The Davis-Putnam-Logemann-Loveland procedure (DPLL) was introduced in the early

Abstract. FDPLL is a directly lifted version of the well-known Davis-Putnam-Logeman-Loveland (DPLL) procedure. While DPLL is based on a splitting rule for case analysis wrt. ground and complementary literals, FDPLL uses a lifted splitting rule, i.e. the case analysis is made wrt. non-ground and complementary literals now. The motivation for this lifting is to bring together successful first-order techniques like unification and subsumption to the propositionally successful DPLL procedure. At the heart of the method is a new technique to represent first-order interpretations, where a literal specifies truth values for all its ground instances, unless there is a more specific literal specifying opposite truth values. Based on this idea, the FDPLL calculus is developed and proven as strongly complete. 1

Abstract. This paper presents a technique for automated theorem proving with free variable tableaux that does not require backtracking. Most existing automated proof procedures using free variable tableaux require iterative deepening and backtracking over applied instantiations to guarantee completeness. If the correct instantiation is hard to find, this can lead to a significant amount of duplicated work. Incremental Closure is a way of organizing the search for closing instantiations that avoids this inefficiency. 1

. Recently Brass and Dix have introduced the semantics D-WFS for general disjunctive logic programs. The interesting feature of this approach is that it is both semantically and proof-theoretically founded. Any program \Phi is associated a normalform res(\Phi), called the residual program, by a non-trivial bottom-up construction using least fixpoints of two monotonic operators. We show in this paper, that the original calculus, consisting of some simple transformations, has a very strong and appealing property: it is confluent and terminating. This means that all the transformations can be applied in any order: we always arrive at an irreducible program (no more transformation is applicable) and this program is already uniquely determined. Moreover, it coincides with the normalform res(\Phi) of the program we started with. The semantics D-WFS can be read off from res(\Phi) immediately. No proper subset of the calculus has these properties --- only when we restrict to certain subclasse...

In this tutorial-overview, which resulted from a lecture course given by the authors at

Abstract. We present a new technique for the optimization of (partially) bound queries over disjunctive datalog programs. The technique exploits the propagation of query bindings, and extends the Magic-Set optimization technique (originally defined for non-disjunctive programs) to the disjunctive case, substantially improving on previously defined approaches. Magic-Set-transformed disjunctive programs frequently contain redundant rules. We tackle this problem and propose a method for preventing the generation of such superfluous rules during the Magic-Set transformation. In addition, we provide an efficient heuristic method for the identification of redundant rules, which can be applied in general, even if Magic-Sets are not used. We implement all proposed methods in the DLV system – the state-of-the-art implementation of disjunctive datalog – and perform some experiments. The experimental results confirm the usefulness of Magic-Sets for disjunctive datalog, and they highlight the computational gain obtained by our method, which outperforms significantly the previously proposed Magic-Set method for disjunctive datalog programs. 1

The present prolegomena consist, as all indeed do, in a critical discussion serving to introduce and interpret the extended works that follow in this book. As a result, the book is not a mere collection of excellent papers in their own specialty, but provides also the basics of the motivation, background history, important themes, bridges to other areas, and a common technical platform of the principal formalisms and approaches, augmented with examples. In the

. Tableau and sequent calculi are the basis for most popular interactive theorem provers for formal verification. Yet, when it comes to automatic proof search, tableaux are often slower than Davis-Putnam, SAT procedures or other techniques. This is partly due to the absence of a bivalence principle (viz. the cut-rule) but there is another source of inefficiency: the lack of constraint propagation mechanisms. This paper proposes an innovation in this direction: the rule of simplification, which plays for tableaux the role of subsumption for resolution and of unit for the Davis-Putnam procedure. The simplicity and generality of simplification make possible its extension in a uniform way from propositional logic to a wide range of modal logics. This technique gives an unifying view of a number of tableaux-like calculi such as DPLL, KE, HARP, hyper-tableaux, BCP, KSAT. We show its practical impact with experimental results for random 3SAT and the industrial IFIP benchmarks for hardware ve...

In this paper we demonstrate how general purpose automated theorem proving techniques can be used to solve realistic model-based diagnosis problems. For this

Three real world applications are depicted which all have in common, that their core component is a full first order theorem prover, based on the hyper tableau calculus. These applications concern information retrieval in electronic publishing, the integration of description logics with other knowledge representation techniques and XML query processing.