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Wolfgang Bibel, Koichi Furukawa, Mark Stickel (Editors): Dagstuhl Wolfgang Bibel, Koichi Furukawa, Mark Stickel (editors): Deducon Dagstuhl-Seminar-Report; 58 08.03.-12.03.93 (9310) ISSN 0940-1121 Copyright © 1993 by IBF I GmbH, Schloß Dagstuhl, 66687 Wadern, Germany Tel.: +49-6871 - 2458 Fax: +49-6871 - 5942 Das Intemationale Begegrungs- und Forschungszentrum für Informatik (IBFI) ist eine gemein- nützige GmbH. Sie veranstaltet regelmäßig wissenschaftliche Seminare, welche nach Antrag der Tagungsleiter und Begutachtung durch das wissenschaftliche Direktorium mit persönlich eingeladenen Gästen durchgeführt werden. Verantwortlich für das Programm: Prof. Dr.-Ing. José Encamagao, Prof. Dr. Winfried Görke, Prof. Dr. Theo Härder, Dr. Michael Laska, Prof. Dr. Thomas Lengauer, Prof. Walter Tichy Ph. D., Prof. Dr. Reinhard Wilhelm (wissenschaftlicher Direktor) Gesellschafter: Universität des Saarlandes, Universität Kaiserslautern, Universität Karlsruhe, Gesellschaft für Informatik e.V., Bonn Träger: Die Bundesländer Saarland und Rheinland-Pfalz Bezugsadresse: Geschäftsstelle Schloß Dagstuhl Informatik, Bau 36 Universität des Saarlandes Postfach 1150 66041 Saarbrücken Germany Tel.: +49 -681 - 302 - 4396 Fax: +49 -681 - 302 - 4397 Dagstuhl Seminar on Deduction VVolfgang Bibel Koichi Furukawa Mark Stickel TechnischeHochschule Darnistadt Keio University SRI Internationa.l Logic is an essentia.lformalism for computer scienceand artificial int.elligence. It is used in such diverse and importa.nt activities as 0 Problem specifica.tion. 0 Program transformation, verification, and synthesis. o Hardware design and verication. 0 Logic programming. 0 Deductive da.tabases. 0 Knowledge representation, reasoning, diagnosis, a.nd planning. o Natural language understanding. 0 Mathematicaltheorem proving. The universality of the la.ngua.geof 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 logica.l operations are realized in the field of a.uto1nated clccluction, which has introduced fundamental techniques such as unification. resolution, and term rewriting, a.nd developed automated deduction systems for propositional, first-order, higher-order, and noncla.ssica.llogics. This meeting was convenedto give international researcherson deduction the opportu- nity to meeta.nd discuss techniques, applications, and research directions for deduction. Presentationscovered many topics of current researchin the eld. At least equally va- luable was the opportunity to discuss our successes,failures, plans, and dreams. Wo have achieved some great successes,such as solving open problems in matl1en1a.tics and verifying a microprocessor design, and deductive techniques are embedded in logic programming,deductive database, a.nd artificial intelligencesystems. However, a.uto mated deduction systems a.re not yet used extensively by mathematicians. logicians, or hardware and software developers. At the start. of a new German national project 011deduction, our discussions of goals for the field, as well as its methods, could prove important. The success of this meeting was due in no small pa.rt to the Dagstuhl Seminar Center and its staff for creating such a friendly a.ndproductive environment. The orga.ni&#39;/.ers a.nd participants greatly appreciate their effort. Contents Avenhaus, I.: 6 Hierarchical Theorem. Proving Using Rewrite Techniques Denzinger, J. Dist-rubted knowledge-basetl equational theorem [)l0&#39;Ut&#39;II._(j Podelski,, A; Sort Unfolding Is Not HornC&#39;lause Resolution Caferra, R; Building mo:/(ls &#39;urhile searching refutations Leitsch, A.: C/J Resolution Decision Procedures and Automated Model Building Héihnle, R; Uses of ./\Iang valued Logic in Ha.r(lwar(- 1-"&#39;¬ric(ztio-n. Dahn, B. 1.: 9 What Thron m Proving can Learn from Model Theory Bnndy, A.: &#39;10 The Prod zzc&#39;l1&#39;rc Use of Failure in Inductive Theorem Proving Walther, (3.: (.7&#39;omputin.g I "ml ucl ion. A;rioms Lusk, E; 11 Recent Throrcm-Proving Activities at Argonne Mc.Al1ester, D; 11 Tractable In.fc;rence and Obvious-ness H algiya,M.: A Typed ,\-(?&#39;a.lculus for Provin.g-l)y-E;ra-mple and Bottom- Up Generali::a.tio12 Procedure Schwichtenberg, II.: Arithmetic for the partial continuous functions Letz, R.: Extensions of Model Elimination Calculi Petermann, U.: Connection calculi with built-in theories 9-6 v-Ir-I Ohlbach, H.-J.: C40 KL-ONE, lVIo(lal Logic, Generalized Quantiers and F irst-Order Predicate Logic Theorem Proving Bledsoe, W.: ab- 00 Some Thoughts on Automated Proof Discovery, Especially HOL and Analysis Sa.to, T; An Inductively Complete Inference System Loveland, D.W.: SATCHMORE: SA TCHA/[0 with RElevancy Hasegawa, R.: Non-Horn Magic Sets on MGTP Bayer, R.S.: e 1 7 ein.Update on .\Ie(&#39;/mn&#39;ieal T&#39;erimlion: :\Im&#39;/zine Code und licvvqirocessmrs Ganzingcr, H.: 1.7 Basic P11ranzm/zl/aiioiz Kapur, D.: l8 Consll&#39;ai-rz.i.s um! [IIIÄCGfITOII Kirchner, C.: 18 Dedu.ctio&#39;n. will: C&#39;ons/rainls Siekmann, J.: 19 Q-1\-IKIIP: .4 Proof De&#39;velop&#39;nzr~nf E1ll7l&#39;l0lIIl2.¬7ll Nipkow, T.: 20 A;r2Tomr1I.ie Type (7lasses Smolka, G; &#39;21 C&#39;on..s&#39;h&#39;a&#39;int Lngic Prag-rannning mil/1 .:&#39;\-"(gallon Mukai, I{.: &#39;22 An Algebra/z}? Ge-n.em.li:aI&#39;ion of In_/o~rnmlion ._S&#39;ll.l)._&#39;~"lllII[)l-&#39;lT()&#39;II Satoh, I\&#39;.: 22 Two P-roceelu-res for log-ic prog-ra-nzs l)(l.S&#39;(&#39;(/ on slablct models Robinson, J.A.: 23 Parallel Reasoning and La-rge info-re-nces Hölldobler, S.: &#39;23 On the Adequafeness of the Co-no-nee!-io-n Mr"-I/zo(l Kleine Biining, H.: &#39;24 Search Space: and Average Proof L¢;~n.gl/2 of I?(-s-olniion Bibel, W.: 2e! Aspects of 1.126.: Proof-..S&#39;y.&#39;wIe--nz IA\&#39;()1\lIE&#39;1l&#39; Goltz, H.-J.: - .25 Cent-rolling Deduction. Iltxroug/2 I)e:elara,lire (-&#39;o-nsl-ruels Leiß, H.: 13:") Solvable Cases of the Sen2.i-I/12.-ijic(1,Irio12 Ilro1)le-n1 Plaisted, D.: 26 Theorem P-rmvi-izg by Model Testing Q5! Hierarchical Theorem Proving Using Rewrite Techniques Jürgen Avenhaus, Klaus Becker, Claus-Peter Wirth Universität Kaiserslautern We present a method to handle rewrite systems R with a builtin a.lgebra A. The algebra A may be a well-known one (such as t.he int.eger or rational numbers) or 1na.y itself be given by a convergent rewrite system R0. The approach a.llows one to dene new (partial) functions on A by positive/ negative conditional rewrite rules. To dene the semantics of such a specication we use a mild form of order-sorted specications to deal with undened terms and give a careful denition of how to evaluate the negative conditions in a rewrite rule. As a result of this denition, adding new equations to the specica.tion is a monotone operation in the sense of logic. \&#39;Ve carry over the well-known methods to prove confluence of the rewrite relation -+3, provided >R is terminating. To prove that R is terminating we extend the RPO- approach to our setting. Such a proof may need to prove a theorem in A. The benets of this work are 0 Hierarchical theorem proving is supported o Explicit knowledge on the world of interest can be stated 0 Efciency of the built-in operators can be used 0 Expressiveness of specication is enhenced 0 Partial functions a.re allowed Distributed knowledge-based equational theorem proving Jörg Denzinger Universität. Kaiserslautern Distributing the theorem proving task to several experts is a promising idea. Our approach, the team work method, allows the experts to compete for a while and then they are forced to cooperate. Each expert has a referee that judges the work done by the expert (competition) a.ndthat selectsuseful results of his expert (thus achieving cooperation). The refereesreport to a supervisorthat usesall results of the best expert and the selectedresults of the other experts to generatea new starting input for a next round. This is repeated until a proof is found. Experts use different tactical control knowledge. referees use assessmentknowledge and the supervisor is based on strategical control knowledge. \-Veused the team work method to rlistrilinte equational theorem proving based on unfailing completion. }?J.\&#39;l)(ri(ll(.(Sshowed that for many examples reinarkable (i.e. "super-linear) speed-ups can be achie\&#39;ed. Sort Unfolding Is Not Horn-Clause Resolution Ha.ssa11 Ait-Kaci , Andreas Podelski Digital Paris R.esearC11Lab VVewill describe. and formally justify. a.n algorithm performing lazy sort. unfolding in the nornialization of or(lersortrfd feature (OSF) structures modulo a.sort theor_v.We will argue that this algorithm has a. radi(&#39;all_\_&#39;different operational effect.and logical sernantics tha.n the resolution-based method used in most other s_ystemswith sort definitions. All other formalisms and systems known to us. most in linguistics. tha.t support sort. definitions, see sorts as monadic predicates defined as llornClausesand tl1e11operationally enforce sort constraints by Ilorn-clause resolution. Tlie essential but very important difference is that our algoritlnn does not generate the solutions of a sort theorys axioms, but rather is a ma.\&#39;imallypassive structural <onstraint <-nliorring schemethat weedsout any violation of a sorts defining axiom by objects claimed or derived to be of that sort. VVe claim that the teclmiques we have developed for this algorithm go lieyong their more use 111fea.ture structure forma.lism. Tliey provide a.n elegant and (&#39;lli«&#39;i(nl.means to incorporate knowldege-based reasoning in a (le(lu(ti0n pro(&#39;(&#39;ssas well as olfer a powerful and clean facility for objectt-oriente(l logic programming. Building models While searching refutations Ri(°ar(lo Caferra LItFIA-IMAG FRAN CE We report results of a previous work (together with  Zabel) and a.
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