Andreas Blass, Yuri Gurevich (auth.), Peter G. Clote, Helmut's Computer Science Logic: 14th InternationalWorkshop, CSL 2000 PDF

By Andreas Blass, Yuri Gurevich (auth.), Peter G. Clote, Helmut Schwichtenberg (eds.)

ISBN-10: 3540446222

ISBN-13: 9783540446224

ISBN-10: 3540678956

ISBN-13: 9783540678953

This e-book constitutes the refereed lawsuits of the thirteenth overseas Workshop on machine technological know-how good judgment, CSL 2000, held in Fischbachau, Germany because the eighth Annual convention of the EACSL in August 2000. The 28 revised complete papers offered including 8 invited papers have been conscientiously reviewed and chosen by way of this system committee. one of the issues coated are automatic deduction, theorem proving, express common sense, time period rewriting, finite version idea, greater order common sense, lambda and combinatory calculi, computational complexity, good judgment programing, constraints, linear good judgment, modal common sense, temporal common sense, version checking, formal specification, formal verification, software transformation, and so forth.

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Extra info for Computer Science Logic: 14th InternationalWorkshop, CSL 2000 Annual Conference of the EACSL Fischbachau, Germany, August 21 – 26, 2000 Proceedings

Example text

To avoid having to introduce new symbols for a multitude of set-theoretic formulas, we adopt the notational convention that ϕ means the set-theoretic formalization of the (informal) statement ϕ. We first define y ∈ t and y = t for all terms t; here y is a variable not free in t. Here are some typical clauses from the definition. – If f is a dynamic function symbol, then y = f (t1 , . . , tj ) is j ∃z1 . . ∃zj zi = ti ∧ y = f (z1 , . . , zj ) . i=1 – y ∈ Pair(t1 , t2 ) is y = t1 ∨ y = t2 . – y ∈ {t(v) : v ∈ r : ϕ(v)} is ∃v ( v ∈ r ∧ true = ϕ(v) ∧ y = t(v) ).

For any other polymer ξ of the same configuration as ξ0 , let α be the motion sending ξ0 to ξ. Write t(ξ) for Val(t, α ˆ (a)). In particular, t(ξ0 ) is the object Val(t, a) that we hope to prove to be supported. Define an equivalence relation E on the set of polymers of the same configuration as ξ0 by ξEξ ⇐⇒ t(ξ) = t(ξ ). One can verify, using the induction hypotheses and Lemma 28, that this E is configuration-determined. The number of equivalence classes of E is the number 38 A. Blass and Y. Gurevich of different elements of the form t(ξ) = Val(t, α ˆ (a).

For the induction step from m to m + 1, we begin with the formula y = f (x1 , . . , xj ) in the sequel as constructed above. Then, for each dynamic function symbol g, we replace each occurrence of a subformula t0 = g(t1 , . . , tk ) with t0 = g(t1 , . . , tk ) at step m . As for the bound B, it can be taken to be the maximum number of variables in any of the formulas y = f (x1 , . . , xj ) in the sequel as f ranges over all the dynamic function symbols. We omit the verification of this; it is a fairly standard application of the idea of re-using variables.

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Computer Science Logic: 14th InternationalWorkshop, CSL 2000 Annual Conference of the EACSL Fischbachau, Germany, August 21 – 26, 2000 Proceedings by Andreas Blass, Yuri Gurevich (auth.), Peter G. Clote, Helmut Schwichtenberg (eds.)


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