By Harald Ganzinger
This ebook constitutes the refereed lawsuits of the sixteenth overseas convention on computerized Deduction, CADE-16, held in Trento, Italy in July 1999 as a part of FLoC'99. The 21 revised complete papers offered have been rigorously reviewed and chosen from a complete of eighty three submissions. additionally integrated are 15 process descriptions and invited complete papers. The publication addresses all present matters in computerized deduction and theorem proving, starting from logical foundations to deduction structures layout and evaluate
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Extra resources for Automated deduction--CADE 16: 16th International; Conference on Automated Deduction, Trento, Italy, July 7-10, 1999 : proceedings
There is a standard translation taking every formula ψ ∈ ML to a first-order formula ψ∗ (x) with one free variable, such that for every Kripke structure K with a distinguished node w we have that K, w |= ψ if and only if K |= ψ∗ (w). This translation takes an atomic proposition P to the atom P x, it commutes with the Boolean connectives, and it translates the modal operators by quantifiers as follows: a ψ ❀ ( a ψ)∗ (x) := ∃y(Ea xy ∧ ψ∗ (y)) [a]ψ ❀ ([a]ψ)∗ (x) := ∀y(Ea xy → ψ∗ (y)) where Ea is the transition relation associated with the modality a.
In C. Kirchner and H. Kirchner, editors, CADE-15, Lindau, Germany, pages 205–219. LNAI 1421, 1998. Pap94. Ch. Papadimitriou. Computational Complexity. Addison-Wesley Publishing Company, 1994. Sah75. H. Sahlqvist. Completeness and correspondence in the first and second order semantics for modal logics. In S. Kanger, editor, 3rd Scandinavian Logic Symposium, pages 110–143. North Holland, 1975. Sch99. R. Schmidt. Decidability by resolution for propositional modal logics. Journal of Automated Reasoning, 1999.
When K4 ⊆ L, φ ∈ L iff (✷(pnew ⇔ ψ) ∧ (pnew ⇔ ψ)) ⇒ φ ∈ L. Proof. (Theorem 6) The key point to define g is to observe that there is a map F : FML × FML → FML and a formula ψF containing at most two atomic propositions, say p and q, such that – F (ϕ1 , ϕ2 ) is obtained from ψF by replacing simultaneously every occurrence of p [resp. q] by ϕ1 [resp. ϕ2 ]; – for any ϕ ∈ FML, f(F(ϕ), 0) = F (f(ϕ, 0), f(ϕ, 1)). p ∧ ¬q. Let φ be a modal formula we wish to translate from LF into L. Let φ1 , . . , φm be an enumeration (without repetition) of all subformulae of φ, in increasing order of size.