Works by George Weaver
37 found
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| George Weaver [31] | George E. Weaver [10] | George Sumner Weaver [1] | George F. Weaver [1] |
- Back and forth constructions in modal logic: An interpolation theorem for a family of modal logics.George Weaver &Jeffrey Welaish -1986 -Journal of Symbolic Logic 51 (4):969-980.
- Homogeneous and universal dedekind algebras.George Weaver -2000 -Studia Logica 64 (2):173-192.A Dedekind algebra is an order pair (B, h) where B is a non-empty set and h is a similarity transformation on B. Each Dedekind algebra can be decomposed into a family of disjoint, countable subalgebras called the configurations of the algebra. There are 0 isomorphism types of configurations. Each Dedekind algebra is associated with a cardinal-valued function on called its configuration signature. The configuration signature counts the number of configurations in each isomorphism type which occur in the decomposition of (...) the algebra. Two Dedekind algebras are isomorphic iff their configuration signatures are identical. It is shown that configuration signatures can be used to characterize the homogeneous, universal and homogeneous-universal Dedekind algebras. This characterization is used to prove various results about these subclasses of Dedekind algebras. (shrink)
- Logical Consequence in Modal Logic.John Corcoran &George Weaver -1969 -Notre Dame Journal of Formal Logic 10 (4):370-384.This paper develops a modal, Sentential logic having "not", "if...Then" and necessity as logical constants. The semantics (system of meanings) of the logic is the most obvious generalization of the usual truth-Functional semantics for sentential logic and its deductive system (system of demonstrations) is an obvious generalization of a suitable (jaskowski-Type) natural deductive system for sentential logic. Let a be a set of sentences and p a sentence. "p is a logical consequence of a" is defined relative to the semantics (...) and "p is demonstrable from a" is defined relative to the deductive system. Main meta-Theorem: p is demonstrable from a if and only if p is a logical consequence of a. Henkin-Type methods are used. The theorems of the logic are exactly those of s5. The deductive system is rigorously developed as a system of linear strings. (shrink)
- The Fraenkel‐Carnap question for Dedekind algebras.George Weaver &Benjamin George -2003 -Mathematical Logic Quarterly 49 (1):92-96.It is shown that the second-order theory of a Dedekind algebra is categorical if it is finitely axiomatizable. This provides a partial answer to an old and neglected question of Fraenkel and Carnap: whether every finitely axiomatizable semantically complete second-order theory is categorical. It follows that the second-order theory of a Dedekind algebra is finitely axiomatizable iff the algebra is finitely characterizable. It is also shown that the second-order theory of a Dedekind algebra is quasi-finitely axiomatizable iff the algebra is (...) quasi-finitely characterizable. (shrink)
- Structuralism and representation theorems.George Weaver -1998 -Philosophia Mathematica 6 (3):257-271.Much of the inspiration for structuralist approaches to mathematics can be found in the late nineteenth- and early twentieth-century program of characterizing various mathematical systems upto isomorphism. From the perspective of this program, differences between isomorphic systems are irrelevant. It is argued that a different view of the import of the differences between isomorphic systems can be obtained from the perspective of contemporary discussions of representation theorems and that from this perspective both the identification of isomorphic systems and the reduction (...) to abstract structures or patterns should be resisted. (shrink)
- Effects of poststimulus study time on recognition of pictures.George E. Weaver -1974 -Journal of Experimental Psychology 103 (4):799.
- Finite Partitions and Their Generators.George Weaver -1974 -Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 20 (13-18):255-260.
- König's Infinity Lemma and Beth's Tree Theorem.George Weaver -2017 -History and Philosophy of Logic 38 (1):48-56.König, D. [1926. ‘Sur les correspondances multivoques des ensembles’, Fundamenta Mathematica, 8, 114–34] includes a result subsequently called König's Infinity Lemma. Konig, D. [1927. ‘Über eine Schlussweise aus dem Endlichen ins Unendliche’, Acta Litterarum ac Scientiarum, Szeged, 3, 121–30] includes a graph theoretic formulation: an infinite, locally finite and connected graph includes an infinite path. Contemporary applications of the infinity lemma in logic frequently refer to a consequence of the infinity lemma: an infinite, locally finite tree with a root has (...) a infinite branch. This tree lemma can be traced to [Beth, E. W. 1955. ‘Semantic entailment and formal derivability’, Mededelingen der Kon. Ned. Akad. v. Wet., new series 18, 13, 309–42]. It is argued that Beth independently discovered the tree lemma in the early 1950s and that it was later recognized among logicians that Beth's result was a consequence of the infinity lemma. The equivalence of these lemmas is an easy consequence of a well known result in graph theory: every connected, locally finite graph has among its partial subgraphs a spanning tree. (shrink)
- Compactness theorems for finitely-many-valued sentenial logics.George Weaver -1978 -Studia Logica 37 (4):413 - 416.
- Retroactive facilitation in short-term retention of minimally learned paired associates.Darryl Bruce &George E. Weaver -1973 -Journal of Experimental Psychology 100 (1):9.
- (1 other version)A Note on the Interpolation Theorem in First Order Logic.George Weaver -1982 -Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 28 (14-18):215-218.
- From finitary to infinitary second‐order logic.George Weaver &Irena Penev -2005 -Mathematical Logic Quarterly 51 (5):499-506.A back and forth condition on interpretations for those second-order languages without functional variables whose non-logical vocabulary is finite and excludes functional constants is presented. It is shown that this condition is necessary and sufficient for the interpretations to be equivalent in the language. When applied to second-order languages with an infinite non-logical vocabulary, excluding functional constants, the back and forth condition is sufficient but not necessary. It is shown that there is a class of infinitary second-order languages whose non-logical (...) vocabulary is infinite for which the back and forth condition is both necessary and sufficient. It is also shown that some applications of the back and forth construction for second-order languages can be extended to the infinitary second-order languages. (shrink)
- First Order Properties of Relations with the Monotonic Closure Property.George Weaver &Raymond D. Gumb -1982 -Mathematical Logic Quarterly 28 (1-3):1-5.
- Reading proofs with understanding.George Weaver -1988 -Theoria 54 (1):31-47.
- The First-Order Theories of Dedekind Algebras.George Weaver -2003 -Studia Logica 73 (3):337-365.A Dedekind Algebra is an ordered pair (B,h) where B is a non-empty set and h is an injective unary function on B. Each Dedekind algebra can be decomposed into a family of disjoint, countable subalgebras called configurations of the Dedekind algebra. There are N0 isomorphism types of configurations. Each Dedekind algebra is associated with a cardinal-valued function on omega called its configuration signature. The configuration signature of a Dedekind algebra counts the number of configurations in the decomposition of the (...) algebra in each isomorphism type.The configuration signature of a Dedekind algebra encodes the structure of that algebra in the sense that two Dedekind algebras are isomorphic iff their configuration signatures are identical. Configuration signatures are used to establish various results in the first-order model theory of Dedekind algebras. These include categoricity results for the first-order theories of Dedekind algebras and existence and uniqueness results for homogeneous, universal and saturated Dedekind algebras. Fundamental to these results is a condition on configuration signatures that is necessary and sufficient for elementary equivalence. (shrink)
- Interpolated task characteristics and interference in short-term memory.Charles P. Bird &George E. Weaver -1975 -Bulletin of the Psychonomic Society 6 (1):93-95.
- A note on definability in equational logic.George Weaver -1994 -History and Philosophy of Logic 15 (2):189-199.After an introduction which demonstrates the failure of the equational analogue of Beth?s definability theorem, the first two sections of this paper are devoted to an elementary exposition of a proof that a functional constant is equationally definable in an equational theory iff every model of the set of those consequences of the theory that do not contain the functional constant is uniquely extendible to a model of the theory itself.Sections three, four and five are devoted to applications and extensions (...) of this result.Topics considered here include equational definability in first order logic, an extended notion of definability in equational logic and the synonymy of equational theories.The final two sections briefly review some of the history of equational logic. (shrink)
- Unifying some modifications of the Henkin construction.George Weaver -1992 -Notre Dame Journal of Formal Logic 33 (3):450-460.
- Henkin's completeness proof: forty years later.Hugues Leblanc,Peter Roeper,Michael Thau &George Weaver -1991 -Notre Dame Journal of Formal Logic 32 (2):212-232.
- The a-b, b-c, a-c mediation paradigm: The effects of variation in a-c study- and test-interval lengths and strength of a-b or b-c.Rudolph W. Schulz &George E. Weaver -1968 -Journal of Experimental Psychology 76 (2p1):291.
- Directed attention and the recognition of pictures.Claudia J. Stanny &George E. Weaver -1980 -Bulletin of the Psychonomic Society 15 (6):410-412.
- Effects of processing tasks on the recognition of pictures.Claudia J. Stanny &George F. Weaver -1985 -Bulletin of the Psychonomic Society 23 (2):116-118.
- A-b, b-c, a-c mediation paradigm: Recall of a-b following varying numbers of trials of a-c learning.George E. Weaver &Rudolph W. Schulz -1968 -Journal of Experimental Psychology 78 (1):113.
- A General Setting for Dedekind's Axiomatization of the Positive Integers.George Weaver -2011 -History and Philosophy of Logic 32 (4):375-398.A Dedekind algebra is an ordered pair (B, h), where B is a non-empty set and h is a similarity transformation on B. Among the Dedekind algebras is the sequence of the positive integers. From a contemporary perspective, Dedekind established that the second-order theory of the sequence of the positive integers is categorical and finitely axiomatizable. The purpose here is to show that this seemingly isolated result is a consequence of more general results in the model theory of second-order languages. (...) Each Dedekind algebra can be decomposed into a family of disjoint, countable subalgebras called the configurations of the algebra. There are ?0 isomorphism types of configurations. Each Dedekind algebra is associated with a cardinal-valued function on ? called its configuration signature. The configuration signature counts the number of configurations in each isomorphism type that occurs in the decomposition of the algebra. Two Dedekind algebras are isomorphic iff their configuration signatures are identical. The second-order theory of any countably infinite Dedekind algebra is categorical, and there are countably infinite Dedekind algebras whose second-order theories are not finitely axiomatizable. It is shown that there is a condition on configuration signatures necessary and sufficient for the second-order theory of a Dedekind algebra to be finitely axiomatizable. It follows that the second-order theory of the sequence of the positive integers is categorical and finitely axiomatizable. (shrink)
- A Note on the Compactness Theorem in First Order Logic.George Weaver -1980 -Mathematical Logic Quarterly 26 (7-9):111-113.
- Classifying ℵo-categorical theories II: The existence of finitely axiomatizable proper class II theories.George Weaver &David Lippel -1998 -Studia Logica 60 (2):275-297.Clark and Krauss [1977] presents a classification of complete, satisfiable and o-categorical theories in first order languages with finite non-logical vocabularies. In 1988 the first author modified this classification and raised three questions about the distribution of finitely axiomatizable theories. This paper answers two of those questions.
- Classifying?0-categorical theories.George Weaver -1988 -Studia Logica 47 (4):327-345.Among the complete ℵ0-categorical theories with finite non-logical vocabularies, we distinguish three classes. The classification is obtained by looking at the number of bound variables needed to isolated complete types. In classI theories, all types are isolated by quantifier free formulas; in classII theories, there is a leastm, greater than zero, s.t. all types are isolated by formulas in no more thanm bound variables: and in classIII theories, for eachm there is a type which cannot be isolated inm or fewer (...) bound variables. ClassII theories are further subclassified according to whether or not they can be extended to classI theories by the addition of finitely many new predicates. Alternative characterizations are given in terms of quantifier elimination and homogeneous models. It is shown that for each primep, the theory of infinite Abelian groups all of whose elements are of orderp is classI when formulated in functional constants, and classIII when formulated in relational constants. (shrink)
- (1 other version)Extending ω‐consistent sets to maximally consistent, ω‐complete sets.George Weaver,Michael Thau &Hugues Leblanc -1990 -Mathematical Logic Quarterly 36 (5):381-383.
- Hermes algebras.George Weaver &Edward Thompson -2002 -Bulletin of the Section of Logic 31 (4):217-229.
- Logical Consequence in Modal Logic: Alternative Semantic Systems for Normal Modal Logics.George Weaver -1977 -Journal of Symbolic Logic 42 (2):317-317.
- Quasi-finitely characterizable and finitely characterizable Dedekind algebras.George Weaver &Benjamin George -2002 -Bulletin of the Section of Logic 31 (2):145-157.
- Simple expansions of classes satisfying Fraenkel-Carnap properties.George Weaver &Irena Penev -2010 -Bulletin of the Section of Logic 39 (3/4):175-186.
- Syntactic features and synonymy relations: A unified treatment of some proofs of the compactness and interpolation theorems.George E. Weaver -1994 -Studia Logica 53 (2):325 - 342.This paper introduces the notion of syntactic feature to provide a unified treatment of earlier model theoretic proofs of both the compactness and interpolation theorems for a variety of two valued logics including sentential logic, first order logic, and a family of modal sentential logic includingM,B,S 4 andS 5. The compactness papers focused on providing a proof of the consequence formulation which exhibited the appropriate finite subset. A unified presentation of these proofs is given by isolating their essential feature and (...) presenting it as an abstract principle about syntactic features. The interpolation papers focused on exhibiting the interpolant. A unified presentation of these proofs is given by isolating their essential feature and presenting it as a second abstract principle about syntactic features. This second principle reduces the problem of exhibiting the interpolant to that of establishing the existence of a family of syntactic features satisfying certain conditions. The existence of such features is established for a variety of logics (including those mentioned above) by purely combinatorial arguments. (shrink)
- Successive interpolation and first-list recall in the A-B, A-C and A-B, D-C paradigms.George E. Weaver &Gary I. Danielson -1969 -Journal of Experimental Psychology 81 (2):394.
- Stimulus meaningfulness, transfer, and retroactive inhibition in the A-B, A-C paradigm.George E. Weaver,Robert L. McCann &Robert J. Wehr -1970 -Journal of Experimental Psychology 85 (2):255.
- The a-b, b-c, a-c mediation paradigm: A-c performance in the absence of study trials.George E. Weaver,Ronald H. Hopkins &Rudolf W. Schulz -1968 -Journal of Experimental Psychology 77 (4):670.No categories
- The Fraenkel-Carnap Question for Limited Higher-Order Languages.George Weaver &B. George -2010 -Bulletin of the Section of Logic 39 (1/2):1-9.No categories
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David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Area Editors:
David Bourget
Gwen Bradford
Berit Brogaard
Margaret Cameron
David Chalmers
James Chase
Rafael De Clercq
Ezio Di Nucci
Esa Diaz-Leon
Barry Hallen
Hans Halvorson
Jonathan Ichikawa
Monte Johnson
Michelle Kosch
Øystein Linnebo
Paul Livingston
Brandon Look
Manolo Martínez
Matthew McGrath
Michiru Nagatsu
Susana Nuccetelli
Giuseppe Primiero
Jack Alan Reynolds
Darrell P. Rowbottom
Aleksandra Samonek
Constantine Sandis
Howard Sankey
Jonathan Schaffer
Thomas Senor
Daniel Star
Jussi Suikkanen
Aness Kim Webster
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