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An Overview of Linear Logic Programming
 in Computational Logic
, 1985
"... Logic programming can be given a foundation in sequent calculus by viewing computation as the process of building a cutfree sequent proof bottomup. The first accounts of logic programming as proof search were given in classical and intuitionistic logic. Given that linear logic allows richer sequen ..."
Abstract

Cited by 7 (1 self)
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Logic programming can be given a foundation in sequent calculus by viewing computation as the process of building a cutfree sequent proof bottomup. The first accounts of logic programming as proof search were given in classical and intuitionistic logic. Given that linear logic allows richer sequents and richer dynamics in the rewriting of sequents during proof search, it was inevitable that linear logic would be used to design new and more expressive logic programming languages. We overview how linear logic has been used to design such new languages and describe briefly some applications and implementation issues for them.
The Calculus of Constructions as a Framework for Proof Search with Set Variable Instantiation
, 2000
"... ..."
Proof Search with Set Variable Instantiation in the Calculus of Constructions
 Automated Deduction: CADE13, volume 1104 of Lecture Notes in Arti Intelligence
, 1996
"... . We show how a procedure developed by Bledsoe for automatically finding substitution instances for set variables in higherorder logic can be adapted to provide increased automation in proof search in the Calculus of Constructions (CC). Bledsoe's procedure operates on an extension of firstorder lo ..."
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Cited by 2 (1 self)
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. We show how a procedure developed by Bledsoe for automatically finding substitution instances for set variables in higherorder logic can be adapted to provide increased automation in proof search in the Calculus of Constructions (CC). Bledsoe's procedure operates on an extension of firstorder logic that allows existential quantification over set variables. The method finds maximal solutions for this special class of higherorder variables. This class of variables can also be identified in CC. The existence of a correspondence between higherorder logic and higherorder type theories such as CC is wellknown. CC can be viewed as an extension of higherorder logic where the basic terms of the language, the simplytyped terms, are replaced with terms containing dependent types. We adapt Bledsoe's procedure to the corresponding class of variables in CC and extend it to handle terms with dependent types. 1 Introduction Both higherorder logic and higherorder type theories serve as th...