Evidence Algorithm and Inference Search in First-Order Logics

In the early 1970s, in Kiev, research on automated theorem proving started in the framework of the so-called Evidence Algorithm (EA) programme, having some general features with the Mizar project and, in particular, being oriented to the development of such a technique for inference search in variou...

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Vydáno v:Journal of automated reasoning Ročník 55; číslo 3; s. 269 - 284
Hlavní autor: Lyaletski, Alexander
Médium: Journal Article
Jazyk:angličtina
Vydáno: Dordrecht Springer Netherlands 01.10.2015
Témata:
Artificial Intelligence
Computer Science
Mathematical Logic and Formal Languages
Mathematical Logic and Foundations
Symbolic and Algebraic Manipulation
First-order logic
Intuitionistic logic
Evidence Algorithm
Maslov’s inverse method
Modal logic
Inference search
Automated theorem proving
Classical logic
Clash-resolution method
Sequent calculus
ISSN:0168-7433, 1573-0670
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Shrnutí:In the early 1970s, in Kiev, research on automated theorem proving started in the framework of the so-called Evidence Algorithm (EA) programme, having some general features with the Mizar project and, in particular, being oriented to the development of such a technique for inference search in various first-order logics that satisfies the following requirements: the syntactic form of a problem under consideration should be preserved, logical transformations should be performed in the signature of the original theory, equality handling should be separated from deduction. For these reasons, the main efforts of the EA developers were concentrated on modifying the sequent formalism to obtain sufficient efficiency in sequent proof search, although some attention was paid to the construction of resolution-type methods. This paper contains a brief summary of the author’s results in this field. It is shown that the proposed approach enables to construct (sound and complete) quantifier-rule-free sequent calculi for classical and non-classical logics, including the intuitionistic and modal cases. Besides, two sound and complete resolution-type methods based on a certain generalization of the notion of a clause are described. One of them gives the possibility to interpret Maslov’s inverse method in resolution terms.
ISSN:0168-7433
1573-0670
DOI:10.1007/s10817-015-9346-0