Automated Deduction - Cade-22: 22nd International Conference by Renate Schmidt

By Renate Schmidt

This ebook constitutes the refereed complaints of the twenty second overseas convention on automatic Deduction, CADE-22, held in Montreal, Canada, in August 2009. The 27 revised complete papers and five method descriptions offered have been rigorously reviewed and chosen from seventy seven submissions. in addition, 3 invited lectures by means of distinctive specialists within the sector have been incorporated. The papers are equipped in topical sections on combos and extensions, minimum unsatisfiability and automatic reasoning help, procedure descriptions, interpolation and predicate abstraction, resolution-based structures for non-classical logics, termination research and constraint fixing, rewriting, termination and productiveness, types, modal tableaux with worldwide caching, mathematics.

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Additional resources for Automated Deduction - Cade-22: 22nd International Conference on Automated Deduction, Montreal, Canada, August 2-7, 2009. Proceedings

Example text

During development, conjectures are usually false. Therefore, it is desirable to have a theorem prover that terminates on satisfiable instances. Satisfiability Modulo Theories (SMT) solvers have proven highly scalable, efficient and suitable for integrated theory reasoning. Superposition-based inference systems are strong at reasoning with equalities, universally quantified variables, and Horn clauses. We describe a calculus that tightly integrates Superposition and SMT solvers. The combination is refutationally complete if background theory symbols only occur in ground formulæ, and non-ground clauses are variable inactive.

This generalizes corresponding simplification rules by unit clauses in the propositional DPLL-procedure. Also, a constrained clause C · Γ is universally redundant wrt. any sequent containing a constrained clause C · Γ such that Γ ⊂ Γ . This can be exploited to finitely bound the number of derivable constrained clauses under certain conditions. , for Bernays-Sch¨onfinkel formulas, then ME+Sup derivations can be finitely bounded, too. 2. If C · Γ is universally redundant wrt. Λ relevant instance of C · Γ wrt.

A rewrite system R is left-reduced (fully reduced ) iff for every rule l → r ∈ R, l is (l and r are) irreducible wrt. R \ {l → r}. In other words, in a fully reduced rewrite system no rule is reducible by another rule, neither its left hand side nor its right hand side. Interpretations. A (Herbrand) interpretation I is a set of ground atoms—exactly those that are true in the interpretation. Validity of ground literals, ground clauses, and clause sets in a Herbrand interpretation is defined as usual.

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