On the calculus of positively constructed formulas for authomated theorem proving
Abstract
The paper deals with an expressive logic language LF and its calculus. Formulas of
this language consist of some large-block structural elements, such as type quanti¯ers.
The language LF contains only two logic symbols for any and is, which form the set of logic
connectives of the language. A logic calculus JF and complete strategy for automated
proof search based on a single unary rule of inference are considered. This calculus has a
number of other features that lead to the reduction of combinatorial complexity of ¯nding
the deductions in comparison with the known systems for automated theorem proving
as the resolution method and Genzen calculus. Problems of effective implementation of JF as a program system for automated theorem proving are considered.
this language consist of some large-block structural elements, such as type quanti¯ers.
The language LF contains only two logic symbols for any and is, which form the set of logic
connectives of the language. A logic calculus JF and complete strategy for automated
proof search based on a single unary rule of inference are considered. This calculus has a
number of other features that lead to the reduction of combinatorial complexity of ¯nding
the deductions in comparison with the known systems for automated theorem proving
as the resolution method and Genzen calculus. Problems of effective implementation of JF as a program system for automated theorem proving are considered.
About the Authors
A. V. Davydov
Институт динамики систем и теории управления СО РАН, г.Иркутск
Russian Federation
Russian Federation
A. A. Larionov
Институт математики, экономики и информатики ИГУ, г.Иркутск
Russian Federation
Russian Federation
E. A. Cherkashin
Институт динамики систем и теории управления СО РАН, г.Иркутск
Russian Federation
Russian Federation
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Review
For citations:
Davydov A.V., Larionov A.A., Cherkashin E.A. On the calculus of positively constructed formulas for authomated theorem proving. Modeling and Analysis of Information Systems. 2010;17(4):60-69. (In Russ.)
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