Cooperation between Top-Down and Bottom-Up Theorem Provers

Top-down and bottom-up theorem proving approaches each have specific advantages and disadvantages. Bottom-up provers profit from strong redundancy control but suffer from the lack of goal-orientation, whereas top-down provers are goal-oriented but often have weak calculi when their proof lengths are considered. In order to integrate both approaches, we try to achieve cooperation between a top-down and a bottom-up prover in two different ways: The first technique aims at supporting a bottom-up with a top-down prover. A top-down prover generates subgoal clauses, they are then processed by a bottom-up prover. The second technique deals with the use of bottom-up generated lemmas in a top-down prover. We apply our concept to the areas of model elimination and superposition. We discuss the ability of our techniques to shorten proofs as well as to reorder the search space in an appropriate manner. Furthermore, in order to identify subgoal clauses and lemmas which are actually relevant for the proof task, we develop methods for a relevancy-based filtering. Experiments with the provers SETHEO and SPASS performed in the problem library TPTP reveal the high potential of our cooperation approaches

Evaluating general purpose automated theorem proving systems

AbstractA key concern of ATP research is the development of more powerful systems, capable of solving more difficult problems within the same resource limits. In order to build more powerful systems, it is important to understand which systems, and hence which techniques, work well for what types of problems. This paper deals with the empirical evaluation of general purpose ATP systems, to determine which systems work well for what types of problems. This requires also dealing with the issues of assigning ATP problems into classes that are reasonably homogeneous with respect to the ATP systems that (attempt to) solve the problems, and assigning ratings to problems based on their difficulty

leanCoP: lean connection-based theorem proving

AbstractThe Prolog programimplements a theorem prover for classical first-order (clausal) logic which is based on the connection calculus. It is sound and complete (provided that an arbitrarily large I is iteratively given), and demonstrates a comparatively strong performance

Let's plan it deductively!

AbstractThe paper describes a transition logic, TL, and a deductive formalism for it. It shows how various important aspects (such as ramification, qualification, specificity, simultaneity, indeterminism etc.) involved in planning (or in reasoning about action and causality for that matter) can be modelled in TL in a rather natural way. (The deductive formalism for) TL extends the linear connection method proposed earlier by the author by embedding the latter into classical logic, so that classical and resource-sensitive reasoning coexist within TL. The attraction of a logical and deductive approach to planning is emphasized and the state of automated deduction briefly described

Spanning Matrices via Satisfiability Solving

We propose a new encoding of the first-order connection method as a Boolean satisfiability problem. The encoding eschews tree-like presentations of the connection method in favour of matrices, as we show that tree-like calculi have a number of drawbacks in the context of satisfiability solving. The matrix setting permits numerous global refinements of the basic connection calculus. We also show that a suitably-refined calculus is a decision procedure for the Bernays-Sch\"onfinkel class

Deduction-Based Software Component Retrieval

Deduction-based software component retrieval is a software reuse technique that uses formal specifications as component descriptors and as search keys; matching components are identified using an automated theorem prover. This dissertation contains a detailed theoretical investigation of the concept as well as the first substantial experimental evaluation of its technical feasibility.Deduktionsbasiertes Kompenentenretrieval ist eine Softwarereusetechnik, in der formale Spezifikationen zur Beschreibung von Komponenten sowie als Anfragen verwendet werden; passende Komponenten werden mit Hilfe eines automatischen Theorembeweisers ermittelt. Diese Arbeit enthält eine detaillierte theoretische Untersuchung dieses Konzeptes und die erste ausführliche experimentelle Evaluierung seiner technischen Realisierbarkeit

Lemmas: Generation, Selection, Application

Noting that lemmas are a key feature of mathematics, we engage in an investigation of the role of lemmas in automated theorem proving. The paper describes experiments with a combined system involving learning technology that generates useful lemmas for automated theorem provers, demonstrating improvement for several representative systems and solving a hard problem not solved by any system for twenty years. By focusing on condensed detachment problems we simplify the setting considerably, allowing us to get at the essence of lemmas and their role in proof search