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tps: A theorem proving system for classical type theory
 Journal of Automated Reasoning
, 1996
"... This is a description of TPS, a theorem proving system for classical type theory (Church’s typed λcalculus). TPS has been designed to be a general research tool for manipulating wffs of first and higherorder logic, and searching for proofs of such wffs interactively or automatically, or in a comb ..."
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Cited by 71 (6 self)
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This is a description of TPS, a theorem proving system for classical type theory (Church’s typed λcalculus). TPS has been designed to be a general research tool for manipulating wffs of first and higherorder logic, and searching for proofs of such wffs interactively or automatically, or in a combination of these modes. An important feature of TPS is the ability to translate between expansion proofs and natural deduction proofs. Examples of theorems which TPS can prove completely automatically are given to illustrate certain aspects of TPS’s behavior and problems of theorem proving in higherorder logic. 7
Some Uses of HigherOrder Logic in Computational Linguistics
 In 24st Annual Meeting of the Association for Computational Linguistics
, 1986
"... Consideration of the question of meaning in the framework of linguistics often requires an allusion to sets and other higherorder notions. The traditional approach to representing and reasoning about meaning in a computational setting has been to use knowledge representation systems that are either ..."
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Cited by 23 (10 self)
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Consideration of the question of meaning in the framework of linguistics often requires an allusion to sets and other higherorder notions. The traditional approach to representing and reasoning about meaning in a computational setting has been to use knowledge representation systems that are either based on firstorder logic or that use mechanisms whose formal justifications are to be provided after the fact. In this paper we shall consider the use of a higherorder logic for this task. We first present a version of definite clauses (positive Horn clauses) that is based on this logic. Predicate and function variables may occur in such clauses and the terms in the language are the typed terms. Such term structures have a richness that may be exploited in representing meanings. We also describe a higherorder logic programming language, called Prolog, which represents programs as higherorder definite clauses and interprets them using a depthfirst interpreter. A virtue of this languag...
TPS: An Interactive and Automatic Tool for Proving Theorems of Type Theory
 Higher Order Logic Theorem Proving and Its Applications: 6th International Workshop, HUG '93, volume 780 of Lecture Notes in Computer Science
, 1994
"... This is a demonstration of TPS, a theorem proving system for classical type theory (Church's typed lcalculus). TPS can be used interactively or automatically, or in a combination of these modes. An important feature of TPS is the ability to translate between expansion proofs and natural deduction ..."
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Cited by 1 (1 self)
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This is a demonstration of TPS, a theorem proving system for classical type theory (Church's typed lcalculus). TPS can be used interactively or automatically, or in a combination of these modes. An important feature of TPS is the ability to translate between expansion proofs and natural deduction proofs. CATEGORY: Demonstration 1. Introduction This presentation is a demonstration of TPS, a theorem proving system for classical type theory (Church's typed 3 lcalculus [14]) which has been under development at Carnegie Mellon University for a number of years. TPS is based on an approach to automated theorem proving called the mating method [2], which is essentially the same as the connection method developed independently by Bibel [13]. The mating method does not require reduction to clausal form. TPS handles two sorts of proofs, natural deduction proofs and expansion proofs. Natural deduction proofs are humanreadable formal proofs. An example of such a proof which was produced aut...