By Robert Nieuwenhuis

ISBN-10: 3540280057

ISBN-13: 9783540280057

This publication constitutes the refereed court cases of the twentieth foreign convention on computerized Deduction, CADE-20, held in Tallinn, Estonia, in July 2005. The 25 revised complete papers and five approach descriptions awarded have been rigorously reviewed and chosen from seventy eight submissions. All present features of automatic deduction are addressed, starting from theoretical and methodological matters to presentation and evaluate of theorem provers and logical reasoning platforms.

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Extra info for Automated deduction, CADE-20: 20th International Conference on Automated Deduction, Tallinn, Estonia, July 22-27, 2005 : proceedings

Example text

Rusinowitch. On word problems in equational theories. In T. Ottmann, editor, 14th International Colloquium on Automata, Languages and Programming, volume 267 of LNCS, pages 54–71, Karlsruhe, Germany, July 1987. Springer-Verlag. 14. -H. Nguyen. Certifying Term Rewriting Proofs in ELAN. In M. van den Brand and R. Verma, editors, Proceedings of the International Workshop RULE’01, volume 59 of Electronic Notes in Theoretical Computer Science. Elsevier Science Publishers, 2001. 15. G. E. Peterson. A technique for establishing completeness results in theorem proving with equality.

This short proof of THM615 can be formalized using of the cut rule with cut formula [H =ι H ⊥]. Since cut is admissible, there must be a derivation S of THM615 without using cut. The only possible rules of Gβfb which can be used to conclude THM615 are contraction or the decomposition rule G(Dec). o Since [H =ι H ⊥] = . ⊥ is not a theorem, one cannot expect a derivation of THM615 to end with the decomposition rule. Instead, one can derive the sequent [Hιo [H ι =ι H ⊥] = . H ⊥], [H o =ι H ⊥] = . ⊥ (2) Reasoning in Extensional Type Theory with Equality 29 and complete the derivation of THM615 using decomposition followed by contraction.

G = . B] ι Γ, [B = . [[G B] = . [∀. [M ∨ . A, B Γ, M G( . M G(∀. W ) Γ, A α Γ, . ) A ∈ cwffo (S) Γ, [[G W ] = . G(βη) Γ, [A 1 = . B ] ··· n Γ, [A ι n Γ, [[H An ] = . [H B ]] G(EUnif2 ) n = . B ] G(Dec) S Fig. 1. Sequent Rules for Gβfb The rules G( ) and G(¬ . ) provides the connection between the logical constants in S and the level of propositions using the operation taking a term A ∈ wffo (S) to a proposition A . The definition of A depends on the head of α the term A. In particular, is . , [¬B] is ¬ .

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Automated deduction, CADE-20: 20th International Conference on Automated Deduction, Tallinn, Estonia, July 22-27, 2005 : proceedings by Robert Nieuwenhuis


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