Download Automated deduction--CADE 16: 16th International; Conference by Harald Ganzinger PDF

By Harald Ganzinger

This ebook constitutes the refereed court cases of the sixteenth foreign convention on automatic Deduction, CADE-16, held in Trento, Italy in July 1999 as a part of FLoC'99. The 21 revised complete papers awarded have been rigorously reviewed and chosen from a complete of eighty three submissions. additionally integrated are 15 approach descriptions and invited complete papers. The e-book addresses all present concerns in computerized deduction and theorem proving, starting from logical foundations to deduction platforms layout and evaluate

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Extra info for Automated deduction--CADE 16: 16th International; Conference on Automated Deduction, Trento, Italy, July 7-10, 1999 : proceedings

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X Z]. 20 St´ephane Demri and Rajeev Gor´e X◦Y X X◦Y Z Z ◦ ∗Y Y Z X ∗X ◦ Z Y◦Z X ◦ ∗Z ∗X Y X ∗Y ∗∗X ∗Y X Y ∗X X ∗Y ◦ X Y Y Y◦Z X X Y X Z ∗∗Y X •Y Y •X Y Fig. 2. Display postulates ⊥ I X I ( ⊥) X ⊥ (⊥ ) I X X X (∧ ) X •φ ( ✷L ) ✷φ ) I ( ) X◦φ ψ ( ⇒) X φ⇒ψ X φ ψ Y (⇒ ) φ ⇒ ψ ∗X ◦ Y φ◦ψ φ∧ψ X ( X X φ Y ψ ( ∧) X◦Y φ∧ψ ∗φ ¬φ X (¬ ) X X X ∗φ ( ¬) ¬φ φ ✷φ φ X ψ Y (∨ ) φ∨ψ X◦Y X X φ◦ψ ( ∨) φ∨ψ X (✷ ) •X Fig. 3. Operational rules Theorem 2. [Kra96] For all φ ∈ FML, I φ has a cut-free proof in δL iff φ ∈ L.

H. Ganzinger, U. Hustadt, and R. Meyer, C. Schmidt. A resolution-based decision procedure for extensions of K4. In 2nd Workshop on Advances in Modal Logic (AiML’98), Uppsala, Sweden, October 1998. to appear. Gor99. R. Gor´e. Tableaux methods for modal and temporal logics. In M. d’Agostino, D. Gabbay, R. H¨ ahnle, and J. Posegga, editors, Handbook of Tableaux Methods. Kluwer, Dordrecht, 1999. To appear. Her89. A. Herzig. Raisonnement automatique en logique modale et algorithmes d’unification. PhD thesis, Universit´e P.

1 ⇒ ψ2 in f(φ, 1) is of the form f(ϕ1 , 0) ⇒ f(ϕ2 , 1) [resp. f(ϕ1 , 1) ⇒ f(ϕ2 , 0)] for some subformulae ϕ1 , ϕ2 of φ; 4. ψ1 ⊕ ψ2 (⊕ ∈ {∧, ∨}) in f(φ, 1) is of the form f(ϕ1 , 1) ⊕ f(ϕ2 , 1) [resp. f(ϕ1 , 0) ⊕ f(ϕ2 , 0)] for some subformulae ϕ1 , ϕ2 of φ; The proof of Lemma 3 is by an easy verification. Lemma 3 is used in the proof of Theorem 5 below. We extend the map f to structures in the following way (i ∈ {0, 1}): def def f(I, i) = I def f(X ◦ Y, i) = f(X, i) ◦ f(Y, i) f(∗X, i) = ∗f(X, 1 − i) def f(•X, i) = •f(X, i) By induction on the structure of φ, the rule below is admissible in δL: f(m(φ, 0), 0) X (adm3) f(φ, 0) X Theorem 5 below is the main result of the paper.

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