This paper describes version 2 of the NuSMV tool. NuSMV is a symbolic model\ud checker originated from the reengineering, reimplementation and extension of\ud SMV, the original BDD-based model checker developed at CMU. The Nu-\ud SMV project aims at the development of a state-of-the-art symbolic model\ud checker, designed to be applicable in technology transfer projects: it is a well\ud structured, open, flexible and documented platform for model checking, and is\ud robust and close to industrial systems standards

The nonmonotonic causal logic defined in this paper can be used to represent properties of actions, including actions with conditional and indirect effects, nondeterministic actions, and concurrently executed actions. It has been applied to several challenge problems in the theory of commonsense knowledge. We study the relationship between this formalism and other work on nonmonotonic reasoning and knowledge representation, and discuss its implementation, called the Causal Calculator

Resolution is the rule of inference at the basis of most procedures for automated reasoning. In these procedures, the input formula is first translated into an equisatisfiable formula in conjunctive normal form (CNF) and then represented as a set of clauses. Deduction starts by inferring new clauses by resolution, and goes on until the empty clause is generated or satisfiability of the set of clauses is proven, e.g., because no new clauses can be generated.\ud In this paper, we restrict our attention to the problem of evaluating Quantified Boolean Formulas (QBFs). In this setting, the above outlined deduction process is known to be sound and complete if given a formula in CNF and if a form of resolution, called “Q-resolution”, is used. We introduce Q-resolution on terms, to be used for formulas in disjunctive normal form. We show that the computation performed by most of the available procedures for QBFs –based on the Davis-Logemann-Loveland procedure (DLL) for propositional satisfiability– corresponds to a tree in which Q-resolution on terms and clauses alternate. This poses the theoretical bases for the introduction of learning, corresponding to recording Q-resolution formulas associated with the nodes of the tree. We discuss the problems related to the introduction of learning in DLL based procedures, and present solutions extending state-of-the-art proposals coming from the literature on propositional satisfiability. Finally, we show that our DLL based solver extended with learning, performs significantly better on benchmarks used in the 2003 QBF solvers comparative evaluation

Abstract. Answer Set Programming (ASP) emerged in the late 1990s as a new logic programming paradigm which has been successfully applied in various application domains. Also motivated by the availability of efficient solvers for propositional satisfiability (SAT), various reductions from logic programs to SAT were introduced in the past. All these reductions either are limited to a subclass of logic programs, or introduce new variables, or may produce exponentially bigger propositional formulas.In this paper, we present a SAT-based procedure, called ASP-SAT, that (i) deals with any (non disjunctive) logic program, (ii) works on a propositional formula without additional variables (except for those possibly introduced by the clause form transformation), and (iii) is guaranteed to work in polynomial space. From a theoretical perspective, we prove soundness and completeness of ASP-SAT. From a practical perspective, we have (i) implemented ASP-SAT in Cmodels, (ii) extended the basic procedures in order to incorporate the most popular SAT reasoning strategies, and (iii) conducted an extensive comparative analysis involving also other state-of-the-art answer set solvers. The experimental analysis shows that our solver is competitive with the other solvers we considered, and that the reasoning strategies that work best on "small but hard" problems are ineffective on "big but easy" problems and vice versa.

The implementation of effective reasoning tools for deciding the satisfiability of Quantified\ud Boolean Formulas (QBFs) is an important research issue in Artificial Intelligence. Many decision\ud procedures have been proposed in the last few years, most of them based on the Davis, Logemann,\ud Loveland procedure (DLL) for propositional satisfiability (SAT). In this paper we show how it is\ud possible to extend the conflict-directed backjumping schema for SAT to the satisfiability of QBFs:\ud When applicable, conflict-directed backjumping allows search to skip over existentially quantified\ud literals while backtracking. We introduce solution-directed backjumping, which allows the same\ud behavior for universally quantified literals. We show how it is possible to incorporate both conflict-\ud directed and solution-directed backjumping in a DLL-based decision procedure for satisfiability of\ud QBFs. We also implement and test the procedure: The experimental analysis shows that, because of\ud backjumping, significant speed-ups can be obtained.\ud Summing up: We present the first algorithm that applies conflict and solution directed backjumping\ud to QBF, and demonstrate the performance of this algorithm via an empirical study