Instance Based Methods

Peter Baumgartner

Programming Logics Group
Max-Planck-Institut für Informatik

Gernot Stenz

Institut für Informatik
Technische Universität München

September 2005

The term ``instance based methods'' (IBM) refers to a family of methods for first-order logic theorem proving. IBMs share the principle of carrying out proof search by maintaining a set of instances of input clauses and analyzing it for satisfiability until completion. IBMs are conceptually essentially different to well established methods like resolution or free-variable analytic tableaux. Also, IBMs exhibit a search space and termination behaviour (in the satisfiable case) different from those methods, which makes them attractive from a practical point of view as a complementary method. This observation is also supported empirically by results obtained with the first serious implementations available (carried out by Letz and Stenz, cf. the system competitions (CASC) at CADE-18 and CADE-19).

The idea behind IBMs is already present in a rudimentary way in the work by Davis, Putnam, Logemann and Loveland in the early sixties. The contemporary stream of research on IBMs was initiated with the Plaisted's Hyperlinking calculus in 1992. Since then, other methods have been developed by Plaisted and his coworkers. Billon's disconnection calculus was picked up by Letz and Stenz and has been significantly developed further since then. New methods have also been introduced by Hooker, Baumgartner and Tinelli, and more recently by Ganzinger and Korovin. The stream of publications over the last years demonstrates a growing interest in IBMs. The ideas presented there show that research on IBMs still is in the middle of development, and that there is high potential further improvements and extensions like equality and theory handling, which is currently investigated.

Contents

In the tutorial, we will cover the following topics: Early IBMs, the common principle behind IBMs; classification of IBMs (one-level vs. two-level calculi), comparison to resolution and free variable tableaux; selected IBMs in greater detail: ordered semantic hyper linking, the disconnection method, the model evolution calculus; the completeness proof of one selected method; extension to equality reasoning; implementation techniques, particularly the disconnection method.

Presenters

Peter Baumgartner has (co-)authored 13 journal articles, 32 conference or referred workshop papers, and five chapters in books. Most publications are concerned with calculi, implementations and applications of first-order logic automated deduction systems. He developed a First-Order version FDPLL of the propositional Davis-Putnam-Logemann-Loveland procedure. This method, and its successor, the Model Evolution Calculus (jointly developed with Cesare Tinelli) are his recent main contributions to instance based methods.

Gernot Stenz has been directly involved in instance based theorem proving for several years. He is the (co-)author of 12 scientific papers and system descriptions at international conferences and some other publications in journals and books. Nearly all of his more recent publications deal with instance based theorem proving in general and the disconnection calculus in particular. The implementation of theorem prover systems is among his principal matters of interest, he was a co-author of the e-SETHEO prover system, where his work also included automated learning methods for theorem provers and he has been developing and improving the DCTP theorem prover implementation of the disconnection calculus. Both of these systems have won trophies at the annual CADE theorem prover competitions.