By Amy P. Felty, Aart Middeldorp

ISBN-10: 3319214004

ISBN-13: 9783319214009

ISBN-10: 3319214012

ISBN-13: 9783319214016

This e-book constitutes the court cases of the twenty fifth overseas convention on computerized Deduction, CADE-25, held in Berlin, Germany, in August 2015.

The 36 revised complete papers provided ( 24 complete papers and 12 approach descriptions) have been conscientiously reviewed and chosen from eighty five submissions. CADE is the most important discussion board for the presentation of study in all points of computerized deduction, together with foundations, purposes, implementations and useful experience.

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Additional resources for Automated Deduction - CADE-25: 25th International Conference on Automated Deduction, Berlin, Germany, August 1-7, 2015, Proceedings

Example text

Plaisted J¨ urg Nievergelt once gave me a depressing view of theorem proving work. He felt that different methods just explored different portions of the search space, so the point was to find the right method to prove a particular theorem. However, this does not tell the whole story. The search space can be reduced, such as by first-order resolution over propositional deduction, and DPLL over propositional resolution. Also, hardware verification tools typically use DPLL (with CDCL) and not propositional resolution, as another indication that a reduction in search space has been achieved.

For a strong model-based system we assume that Wi is the universal closure of a formula Wi and require that Ji should satisfy the universal closure of the negation of Wi , and similarly for results of inferences. By a model-based method we mean either something that fits into the AMB formalism or something that is in the same style even if it doesn’t exactly fit the formalism. Model Evolution [5] is one of the few strategies that is first-order and appears to be model-based in this sense. Perhaps it is a strong method.

History and Prospects for First-Order Automated Deduction 19 Define WDP LL (S) for propositional clause set S by if S is T or S is F then WDP LL (S) = 1 else let P be an atom appearing in S. WDP LL (S) = if S(P ← T ) and S(P ← F ) are satisfiable then 1 + (WDP LL (S(P ← T )) + WDP LL (S(P ← F )))/2 else if S(P ← T ) and S(P ← F ) are unsatisfiable then 1 + WDP LL (S(P ← T )) + WDP LL (S(P ← F )) else if S(P ← T ) is satisfiable and S(P ← F ) is unsatisfiable then 1 + WDP LL (S(P ← T )) + WDP LL (S(P ← F ))/2 else if S(P ← T ) is unsatisfiable and S(P ← F ) is satisfiable then 1 + WDP LL (S(P ← F )) + WDP LL (S(P ← T ))/2 This is to within a polynomial an upper bound on the average time taken by DPLL on S with a random choice of whether to do P ← T or P ← F first, because if S(P ← F ) or S(P ← F ) is satisfiable then the other case is omitted.

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Automated Deduction - CADE-25: 25th International Conference on Automated Deduction, Berlin, Germany, August 1-7, 2015, Proceedings by Amy P. Felty, Aart Middeldorp


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