Deduction

Motivation

Logic is an essential formalism for computer science and artificial intelligence. It is used in such diverse and important activities as

• Problem specification;
• Program transformation, verification, and synthesis;
• Hardware design and verification;
• Logic programming;
• Deductive databases;
• Knowledge representation, reasoning, diagnosis, and planning;
• Natural language understanding;
• Mathematical theorem proving.

The universality of the language of logic, the certainty about the meaning of statements in logic, and the implementability of operations of logic, all contribute to its usefulness in these endeavors.

Implementations of logical operations are realized in the field of automated deduction, which has introduced fundamental techniques such as unification, resolution, and term rewriting, and developed automated deduction systems for propositional, first-order, higher-order, and non-classical logics.

The 1995 Dagstuhl Seminar on Deduction, succeeding the one in 1993, was convened to give international researchers on deduction the opportunity to meet and discuss techniques, applications and research directions for deduction. It featured 38 presentations, a panel discussion, and an excursion. Some of the results were deemed really exciting by the audience; among those are the discovery of proofs for a number of new mathematical theorems (in algebraic geometry, quasi-groups etc.) which were established with substantial participation of automatic systems; further the mechanical proofs of large parts of mathematical books on set theory, automata theory, and so forth. With the comfortable facilities available at Dagstuhl, system demonstrations were given such as a geometry prover, remarkable not only for its proof power but also for its amazing interface featuring geometrical constructions along with the formal theories and theorems. To an extent limited by the restricted number (43) of participants the seminar provided also a forum for presenting results obtained in a German project (DFG Schwerpunktprogramm) on deduction to the international participants.

The success of this meeting was due in no small part to the Dagstuhl Seminar Center and its staff for creating such a friendly and productive environment. The organizers and participants greatly appreciate their effort. The organizers also thank Uwe Egly for his support in many organizational details. Financial support from NSF and CEU (directly and through Compulog) are also greatly appreciated.