We present an "unfailing" extension of the standard KnuthBendix completion procedure that is guaranteed to produce a desired canonical system, provided certain conditions are met. Weprove that this unfailing completion method is refutationally complete for theorem proving in equational theories. The method can also be applied to Horn clauses with equality, in which case it corresponds to positive unit resolution plus oriented paramodulation, with unrestricted simplification.

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This article discusses the two incarnations of Otter entered in the CADE-13 Automated Theorem Proving Competition. Also presented are some historical background, a summary of applications that have led to new results in mathematics and logic, and a general discussion of Otter.

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, easy-to-find 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

This paper shows how a question-answering system can use first-order logic as its language and an automatic theorem prover, based upon the resolution inference principle, as its deductive mechanism. The resolution proof procedure is extended to a constructive proof procedure. An answer construction algorithm is given whereby the system is able not only to produce yes or no answers but also to find or construct an object satisfying a specified condition. A working computer program, QA3, based on these ideas, is described. The performance of the program, illustrated by extended examples, compares favorably with several other question-answering programs. Methods are presented for solving state transformation problems. In addition to question-answering, the program can do automatic programming

First-order predicate logic essentially is a language to express knowledge concerning objects and relationships between objects in a domain. Many medical problems can be cast naturally in such terms. In this paper the suitability of logic as a knowledge-representation formalism in building medical expert system is investigated. In particular, we investigate the logical representation of three typical reasoning models in medicine: diagnostic, anatomical and causal reasoning. It turns out that each of these models has its own characteristic logical structure. Furthermore, the pragmatics of using theorem-proving techniques in consulting such logic-based medical expert systems is discussed. In particular, attention is paid to the use of a meta-level architecture to improve the applicability of theorem-proving techniques in building expert systems.

Number 644

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Automated reasoning systems, also called automatic theorem provers, have been a focus of study since computer science expanded to include the study of symbolic computation in the 1950's. More recently, the so-called "logic programming" language Prolog has been the focus of much study that has generated very efficient implementations of a language once noted for its expressive power, but now noted for its performance as well. The joining of Prolog technology with an early system of inference called Model Elimination led to the development of theorem proving systems with a very high rate of inference. This dissertation focuses on the study of automated reasoning based on Model Elimination. A theorem proving architecture and system called METEOR is described and is implemented that is the foundation of a reasoning system that runs on sequential computers, NUMA shared-memory MIMD computers, and in a message-passing distributed computing environment; this reasoning system has the highest r...

In this paper, the authors describe their initial investigations in computational metaphysics. Our method is to implement axiomatic metaphysics in an automated reasoning system. In this paper, we describe what we have discovered when the theory of abstract objects is implemented in prover9 (a first-order automated reasoning system which is the successor to otter). After reviewing the second-order, axiomatic theory of abstract objects, we show (1) how to represent a fragment of that theory in prover9's first-order syntax, and (2) how prover9 then finds proofs of interesting theorems of metaphysics, such as that every possible world is maximal. We conclude the paper by discussing some issues for further research.