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D2.1 (PL models and assignments) i. A PL model is a pair M = 〈DM, ·M〉 such that (a) DM is a non-empty set, and (b) ·M maps each A ∈ Con to AM ∈ DM, and each B ∈ Prdn to BM  (DM)n. ii. GM = {g| g: Var  DM} is the set of M-assignments. For any g ∈ GM, u ∈ Var, d ∈ DM, g[u/d] := (g\{u, g(u)})  {u, d} is the u-to-d alternative to (...) g. (shrink)

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• A-not-A analysis basic idea: “the comparative introduces a threshold the subject […] meets or exceeds & the complement is a negative statement elaborating on that threshold.” (Schwarzschild 2008:6).

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• 1st try: Free variables in PL (Predicate Logic) (1) Jim1 came in. He1 sat down. (antecedent Jim1 … anaphoric he1) |=M, g cm ιx(x = z1  z1 = jim)  sit z1 iff g(z1) ∈ cm & g(z1) = jim & g(z1) ∈ sit.

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1. {0}εx  DxH1 =  2. K: {0}εxK =  & KDxH1 =  D3. 3. K: {0}(x) =  & {0} x K & K = H1 & K(x) ∈ D D3.εu, β 4. KA: {0}[x/A] = K & K = H1 & K(x) ∈ D D2.0, G u H 5. A: {0}[x/A] = H1 & H1(x) ∈ D elim. K 6. A: {0}[x/A] = H1 & A\{} ∈ D D2.G..

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(2) a. John and Mary are students. distributive VP b. John is a student. (2a) |= (2b).

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(1) Adam and Beth lifted (a stack of) three crates (together). collective VP (2) Adam and Beth (each) lifted (the same stack of) three crates. dist. VP, wide obj (3) Adam and Beth (each) lifted (a different stack of) three crates. dist. VP, narrow obj..

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(1) Mostx menx who own ay donkey beat ity. e.g. |≠M, g (1) if man = {m0, …, m9} & m0 owns & beats donkey d0, …, d9 & m1 owns & beats donkeys d10, …, d19 & m2 owns donkey d20 (only) but doesn’t beat d20..

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D1.2 (UCω syntax) For any type a ∈ Θ, the set of a-terms, Trma, is defined as follows: b. A ∈ Trma a. BA ∈ Trmb..

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UPDATE WITH NOMINAL CENTERING (UCδ) D1.0 (UCδ types) The set of UCδ types Θ is the smallest set such that: i. t, δ, s ∈ Θ ii. (ab) ∈ Θ, if a, b ∈ Θ D1.1 (UCδ basic terms). For each a ∈ Θ, a set of a-constants Cona and a-variables Vara, incl.: Conδ = {a, b, c} Var(sδ) = {x, y, z}.

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D1.2 (UCδ+ syntax) Rules b, a, λ, =, ¬, , n, m, {}, , ; as for UCΔ. . (A  B) ∈ Trmδ if A, B ∈ Trmδ (A) ∈ Trmδ if A ∈ Trm(δt) o. (A), (A) ∈ Trmδ if A ∈ Trmδ A(A), N(A) ∈ Trmδt if A ∈ Trmδ r. A  B ∈ Trmt..

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