Download Logic, Language, Information and Computation: 18th by Rajeev Alur (auth.), Lev D. Beklemishev, Ruy de Queiroz PDF

By Rajeev Alur (auth.), Lev D. Beklemishev, Ruy de Queiroz (eds.)

This ebook constitutes the refereed court cases of the 18th Workshop on common sense, Language, info and conversation, WoLLIC 2011, held in Philadelphia, PA, united states, in could 2011. The 21 revised complete papers awarded have been rigorously reviewed and chosen from 35 submissions. one of the subject matters lined are numerous facets of mathematical good judgment, desktop technological know-how logics, philosophical logics, comparable to complexity concept, version concept, partial order, Hoare logics, hybrid logics, Turing machines, etc.

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Additional resources for Logic, Language, Information and Computation: 18th International Workshop, WoLLIC 2011, Philadelphia, PA, USA. Proceedings

Example text

Yn : Cn A, then there is a t(s1 , . . , sm , y1 , . . , yn ) : A for fresh variables y1 , . . , yn . Corollary 8 (Constructive Necessitation). For any formula A, if then there is a ground term t such that t : A. 3 A, Semantics We adapt the Kripke-style semantics for Justification Logic due to Fitting [9]. A similar semantics for JPAL was presented in [7]. Our semantics uses Kripke models augmented by an evidence function that relates each world–term pair (w, t) to a set of formulas E(w, t) that the term t can justify at the world w.

Ak } ⊆ W with ai Rai+1 , and every a ∈ W there is a B = {b1 , . . , bk } ⊆ W with bi R bi+1 and b ∈ W such that (A, a) ∼ (B, b) 2. for every B = {b1 , . . , bk } ⊆ W , and every b ∈ W there is A = {a1 , . . , ak } ⊆ W with ai Rai+1 and a ∈ M such that (A, a) ∼ (B, b). Theorem 12. Let C be any elementary frame class closed under generated subframes and bisimulation products. Then MLm ( r ) and MLm ( r , f ) have interpolation over propositions and k relative to the class of all models with frame in C.

The idea is that the evidence function E σ models the “evidential situation” that arises after the formulas in σ have been publicly announced. Definition 11 (OPAL Model). A model is a structure M = (W, R, E, ν), where (W, R) is a K4-frame, ν : Prop → P(W ) is a valuation, and function E maps finite sequences σ of formulas to evidence functions E σ on (W, R) and satisfies A → [A]B ∈ E σ (w, t) implies B ∈ E σ,A (w, ⇑ t) , (3) B ∈ E σ,A (w, t) implies A → [A]B ∈ E σ (w, ⇓ t) , (4) E σ,A,B (w, t) = E σ,A∧[A]B (w, t) .

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