Given a k-ary predicate P , a random instance of a constraint satisfaction problem (CSP) is a set of m constraints on n variables. Each constraint is P applied to k random literals. Such an instance is unsatisfiable with high probability when m n. Although this fact can be proven via a simple probabilistic argument, certifying that a given randomly chosen instance is unsatisfiable, a task calle...

Abstrract:For many application domains the best way to produce intelligent behavior is to encode knowledge about this domain to knowledge base. Verification of KB is one of the crucial issues in developing reliable knowledgebased systems. SAT techniques as resolution and DPLL can be used for verifying knowledge bases. We give a transformation of a DPLL refutation to a resolution refutation of a...

D A transformation technique is introduced which, given the Horn-clause definitions of a set of predicates p,, synthesizes the definitions of new predicates pi which can be used, under a suitable refutation procedure, to compute the finite failure set of pi. This technique exhibits some computational advantages, such as the possibility of computing nonground negative goals still preserving the ...

Much effort has been devoted in the past decade to the development of decision procedures for quantified Boolean formulas (QBFs) in order to improve their performance. Besides solving the decision problem of whether a closed QBF is true and returning yes or no, modern QBF solvers can produce clause or cube proofs to certify their answer. These proofs can be used to derive solutions to problems ...

Database and Artiicial Intelligence applications are brieey discussed and it is argued that they need deduction methods that are not only refutation complete but also complete for nite satissability. A novel deduction method is introduced for such applications. Instead of relying on Skolemization, as most refutation methods do, the proposed method processes existential quantiiers in a special m...

The schematic CERES method is a method of cut elimination for proof schemata, that is a sequence of proofs with a recursive construction. Proof schemata can be thought of as a way to circumvent the addition of an induction rule to the LK-calculus. In this work, we formalize a schematic version of the Infinitary Pigeonhole Principle (IPP), in the LKS-calculus [9], and analyse the extracted claus...

Let R be a resolution refutation, given as a sequence of clauses without explicit description of the underlying dag. Then, it is NPcomplete to decide whether R is a regular resolution refutation.