SPASS-SATT: A CDCL(LA) Solver

International audienceSPASS-SATT is a CDCL(LA) solver for linear rational and linear mixed/integer arithmetic. This system description explains its specific features: fast cube tests for integer solvability, bounding transformations for unbounded problems, close interaction between the SAT solver and the theory solver, efficient data structures, and small-clause-normal-form generation. SPASS-SATT is currently one of the strongest systems on the respective SMT-LIB benchmarks

A Resolution-Based Calculus For Temporal Logics

The increasing interest in applying temporal logics in various areas of computer science requires the development of efficient means that allow to reason within such logics. Usually this is realized by an implementable calculus and indeed remarkable progress has been made in the last two decades. The approaches developed so far can be roughly divided into two main categories: Either known techniques are extended to cope with the temporal logic syntax, or translation techniques into predicate logic are defined which allow to exploit already existing calculi. The approach proposed in this work is based on a particular translation method into classical first-order predicate logic which utilizes certain interesting translational invariants.Das ständig wachsende Interesse an Temporallogiken in zahlreichen Gebieten der Informatik verlangt nach Methoden, mit deren Hilfe effizient und schnell Schlussfolgerungen in diesen Logiken gezogen werden können. Üblicherweise geschieht dies durch die Entwicklung eines implementierten Kalküls, und tatsächlich wurden in den vergangenen Jahren bemerkenswerte Fortschritte in diese Richtung erzielt. Die bis heute bekannten Verfahren können grob in zwei Hauptkategorien eingeteilt werden: Entweder werden schon bekannte Techniken für andere Logiken (üblicherweise klassische Prädikatenlogik erster Stufe) erweitert, um mit der neuen Syntax zurechtzukommen, oder Übersetzungstechniken in die Prädikatenlogik werden definiert, welche es erlauben schon bekannte Kalküle wiederzuverwenden. Der Ansatz, der in dieser Arbeit vorgestellt wird, basiert auf einer bestimmten Übersetzungsmethode in die klassische Prädikatenlogik erster Stufe und einem darauf aufbauenden Kalkül, der gewisse interessante Übersetzungsvarianten ausnützt

Auxiliary Modal Operators and the Characterization of Modal Frames

In modal logics we are interested in classes of frames which determine the logic under consideration. Such classes are usually distinguished by their respective frame properties, often also called the modal logic's background theory. In general these characterizations are not unique and it is desireable (and that not only from a theorem prover's perspective) to find a strongest possible. In this paper an approach is presented which helps in this respect. It allows us to transform a given background theory into one which is more general and which modal logics cannot distinguish from the former because of their syntactic and semantic restrictions. The underlying technique is based on the idea to find conservative extensions (of a given logic) whose determining properties serve as a starting point from which it is possible to extract significantly stronger characterizations of the original logic. Keywords Modal logic, correspondence, completeness, frame properties, auxiliary modal operat..

A Resolution-Based Calculus For Temporal Logics

The increasing interest in applying temporal logics in various areas of computer science requires the development of efficient means that allow to reason within such logics. Usually this is realized by an implementable calculus and indeed remarkable progress has been made in the last two decades. The approaches developed so far can be roughly divided into two main categories: Either known techniques are extended to cope with the temporal logic syntax, or translation techniques into predicate logic are defined which allow to exploit already existing calculi. The approach proposed in this work is based on a particular translation method into classical first-order predicate logic which utilizes certain interesting translational invariants.Das ständig wachsende Interesse an Temporallogiken in zahlreichen Gebieten der Informatik verlangt nach Methoden, mit deren Hilfe effizient und schnell Schlussfolgerungen in diesen Logiken gezogen werden können. Üblicherweise geschieht dies durch die Entwicklung eines implementierten Kalküls, und tatsächlich wurden in den vergangenen Jahren bemerkenswerte Fortschritte in diese Richtung erzielt. Die bis heute bekannten Verfahren können grob in zwei Hauptkategorien eingeteilt werden: Entweder werden schon bekannte Techniken für andere Logiken (üblicherweise klassische Prädikatenlogik erster Stufe) erweitert, um mit der neuen Syntax zurechtzukommen, oder Übersetzungstechniken in die Prädikatenlogik werden definiert, welche es erlauben schon bekannte Kalküle wiederzuverwenden. Der Ansatz, der in dieser Arbeit vorgestellt wird, basiert auf einer bestimmten Übersetzungsmethode in die klassische Prädikatenlogik erster Stufe und einem darauf aufbauenden Kalkül, der gewisse interessante Übersetzungsvarianten ausnützt

Modalities in Knowledge Representation

Standard knowledge representation systems are supposed to be able to represent either common or individual knowledge about the world. In this paper we propose an extension to such knowledge representation systems which, in a uniform manner, allows to express beliefs of multiple agents as well as knowledge, desire, time and in fact any modality which has a first-order predicate logic possible world semantics. 1 Introduction Since the mid-seventies a variety of knowledge representation systems in the tradition of semantic networks and terminological logics has been proposed. The most famous example is KL-ONE 3 which first appeared in 1977 in R. J. Brachman's Ph.D. thesis. Other examples are KRYPTON 2 , NIKL 12 , and KRIS 1 . All these systems can be used to represent common or individual knowledge about the world. Recently, terminological logics have been extended to allow the representation of the knowledge or the beliefs of multiple agents in one knowledge base 4; 7 . In th..

A Fixpoint Approach to Second-Order Quantifier Elimination with Applications to Correspondence Theory

This paper is about automated techniques for (modal logic) correspondence theory. The theory we deal with concerns the problem of finding fixpoint characterizations of modal axiom schemata. Given a modal schema and a semantics based method of translating modal formulae into classical ones, we try to derive automatically a fixpoint formula characterizing precisely the class of frames validating this schema. The technique we consider can, in many cases, be easily applied without any computer support. Although we mainly concentrate on Kripke semantics, our fixpoint approach is much more general, as it is based on the elimination of second-order quantifiers from formulae. Thus it can be applied in second-order theorem proving as well. We show some application examples for the method which may serve as new, automated proofs of the respective correspondences

On Generating Small Clause Normal Forms

In this paper we focus on two powerful techniques to obtain compact clause normal forms: Renaming of formulae and refined Skolemization methods. We illustrate their effect on various examples. By an exhaustive experiment of all first-order TPTP problems, it shows that our clause normal form transformation yields fewer clauses and fewer literals than the methods known and used so far. This often allows for exponentially shorter proofs and, in some cases, it makes it even possible for a theorem prover to find a proof where it was unable to do so with more standard clause normal form transformations.