We characterize provability in intuitionistic predicate logic in terms of derivation skeletons and constraints and study the problem of instantiations of a skeleton to valid derivations. We prove that for two different notions of a skeleton the problem is respectively polynomial and NP-complete. As an application of our technique, we demonstrate PSPACE-completeness of the prenex fragment of intuitionistic logic. We outline some applications of the proposed technique in automated reasoning. y y Copyright c fl 1995, 1996 Andrei Voronkov. This technical report and other technical reports in this series can be obtained at http://www.csd.uu.se/~thomas/reports.html or at ftp.csd.uu.se in the directory pub/papers/reports. Some reports can be updated, check one of these addresses for the latest version. Section 1 Introduction The characterization of provability for classical logic in terms of matrices was given by Kanger [9, 10] and Prawitz [19, 20] and is in a fact a reformulation of the...

In this paper, stepwise and nearly stepwise simulation results for a number of first-order proof calculi are presented and an overview is given that illustrates the relations between these calculi. For this purpose, we modify the consolution calculus in such a way that it can be instantiated to resolution, tableaux model elimination, a connection method and Loveland's model elimination.

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This thesis explores the relative complexity of proofs produced by the automatic theorem proving procedures of analytic tableaux, linear resolution, the connection method, tree resolution and the Davis-Putnam procedure. It is shown that tree resolution simulates the improved tableau procedure and that SL-resolution and the connection method are equivalent to restrictions of the improved tableau method. The theorem by Tseitin that the Davis-Putnam Procedure cannot be simulated by tree resolution is given an explicit and simplified proof. The hard examples for tree resolution are contradictions constructed from simple Tseitin graphs.

We overview recent results related to Herbrand's theorem and tableau-like methods of automated deduction. Based on an analysis and discussion of these results, open problems are posed and new research directions are suggested. Section 1 Introduction Numerous results related to the Herbrand theorem and the foundations of semantics tableaux were obtained recently. These results shed a new light on the nature of such methods and computational complexity of several problems related to the Herbrand theorem. The aim of this paper is to overview these results, sketch new research directions and pose some open problems. We also prove several new results. The main questions we ask in the paper are the following. ffl Are tableaux and related methods inherently inefficient? ffl In what cases are these methods efficient? ffl In what cases and how can we increase efficiency of these methods? This paper is structured as follows. In Section 3 we give a short description of the tableau and relate...

Abstract. Several classes of propositional formulas have been used as target languages for knowledge compilation. Some are based primarily on c-paths (essentially, the clauses in disjunctive normal form); others are based primarily on dpaths. Such duality is not surprising in light of the duality fundamental to classical logic. There is also duality among target languages in terms of how they treat links (complementary pairs of literals): Some are link-free; others are pairwise-linked (essentially, each pair of clauses is linked). In this paper, both types of duality are explored, first, by investigating the structure of existing forms, and secondly, by developing new forms for target languages. 1

Decomposable negation normal form (DNNF) was developed primarily for knowledge compilation. Formulas in DNNF are linkless, in negation normal form (NNF), and have the property that atoms are not shared across conjunctions. Full dissolvents are linkless NNF formulas that do not in general have the latter property. However, many of the applications of DNNF can be obtained with full dissolvents. Two additional methods — regular tableaux and semantic factoring — are shown to produce equivalent DNNF. A class of formulas is presented on which earlier DNNF conversion techniques are necessarily exponential; path dissolution and semantic factoring handle these formulas in linear time.

Decomposable negation normal form (DNNF) was developed primarily for knowledge compilation. Formulas in DNNF are linkless, in negation normal form (NNF), and have the property that atoms are not shared across conjunctions.

This package contains the following items: A brief overview of the course. A package of slides and notes for the course. A set of practice exercises for the course material. Solutions to selected exercises. A short bibliography.