Restricted on the proof of unsatisfiability of unsatisfiable formulas, a modified DPLL — RSMLS algorithm is presented. The new algorithm has a symmetry rule (Literal renaming ) and three simplified rule ((1,*)-Resolution, Subformula, and Multiple ). As an example, RSMLS algorithm is applied for the proof of unsatisfiability of pigeon-hole formula . We show with respect to RSMLS algorithm that h...

The Davis-Putnam-Logemann-Loveland algorithm is one of the most popular algorithms for solving the satis ability problem. Its e ciency depends on its choice of a branching rule. We construct a sequence of instances of the satis ability problem that fools a variety of \sensible" branching rules in the following sense: when the instance has n variables, each of the \sensible" branching rules brin...

In AI Planning, as well as Verification, a successful method is to compile the application into boolean satisfiability (SAT), and solve it with state-of-the-art DPLL-based procedures. There is a lack of formal understanding why this works so well. Focussing on the Planning context, we identify a form of problem structure concerned with the symmetrical or asymmetrical nature of the cost of achie...

Hybrid MKNF knowledge bases have been considered one of the dominant approaches to combining open world ontology languages with closed world rule-based languages. Currently, the only known inference methods are based on the approach of guess-and-verify, while most modern SAT/ASP solvers are built under the DPLL architecture. The central impediment here is that it is not clear what constitutes a...

Dependency Quantified Boolean Formulas (DQBF) comprise the set of propositional formulas which can be formulated by adding Henkin quantifiers to Boolean logic. We are not aware of any published attempt in solving this class of formulas in practice. However with DQBF being NEXPTIME-complete, efficient ways of solving it would have many practical applications. In this paper we describe a DPLL-sty...

“Determinization” of resolution is usually done by employing a DPLL-like procedure that operates on partial assignments. We introduce a resolution-based SAT-solver that operates on complete assignments and give a theoretical justification for determinizing resolution in such a way. This justification is based on the notion of a point image of a resolution proof. We give experimental results con...

Reasoning semantically in first-order logic is notoriously a challenge. This paper surveys a selection of semantically-guided or modelbased methods that aim at meeting aspects of this challenge. For firstorder logic we touch upon resolution-based methods, tableaux-based methods, DPLL-inspired methods, and we give a preview of a new method called SGGS, for Semantically-Guided Goal-Sensitive reas...