Lecture Notes in Artificial Intelligence 535 Subseries of Lecture Notes in Computer Science Edited by J. Siekmann Lecture Notes in Computer Science Edited by G. Goos and J. Hartmanis Ph. Jorrand J. Kelemen (Eds.) Fundal ntals of Artificial Intelligence Research International Workshop FAIR'91 Smolenice, Czechoslovakia, September 8-13, 1991 Proceedings Springer-Verlag Berlin Heidelberg NewYork London Paris Tokyo Hong Kong Barcelona Budapest Series Editor J/~rg Siekmann Institut for Informatik, Universit~it Kaiserslautern Postfach 3049, W-6750 Kaiserslautern, FgG Volume Editors Philippe Jorrand Institut IMAG-LIFIA 46, Avenue Felix Viallet F-38031 Grenoble Cedex, France Jozef Kelemen Department of Artificial Intelligence Faculty of Mathematics and Physics, Comenius University Mlynsk~idolina, 842 15 Bratislava, Czechoslovakia CR Subject Classification (1991): 1.2.3-4, E4.1-2, 1.2.6 ISBN 3-540-54507-7 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-54507-7 Springer-Verlag New York Berlin Heidelberg This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provisions of the German Copyright Law of September 9, 1965, in its current version, and a copyright fee must always be paid. Violations fall under the prosecution act of the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1991 Printed in Germany Typesetting: Camera ready by author Printing and binding: Druckhaus Beltz, Hemsbach/Bergstr. 2145/3140-543210 - Printed on acid-free paper Foreword This volume contains the text of 7 invited lectures and 13 submitted con- tributions to the scientific programme of the international workshop Fun- damentals of Artificial Intelligence Research, FAIR '91, held at Smolenice Castle, Czechoslovakia, September 8-12, 1991. The international workshop Fundamentals of Artificial Intelligence Re- search was jointly organized by the Association of Slovak Mathematicians and Physicists, by the Laboratory of Fundamental Informatics and Artifi- cial Intelligence of the Institute of Informatics and Applied Mathematics of Grenoble, France, and by the Department of Artificial Intelligence of the Comenius University, Bratislava, Czechoslovakia, under the sponsorship of the European Coordinating Committee for Artificial Intelligence, ECCAI. FAIR '91, the first one of an intended series of international workshop- s, adresses issues which belong to the theoretical foundations of Artificial Intelligence (AI) considered as a discipline focused on concise theoretical de- scription of some aspects of intelligence by tools and methods adopted from mathematics, logics, and theoretical computer science. The intended goal of the FAIR workshops is to provide a forum for the exchange of ideas and results in a domain where theoretical models play an essential role. Such theoretical studies, their development and their relations to AI experiments and applications have to be promoted in the AI research community. The scientific programme of FAIR '91 was prepared by the Programme Committee consisting of Steffen HSlldobler (Technical University Darmstadt, Germany), Klaus - Peter Jantke (Technical University Leipzig, Germany), Philippe Jorrand (chairman, Institute IMAG - LIFIA, Grenoble, France), Jozef Kelemen (Comenius University, Bratislava, Czechoslovakia), Augustin Lux (Institute IMAG - LIFIA, Grenoble, France), Alberto Martelli (Uni- versity of Torino, Italy), and Henri Prade (Institute IRIT - LSI, Toulouse, France). The editors wish to thank all of them for their meritorious work in consultating the invited speakers and evaluating the papers submitted to response to the call for papers as well as to all of subreferees who assisted the Programme Committee members. On behalf of all the participants of FAIR '91 we express our gratitude to the members of the organizational staff of the workshop, especially to Peter Mikuleck:~ for chairing the Organizing Committee, to Juraj Waczullk, Richard Nemec, and Michal Winczer for technical assistance, and to Alica Kelemenov£ for her substantial help in finishing the editorial work. Yl We are highly indebted to all the contributors for preparing their texts carefully and on time. We would also like to gratefully acknowledge the sup- port of all the above mentioned cooperating institutions. Last but not least we wish to thank Springer-Verlag for excellent cooperation in publication of this volume. July 1991 Philippe Jorrand Jozef Keleraen Contents Part I: Invited Lectures R. Caferra, M. Herment and N. Zabel User-oriented theorem proving with the ATINF graphic proof editor ..... 2 L. Faxifias del Cerro and A. Herzig A modal analysis of possibility theory ................................. 11 D. Gabbay and A. Hunter Making inconsistency respectable: a logical framework for inconsistency in reasoning ........................................ 19 E. Orlowska Relational proof systems for some AI logics ........................... 33 Gh. Phun Formal grammars and cognitive architectures ......................... 48 J. Wiedermann EJ~cient simulations of nondeterministic computations and their speed-up by the ring of cooperating machines ................ 59 Part II: Selected Contributions M. Freund A semantic characterization of disjunctive relations ................... 72 A. Hunter Execution of defeasible temporal clauses for building preferred models ..................................................... 84 M. Klopotek On the phenomenon of flattening "flexible prediction" concept hierarchy ..................................................... 99 VIii J. Lang Possibilistic logic as a logical framework for rain-max discrete optimisation problems and prioritized constraints ............ 112 Z. Markov An approach to data-driven learning ................................. 127 P. Marquis Extending abduction from propositional to frst-order logic ............ 141 U. Petermann Building in equational theories into the connection method ........... 156 J. Pfalzgraf Logical fiberings and polycontextural systems ......................... 170 M. Rusinowitch and L. Vigneron Automated deduction with associative commutative operators ......... 185 A. Strasser Towards a lattice of knowledge representation systems ................ 200 J. Sefr£nek Inconsistencies handling: nonmonotonic and paraconsistent reasoning ........................................................... 214 G. Tau~aite and J. Laurinskas An approach to structural synthesis of data processing programs ...... 220 J. Vauzeilles Negation as failure and intuitionistic three-valued logic ............... 227 Part III: Appendix A. Miola Symbolic Computation and Artificial Intelligence ..................... 244 Part I Invited Lectures User-oriented theorem proving with the ATINF graphic proof editor* Ricardo Caferra, Michel Herment & Nicolas Zabel LIFIA-IMAG 46 Av. F61ix Viallet, 38031 Grenoble Cedex, FRANCE {[email protected]; [email protected]; [email protected]} Abstract An inference laboratory called ATINF, developed at LIFIA since 1985 is presented. Its main design principles and some of its components are described. The presentation gives the greatest place to the graphic proof editor of ATINF and an example shows how proof edition can be profitably used in user- oriented theorem proving. Particularly interesting in this concern are the hierarchical presentation of proofs and the possibility of handling natural tricks such as renaming and taking advantage of symmetries. 1. Introduction In 1965 J.A. Robinson published his seminal paper on theorem proving "A machine-oriented logic based on the resolution principle". The resolution principle, born in 1963, was 25 years old in 1988. In this occasion, during CADE- 9, J.A. Robinson gave a very nice -unfortunately unpublished- talk entitled (if we recall correctly) "How human-oriented can a mechanical proof be?". In his conference Robinson emphasized the key concept of proof outline, which is a very natural notion, especially if one really wants to use a mechanical theorem prover as an assistant mathematician (in the sense for example of [Wos88]). The philosophy underlying this talk illustrates very well the evolution of theorem proving in the last 25 years. It is worthwhile to notice a convergence with ideas coming from Mathematics, particularly with a deep reflection about a broad sense of the notion of "mathematical proof" and on the impossibility to understand or to communicate "big proofs" (see for example [DLP79], [DH86]). These ideas lead naturally to the conclusion that it is necessary to have in a theorem prover different levels of presentation of proofs. This necessity has been one of the guiding principles of our project of Inference Laboratory, named ATINF and developed at LIFIA since 1985. In this paper we give in section 2 an overview of the present state of the ATINF project. In section 3, one of its major components, a graphic proof editor, is * This work was partially supported by MEDLAR (Mechanizing Deduction in the Logic of Practical Reasoning) ESPRIT-BRA 3125 project. described and some of its original features are evidenced. Finally in section 4 a "long proof" of a nontrivial theorem is presented. The capabilities of the proof editor and a unified approach theorem proving/proof checking allows us to