be taken to be resource situationsfor the definite descriptionsthe man andthe donkeyin the consequent of (38). (39) also quantifies over parts of thetopic situation that exemplify the antecedent proposition, but as inthe case of 37(b), considering all exemplifying situations wouldviolate the Counting Principle, and we therefore need a countingcriterion. (39) might then quantify over maximal self-connectedsituations exemplifying the proposition expressed bysnow fallsaround here. Those situations include complete snowfalls, then,and if it does indeed snow a lot around here whenever it snows, (39)might very well wind up true.

Not all propositions that look like perfectly acceptable candidatesfor sentence denotations have exemplifying situations. Consider 40(b),for example:

(40)

a.: There is more than five tons of mud.
b.: λs ∃x [mud(x)(s)&f_ton(x) > 5]

Whenever there is a situation that has more than five tons of mud init, there are parts that have just five tons or less. But none ofthose parts can be part of any minimal situation with more than fivetons of mud, since there are no such situations.

In a situation semantics, it often happens that there are severaloptions for assigning subtly different propositions to sentences, andsometimes the options are hard to distinguish on truth-conditionalgrounds. Insisting on both adequate truth-conditions and adequateexemplification conditions might help narrow down the field ofcandidates. 40(a) can also be paraphrased as saying that the totalamount of mud in some contextually salient resource situation weighsmore than five tons. The denotation of 40(a) could be (41), then,which includes a contextualized maximalization condition:

(41): λs ∃x [x≤_ps & [x =σz mud(z)(s′)] &f_ton(x) > 5]

(41) is true in a situations if it contains all the mud ofsome salient resource situations′ (possibly the actualworld as a whole), and that mud weighs more than 5 tons. (41) isexemplified by the mud ins′, provided it weighs morethan five tons. Sentences may contain noun phrases that provideanchors for the maximalization condition. (42) is a case inquestion:

(42)

a.: There is more than five tons of mud in this ditch.
b.: λs ∃x [x≤_ps &x =σz [mud(z)(w_s)& in(this ditch)(z)(w_s)]&f_ton(x) > 5]

42(b) is exemplified by the mud in this ditch, as long as it weighsmore than five tons.

Maximalized interpretations formore than n and similar kindsof indefinites likeat least n are discussed in Reinhart1986, Kadmon (1987, 1990, 2001), Schein 1993, and Landman (2000,2004). Some of the original observations go back to Evans 1977. Asnoted by Reinhart and Kadmon,more than n noun phrasesproduce maximality effects of the kind illustrated in (43):

(43): There was more than 5 tons of mud in this ditch. The mud wasremoved.

(43) would be considered false in a situation where there was in fact7 tons of mud in this ditch, but only six tons were removed. Thisjudgment can be accounted for by assuming that utterances of thesecond sentence in (43) are about a particular past situation thatexemplifies the first sentence. This situation can then serve as aresource situation for the interpretation of the definite descriptionthe mud. If sentences like 42(a) have maximalizedinterpretations, it follows that the mud that was removed was all themud in the ditch.

There are other numeral expressions that trigger maximalization. (44)is an example:

(44)

a.: There were between two and four teapots on this shelf.
b.: λs ∃x [x≤_ps &x =σz[teapots(z)(w_s) & on(thisshelf)(z)(w_s)] & 2 ≤|{z: teapot(z)(w_s)&z ≤_px }| ≤ 4]
c.: There were between two and four teapots on this shelf. They weredefective.

44(c), too, would be considered false in situations where only some ofthe teapots on the shelf are defective. Even simple numeral phraseslikefour teapots can have maximalized interpretations.

(45): There were four teapots on the shelf. They were defective.

Intuitions for (45) are not so clear, but (46) brings out a sharpdifference between simple and complex numeral phrases.

(46)

a.: Every time I sell two teapots on a single day, I am entitled to a$5 bonus.
b.: Every time I sell more than two teapots on a single day, I amentitled to a $5 bonus.
c.: Every time I sell between two and five teapots on a single day, Iam entitled to a $5 bonus.

Imagine that I sold exactly four teapots yesterday. 46(a) has aninterpretation where I am entitled to a $10 bonus. On this reading,our quantification domain is some set of non-overlapping situationsthat are minimal situations in which I sold two teapots on the sameday. Regardless of how we pair up yesterday’s four teapot salesto construct an acceptable counting domain, we always end up withexactly two bonus-qualifying situations. This shows that numeralexpressions liketwo teapots do not obligatorily havemaximalized interpretations. 46(a) contrasts with 46(b) and (c). 46(c)has no interpretation where I qualify for a $10 bonus if I sold fourteapots yesterday. And 46(b) has no interpretation where I get $10dollars if I sold six, for example. We can conclude, then, thatnumeral expressions of the formmore than n NP orbetweenn and m NP trigger denotations that are obligatorily maximalized,but this is not the case for simple numerals of the formnNP.

Returning to the donkey sentences we looked at earlier, we nowunderstand why 47(a) and (b) (repeated from above) do not simplyquantify over minimal situations in a naïve sense:

(47)

a.: When a cat eats more than one can of Super Supper in a day, itgets sick.
b.: Whenever there are between 20 and 2000 guests at a wedding, asingle waiter can serve them.

The antecedents of 47(a) and (b) involve maximalization. For 47(a),for example, the proposition expressed by the antecedent could be48(b):

(48)

a.: When a cat eats more than one can of Super Supper in a day…
When the amount of Super Supper a cat eats within a day is more thanone can …
b.: λs ∃x ∃y[cat(x)(s) &f_day(s) = 1 &y =σz[Super-Supper(z)(w_s) &eat(z)(x)(s)] &f_can(y) > 1]

48(b) restricts the situations quantified over to those whose temporalextension is a day, which could be a calendar day, or, more plausibly,a 24-hour period. The maximality condition can then pick out all thefood eaten during such a period by the relevant cats, regardless ofwhether they ate just a little more than what comes in a can or muchmore than that. There is no pressure to keep the portions small.However, Fox & Hackl (2006) have drawn attention to a class ofcases where thereis pressure to keep amounts small insentences withmore than n noun phrases. (49) below would besuch a case:

(49): Whenever the ballot count showed that a candidate had won morethan 50% of all votes, the winning candidate appeared on TV fiveminutes later.

(49) suggests that candidates appeared on TV five minutes after itbecame clear that they had won the majority of votes. If 500 voteswere cast in all, for example, and the ballot count showed at 8:00 pmthat one of the candidates had won 251 votes, the winning candidate isclaimed to have appeared on TV at 8:05 pm. This judgment is expectedif (49) quantifies over situations that exemplify the propositionexpressed by its antecedent. Factoring in maximalization triggered bymore than 50% of all votes, the antecedent can be paraphrasedas (50):

(50): The ballot count showed that the number of votes won by acandidate was more than 50% of all votes.

The exemplifying situations for the proposition expressed by (50) areminimal ballot count situations that establish that one of thecandidates has carried the majority of votes. If there are 500 ballotsin all, the exemplifying situations are all situations where 251ballots have been counted.

The last case to discuss concerns negative quantifiers.

(51)

a.: There is no teapot.
b.: λs ¬∃xteapot(x)(s)

51(b) is exemplified by the situations in which it is true. This makesthe situations exemplifying negative sentences a rather disparatebatch that do not resemble each other in any intuitive sense. If wewant to quantify over situations exemplifying the propositionsexpressed by negative sentences, as we do in (52) below (repeated fromabove), contextual restrictions for the topic situation must play amajor role, including those contributed by the topic-focusarticulation and presuppositions (Kratzer 1989, 2012; von Fintel 1994,2004a). Exemplification is not expected to make any contribution here,which is the result we want to derive.

(52): Whenever nobody showed up, we canceled the class.

This section discussed and tested a particular possibilistic accountof the relation between a proposition and its exemplifying situations.The test cases were conditionals that quantify over situations thatare “minimal” in a way that is responsive to specificproperties of their antecedents: the presence of count nouns versusmass nouns, telic versus atelic verb phrases, modified versusunmodified numerals, negative versus positive quantifiers. The accountshowed the right responsiveness in interaction with independentlymotivated interpretations for the sentences involved. Interestingly,once possible maximalizations are factored into sentence denotations,the exemplification account spelled out in definition (29) coincideswith the naïve minimalization account in most cases. The onlysystematic exceptions seem to be atelic antecedents, including thoseinvolving negation. Contrary to initial appearance, then, thenaïve minimalization accounts found in most existing analyses ofdonkey sentences within a possibilistic situation semantics are closeto correct (but see section 9 for discussion of another potentiallyproblematic case, example (61)).

8. Exemplification and exhaustive interpretations

Minimal interpretations of sentences are a common phenomenon and arenot only found in the antecedents of donkey sentences. Among the mostwidely discussed cases are exhaustive answers to questions, or moregenerally, exhaustive interpretations (Groenendijk & Stokhof 1984,Bonomi & Casalegno 1993, Sevi 2005, Schulz and van Rooij 2006,Spector 2006, Fox 2007, Fox & Hackl 2006; see also the entryimplicature). Here is an illustration.

(53)

Josephine:	Who caught anything?
Beatrice:	Jason and Willie did.

We tend to understand Beatrice’s answer as suggesting that Jasonand Willie were the only ones who caught something. This is theexhaustive interpretation of Beatrice’s answer. Non-exhaustiveor “mention some” answers are often marked with specialintonation or particles, as in (54), for example:

(54)

Josephine:	Who caught anything?
Beatrice:	Jason and Willie did for sure.

In this case, Beatrice indicates that she does not mean her answer tobe understood exhaustively. In combination with Groenendijk andStokhof’s 1984 analysis of questions, the exemplificationrelation allows a strikingly simple characterization of exhaustive andnon-exhaustive answers. If we import Groenendijk and Stokhof’sanalysis into a situation semantics, the extension ofJosephine’s question in (54) is the proposition in (55):

(55): λs [λx ∃ycaught(y)(x)(s) = λx∃ycaught(y)(x)(w₀)]

(55) describes possible situations in which the set of those whocaught something is the same as the set of those who caught somethingin the actual world. Since question extensions are propositions, theycan be exemplified. Suppose Jason, Willie, and Joseph are the onlyones who caught anything in the actual world. Then (55) is exemplifiedby all minimal situations in which Jason, Willie, and Joseph caughtsomething. If nobody caught anything in the actual world, then anyactual situation exemplifies (55). Bringing in the Austinianperspective, we can now say that answers to questions are alwaysunderstood as claims about the actual situations that exemplify thequestion extension. Via their exemplifying situations, then, questionextensions determine possibly multiple topic situations that answersare understood to make claims about. When an answer is interpreted asexhaustive, the proposition it expresses is understood asexemplified by the topic situations. When an answer isinterpreted as non-exhaustive, the proposition it expresses isunderstood as being merelytrue in the topic situations. Wehave, then:

(56)

Question extension	A proposition. The set of situations that answer the question inthe same way as the actual world does.
Austinian topic situations	All actual situations that exemplify the questionextension.
Exhaustive answers	Propositional answers that are understood as exemplified by thetopic situations.
Non-exhaustive answers	Propositional answers that are understood as true in the topicsituations.

The proposition expressed by Beatrice’s exhaustive answer in(53) is understood as exemplified by the topic situations determinedby Josephine’s question, and that implies that Jason and Williewere the only ones who caught anything. In contrast, Beatrice’snon-exhaustive answer in (54) is understood as being true in the topicsituations, and that allows for the possibility that there were otherswho caught something.

It might be useful to consider a few more possible answers thatBeatrice might have given in response to Josephine’s questionand find out what the exemplification approach would predict if theanswers are understood exhaustively:

(57)

a.: Two cats did.
b.: Between two and five cats did.
c.: Nobody did.

The proposition expressed by 57(a) is exemplified by minimalsituations in which two cats caught something. If the topic situationsare of this kind, they, too, are minimal situations in which two catscaught something. But then the only ones who caught anything in theactual world are two cats. Building in maximalization, the propositionexpressed by 57(b) is exemplified by minimal situations in which abunch of two to five cats that consisted of all the cats that caughtsomething in some salient resource situation caught something. If thetopic situations are of this kind, then only cats caught something,and there were between two and five of them. For 57(c), the set ofsituations that exemplify the proposition it expresses coincides withthe set of situations in which it is true. Consequently, there is nodifference between an exhaustive and a non-exhaustive interpretation.The topic situations include the actual world, and what is beingclaimed about them is that nobody caught anything.

The examples discussed suggest that the notion of minimality that isneeded for the analysis of donkey conditionals also accounts forexhaustive interpretations of answers. A third area where what lookslike the same notion of minimality shows up is Davidsonian eventpredication.

9. Situation semantics and Davidsonian event semantics

Situations and events seem to be the same kinds of things. Ifsituations are particulars, so are events. If situations are builtfrom relations and individuals standing in those relations, so areevents. We don’t seem to need both of those things. Wedon’t seem to need both situation semantics and Davidsonianevent semantics (see entriesDonald Davidson andevents).

The core of a Davidsonian event semantics are predications like thefollowing:

(58): swim(Ewan)(e)

(58) is the classical Davidsonian formalization of the tenselesssentenceEwan swim. The predication in (58) is standardlyread as “e is a swim by Ewan”. Crucially, thisformula is not understood as ‘e is an event thatcontains a swim by Ewan’ or as “e is an eventin which Ewan is swimming”. In other words, unlike thebasic predications in situation semantics, Davidsonian basicpredications have a built-in minimality condition. This is a majordifference between situation semantics and Davidsonian eventsemantics, maybethe difference. Without the minimalitycondition, we couldn’t do many things we want to do with aDavidsonian semantics. As an illustration, consider the followingexample:

(59)

a.: Ewan swam for 10 hours.
b.: ∃e [swim(Ewan)(e) &f_hour(e) = 10]

If the simple predicationswim(Ewan)(e) in 59(b) could beunderstood as “e is an event in which Ewanswims”, then 59(b) could describe an event where Ewan swam forjust five minutes, but a lot of other things went on as well in thatevent: He rode his bike, his sister slept, his mother harvestedshallots, his father irrigated fields, and taken together, thoseactivities took a total of 10 hours. 59(a) doesn’t describeevents of this kind, hence 59(b) couldn’t be a formalization of59(a). The standard way of understanding 59(b) is as saying that therewas a swim by Ewan that took 10 hours.

But what is a swim by Ewan? A swim is typically a self-connectedsituation in which someone is swimming, and which is“minimal” in a sense that it excludes other activitieslike riding a bike, sleeping or farm work. It doesn’t excludeparts of the actual swimming, like movement of arms and legs. Mostimportantly, a swim by Ewan doesn’tliterally have tobe a minimal situation in which Ewan is swimming, which would be avery short swim, if there are minimal swimming situations at all. Therelevant notion of minimality is by now familiar: a swim by Ewan is asituation that exemplifies the proposition “Ewan isswimming”. This suggests that the exemplification relation canbe used to actually define basic Davidsonian event predications withina situation semantics. The exemplification relation relates possiblyvery complex sentences to their exemplifying situations. Davidsonianevent predications emerge as those special cases where the sentencesthat are related to exemplifying situations are atomic.

If verbs have an event argument, as Davidson proposed, then simplesentences consisting of a verb and its arguments always involveDavidsonian event predication, and hence exemplification. ImportingDavidsonian event semantics into situation semantics, the propositionexpressed by 59(a), for example, might be formalized as follows:

(60): λs [past(s) & ∃e[e ≤_ps &swim(Ewan)(e) &f_hour(e) =10] ]

The formula in (60) incorporates the usual notation for Davidsonianevent predication. Within a situation semantics, this notation is justa convenient way to convey thatswim(Ewan)(e) is to beinterpreted in terms of exemplification: we are not talking aboutsituations in which Ewan swims, but about situations that exemplifythe proposition “Ewan swims”.

If Davidsonian event predication is part of the antecedent of aconditional, exemplification may come in more than once whendetermining the situations the conditional quantifies over. This iscrucial for examples like (61):

(61): Whenever a man rides a donkey, the man gives a treat to thedonkey.

(61) quantifies over situations that contain just one man and just onedonkey, but it does not seem to quantify over minimal donkey rides.There is no pressure to keep the rides short and multiply the treatsaccordingly. A single shift from descriptions of merely verifying toexemplifying situations would not yield the correct quantificationdomain for (61). If we tried to keep the situations small enough so asto contain no more than a single man and a single donkey we would haveto keep the rides short as well. However, if the antecedent of (61)contains Davidsonian event quantification, we can keep the situationsquantified over small enough to prevent the presence of more than oneman or donkey, but still big enough to contain complete donkey rides.The proposition expressed by the antecedent of (61) would be (62):

(62): λs ∃x ∃y[man(x)(s) & donkey(y)(s)& ∃e [e ≤_ps & ride(y)(x)(e)] ]

If the domain for the event quantifier in (62) is established on thebasis of some suitable counting criterion, it could quantify overmaximal spatiotemporally connected donkey rides. The proposition in(62) can then be exemplified by minimal situations that contain asingle manx and a single donkeyy and a maximalspatiotemporally connected event of ridingy byx.

The goal of bringing together situation semantics and Davidsonianevent semantics, at least in certain areas, is pursued in a number ofworks, including Lasersohn (1988, 1990), Zucchi (1988), Portner(1992), Cooper (1997), and Kratzer (1998).

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Evans, W., 2005,Small Worlds of Discourse and the Spectrum of Accommodation, Honors Thesis, Linguistics Department, University ofMassachusetts/Amherst.
Kratzer, A., 1990, “How Specific is a Fact?,” delivered at the Conference on Theories of Partial Information,Austin, TX: Center for Cognitive Science, University ofTexas/Austin.

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