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Otter: The CADE13 Competition Incarnations
 JOURNAL OF AUTOMATED REASONING
, 1997
"... This article discusses the two incarnations of Otter entered in the CADE13 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. ..."
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Cited by 44 (3 self)
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This article discusses the two incarnations of Otter entered in the CADE13 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.
OTTER 3.3 Reference Manual
"... by the United States Government and operated by The University of Chicago under the provisions of a contract with the Department of Energy. DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any a ..."
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Cited by 42 (5 self)
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by the United States Government and operated by The University of Chicago under the provisions of a contract with the Department of Energy. DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor The University of Chicago, nor any of their employees or officers, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privatelyowned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of document authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof, Argonne National Laboratory, or The University of Chicago. ii
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 "ou ..."
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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
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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Cited by 22 (2 self)
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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...
Implementing the binding and accommodation theory for anaphora resolution and presupposition projection
 COMPUTATIONAL LINGUISTICS
, 2003
"... ... this article. BAT is reformulated to meet requirements for computational implementation, which include operations on discourse representation structures (renaming and merging), the representation of presuppositions (allowing for selective binding and determining free and bound variables), and a ..."
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Cited by 12 (6 self)
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... this article. BAT is reformulated to meet requirements for computational implementation, which include operations on discourse representation structures (renaming and merging), the representation of presuppositions (allowing for selective binding and determining free and bound variables), and a formulation of the acceptability constraints imposed by BAT. An efficient presupposition resolution algorithm is presented, and several further improvements such as preferences for binding and accommodation are discussed and integrated in this algorithm. Finally, innovative use of firstorder theorem provers to carry out consistency checking of discourse representations is investigated.
Model Building for Natural Language Understanding
 in: Proceedings of ICoS4
, 2001
"... Contents 1 Introduction 1 2 Model Building 3 2.1 FirstOrder Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Constructing Models for Logical Theories . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 Inconsistent Theories . . . . . . . . . . . . . . . . . . . . ..."
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Cited by 7 (0 self)
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Contents 1 Introduction 1 2 Model Building 3 2.1 FirstOrder Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Constructing Models for Logical Theories . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 Inconsistent Theories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3 Linguistic Applications 5 3.1 Information Seeking Dialogue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.2 Controlling a Mobile Robot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.3 Question Answering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 4 Using Inference Tools 8 4.1 Automated Model Builders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 4.2 Automated Theorem Provers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 4.3 System Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10<F18.67
Generating Hard Tautologies Using Predicate Logic and the Symmetric Group
 the Symmetric Group, Appeared in the 5th Workshop on Logic, Language, Information and Computation (WoLLIC
, 1998
"... We introduce methods to generate uniform families of hard propositional tautologies. The tautologies are essentially generated from a single propositional formula by a natural action of the symmetric group S n . ..."
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Cited by 6 (2 self)
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We introduce methods to generate uniform families of hard propositional tautologies. The tautologies are essentially generated from a single propositional formula by a natural action of the symmetric group S n .
Automated theorem proving in quasigroup and loop theory
 NORTHERN MICHIGAN UNIVERSITY, MARQUETTE, MI 49855 USA
"... We survey all known results in the area of quasigroup and loop theory to have been obtained with the assistance of automated theorem provers. We provide both informal and formal descriptions of selected problems, and compare the performance of selected stateofthe art first order theorem provers on ..."
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Cited by 3 (2 self)
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We survey all known results in the area of quasigroup and loop theory to have been obtained with the assistance of automated theorem provers. We provide both informal and formal descriptions of selected problems, and compare the performance of selected stateofthe art first order theorem provers on them. Our analysis yields some surprising results, e.g., the theorem prover most often used by loop theorists does not necessarily yield the best performance.
Computational Discovery in Pure Mathematics
"... Abstract. We discuss what constitutes knowledge in pure mathematics and how new advances are made and communicated. We describe the impact of computer algebra systems, automated theorem provers, programs designed to generate examples, mathematical databases, and theory formation programs on the body ..."
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Abstract. We discuss what constitutes knowledge in pure mathematics and how new advances are made and communicated. We describe the impact of computer algebra systems, automated theorem provers, programs designed to generate examples, mathematical databases, and theory formation programs on the body of knowledge in pure mathematics. We discuss to what extent the output from certain programs can be considered a discovery in pure mathematics. This enables us to assess the state of the art with respect to Newell and Simon’s prediction that a computer would discover and prove an important mathematical theorem. 1