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Comparing approaches to the exploration of the domain of residue classes
 ARTICLE SUBMITTED TO JOURNAL OF SYMBOLIC COMPUTATION
, 2002
"... We report on a case study on combining proof planning with computer algebra systems. We construct proofs for basic algebraic properties of residue classes as well as for isomorphisms between residue classes using different proof techniques, which are implemented as strategies in a multistrategy ..."
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Cited by 25 (13 self)
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We report on a case study on combining proof planning with computer algebra systems. We construct proofs for basic algebraic properties of residue classes as well as for isomorphisms between residue classes using different proof techniques, which are implemented as strategies in a multistrategy proof planner. The search space of the proof planner can be drastically reduced by employing computations of two computer algebra systems during the planning process. To test the eectiveness of our approach we carried out a large number of experiments and also compared it with some alternative approaches. In particular, we experimented with substituting computer algebra by model generation and by proving theorems with a first order equational theorem prover instead of a proof planner.
Automatic Proofs and Counterexamples for Some Ortholattice Identities
 Information Processing Letters
, 1998
"... This note answers questions on whether three identities known to hold for orthomodular lattices are true also for ortholattices. One identity is shown to fail by MACE, a program that searches for counterexamples, an the other two are proved to hold by EQP, an equational theorem prover. The problems, ..."
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This note answers questions on whether three identities known to hold for orthomodular lattices are true also for ortholattices. One identity is shown to fail by MACE, a program that searches for counterexamples, an the other two are proved to hold by EQP, an equational theorem prover. The problems, from work in quantum logic, were given to us by Norman Megill. Keywords: Automatic theorem proving, ortholattice, quantum logic, theory of computation. 1 Introduction An ortholattice is an algebra with a binary operation (join) and a unary operation 0 (complement) satisfying the following (independent) set of identities. x y = (x 0 y 0 ) 0 (definition of meet) x y = y x (x y) z = x (y z) x (x y) = x x 00 = x x (y y 0 ) = y y 0 Supported by the Mathematical, Information, and Computational Sciences Division subprogram of the Office of Computational and Technology Research, U.S. Department of Energy, under Contract W31109Eng38. From these identities one can...
33 Basic Test Problems: A Practical Evaluation of Some Paramodulation Strategies
, 1996
"... Introduction Many researchers who study the theoretical aspects of inference systems believe that if inference rule A is complete and more restrictive than inference rule B, then the use of A will lead more quickly to proofs than will the use of B. The literature contains statements of the sort &qu ..."
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Cited by 24 (5 self)
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Introduction Many researchers who study the theoretical aspects of inference systems believe that if inference rule A is complete and more restrictive than inference rule B, then the use of A will lead more quickly to proofs than will the use of B. The literature contains statements of the sort "our rule is complete and it heavily prunes the search space; therefore it is efficient". 2 These positions are highly questionable and indicate that the authors have little or no experience with the practical use of automated inference systems. Restrictive rules (1) can block short, easytofind proofs, (2) can block proofs involving simple clauses, the type of clause on which many practical searches focus, (3) can require weakening of redundancy control such as subsumption and demodulation, and (4) can require the use of complex checks in deciding whether such rules should be applied. The only way to determ
Goal Oriented Equational Theorem Proving Using Team Work
 University of Kaiserslautern
, 1994
"... The team work method is a concept for distributing automated theorem provers and so to activate several experts to work on a given problem. We have implemented this for pure equational logic using the unfailing KnuthBendix completion procedure as basic prover. In this paper we present three classes ..."
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The team work method is a concept for distributing automated theorem provers and so to activate several experts to work on a given problem. We have implemented this for pure equational logic using the unfailing KnuthBendix completion procedure as basic prover. In this paper we present three classes of experts working in a goal oriented fashion. In general, goal oriented experts perform their job "unfair" and so are often unable to solve a given problem alone. However, as a team member in the team work method they perform highly efficient, even in comparison with such respected provers as Otter 3.0 or REVEAL, as we demonstrate by examples, some of which can only be proved using team work. The reason for these achievements results from the fact that the team work method forces the experts to compete for a while and then to cooperate by exchanging their best results. This allows one to collect "good" intermediate results and to forget "useless" ones. Completion based proof methods are fr...
Short Single Axioms for Boolean Algebra
 J. Automated Reasoning
, 2002
"... We present short single equational axioms for Boolean algebra in terms of disjunction and negation and in terms of the Sheffer stroke. Previously known single axioms for these theories are much longer than the ones we present. We show that there is no shorter axiom in terms of the Sheffer stroke tha ..."
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Cited by 22 (9 self)
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We present short single equational axioms for Boolean algebra in terms of disjunction and negation and in terms of the Sheffer stroke. Previously known single axioms for these theories are much longer than the ones we present. We show that there is no shorter axiom in terms of the Sheffer stroke than the ones we present. Automated deduction techniques were used for several different aspects of the work. Keywords: Boolean algebra, Sheffer stroke, single axiom 1. Background and
High Performance ATP Systems by Combining Several AI Methods
 IN PROC. FIFTEENTH INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE (IJCAI ’97
, 1997
"... We present a concept for an automated theorem prover that employs a search control based on ideas from several areas of artificial intelligence (AI). The combination of casebased reasoning, several similarity concepts, a cooperation concept of distributed AI and reactive planning enables a system u ..."
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We present a concept for an automated theorem prover that employs a search control based on ideas from several areas of artificial intelligence (AI). The combination of casebased reasoning, several similarity concepts, a cooperation concept of distributed AI and reactive planning enables a system using our concept to learn form previous successful proof attempts. In a kind of bootstrapping process easy problems are used to solve more and more complicated ones. We provide case studies from two domains of interest in pure equational theorem proving taken from the TPTP library. These case studies show that an instantiation of our architecture achieves a high grade of automation and outperforms stateoftheart conventional theorem provers.
Common Syntax of the DFGSchwerpunktprogramm "Deduktion"
 HLS + 96] DIETER HUTTER, BRUNO LANGENSTEIN, CLAUS SENGLER, JORG
, 1996
"... A common exchange format for logic problems to be used by members of the DFGSchwerpunktprogramm "Deduktion" is introduced. It is thought to be an internal format that can easily be parsed such that it forms a compromise between the needs of the different groups. It is not intended to be a ..."
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Cited by 20 (1 self)
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A common exchange format for logic problems to be used by members of the DFGSchwerpunktprogramm "Deduktion" is introduced. It is thought to be an internal format that can easily be parsed such that it forms a compromise between the needs of the different groups. It is not intended to be a highlevel general logic language that is easy to read or to write. The language is more general than other popular exchange formats such as Otter or TPTP in allowing nonclausal and sorted formulas as well as userdefined operators and quantifiers. The latter feature makes it also useful for nonclassical logics.
Learning and using relational theories
 In Advances in Neural Information Processing Systems
"... Much of human knowledge is organized into sophisticated systems that are often called intuitive theories. We propose that intuitive theories are mentally represented in a logical language, and that the subjective complexity of a theory is determined by the length of its representation in this langua ..."
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Much of human knowledge is organized into sophisticated systems that are often called intuitive theories. We propose that intuitive theories are mentally represented in a logical language, and that the subjective complexity of a theory is determined by the length of its representation in this language. This complexity measure helps to explain how theories are learned from relational data, and how they support inductive inferences about unobserved relations. We describe two experiments that test our approach, and show that it provides a better account of human learning and reasoning than an approach developed by Goodman [1]. What is a theory, and what makes one theory better than another? Questions like these are of obvious interest to philosophers of science but are also discussed by psychologists, who have argued that everyday knowledge is organized into rich and complex systems that are similar in many respects to scientific theories. Even young children, for instance, have systematic beliefs about domains including folk physics, folk biology, and folk psychology [2]. Intuitive theories like these play many of the same roles as scientific theories: in particular, both kinds of theories are used to explain and
Recording, Analyzing and Presenting Distributed Deduction Processes
 Proc. 1st PASCO, Hagenberg/Linz
, 1994
"... : Distributed models for deduction allow for more powerful proof systems, but also lead to new problems. In particular, the analysis of the deduction process becomes harder, as a number of largely independent agents may contribute to the proof. In a system including cooperating agents timing conside ..."
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Cited by 17 (10 self)
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: Distributed models for deduction allow for more powerful proof systems, but also lead to new problems. In particular, the analysis of the deduction process becomes harder, as a number of largely independent agents may contribute to the proof. In a system including cooperating agents timing considerations can lead to further problems. In this paper we first introduce the TEAMWORK method and the DISCOUNT system for distributed equational reasoning. We point out the difficulties in obtaining a detailed representation of the proofs generated by a distributed system with completely distributed memory and present our solution for the TEAMWORK approach. Using this solution we are able to explain some of the speedups DISCOUNT was able to obtain in distributed mode. Finally we show how the machinefriendly representation of an equational proof can be transformed into a proof easily readable by humans. Keywords: Distributed deduction, equational reasoning, proof representation, TEAM...
Some Experiments on the Applicability of Folding Architecture Networks to Guide Theorem Proving
, 1997
"... One of the major problems in theorem proving is control of the proof search. A promising approach is the application of machine learning techniques for the acquisition of search control knowledge by learning from successful proof searches. In this paper we briefly discuss this idea and existing mach ..."
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Cited by 17 (6 self)
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One of the major problems in theorem proving is control of the proof search. A promising approach is the application of machine learning techniques for the acquisition of search control knowledge by learning from successful proof searches. In this paper we briefly discuss this idea and existing machine learning techniques for this task. We suggest neural folding architecture networks together with supervised training algorithms as a very promising candidate for learning search control knowledge. This suggestion is based on two sets of experiments in which we applied folding architecture networks to term ordering problems and clause classification tasks resulting from the proof search of the equational theorem prover DISCOUNT.