Сибирский федеральный университет

Тип публикации: статья из журнала

Год издания: 2021

Идентификатор DOI: 10.26516/1997-7670.2021.37.104

Ключевые слова: modal logic, frame and model Kripke, Admissible inference rule, weak co-cover property, модальная логика, фрейм и модель Крипке, допустимое правило вывода, слабое свойство ко-накрытий

Аннотация: Как правило, семантические свойства нестандартных логик описываются с помощью формул, аксиом. Допустимые правила вывода предоставляют более гибкий и мощный аппарат для исследования неклассических логик. В начале 2000-х гг. появилось несколько статей, в которых описывался явный базис для допустимых правил вывода неклассических логик <i>S</i>4, <i>K</i>4, <i>Grz</i>, <i>Int</i>, т. е. набор допустимых правил вывода для заданной логики, из которых все остальные допустимые правила выводятся как следствия. Ключевым свойством логик при построении этих явных базисов, на наш взгляд, является слабое свойство ко-накрытий, что мотивирует данное исследование. Для финитно аппроксимируемых расширений логики <i>GL</i> описано семантическое свойство адекватных логике фреймов через допустимость в логике некоторого набора правил вывода. Финитно аппроксимируемая модальная логика над <i>GL</i> имеет слабое свойство ко-накрытий, если и только если в логике допустим заданный набор правил вывода. Firstly semantic property of nonstandart logics were described by formulas which are peculiar to studied a models in general, and do not take to consideration a variable conditions and a changing assumptions. Evidently the notion of inference rule generalizes the notion of formulas and brings us more flexibility and more expressive power to model human reasoning and computing. In 2000-2010 a few results on describing of explicit bases for admissible inference rules for nonstandard logics (<i>S</i>4, <i>K</i>4, <i>H</i> etc.) appeared. The key property of these logics was weak co-cover property. Beside the improvement of deductive power in logic, an admissible rule are able to describe some semantic property of given logic. We describe a semantic property of modal logics in term of admissibility of given set of inference rules. We prove that modal logic over logic <i>GL</i> enjoys weak co-cover property iff all given rules are admissible for logic. Firstly semantic property of nonstandart logics were described by formulas which are peculiar to studied a models in general, and do not take to consideration a variable conditions and a changing assumptions. Evidently the notion of inference rule generalizes the notion of formulas and brings us more flexibility and more expressive power to model human reasoning and computing. In 2000-2010 a few results on describing of explicit bases for admissible inference rules for nonstandard logics (S4, K4, H etc.) appeared. The key property of these logics was weak co-cover property. Beside the improvement of deductive power in logic, an admissible rule are able to describe some semantic property of given logic. We describe a semantic property of modal logics in term of admissibility of given set of inference rules. We prove that modal logic over logic GL enjoys weak co-cover property iff all given rules are admissible for logic. Firstly semantic property of nonstandart logics were described by formulas which are peculiar to studied a models in general, and do not take to consideration a variable conditions and a changing assumptions. Evidently the notion of inference rule generalizes the notion of formulas and brings us more flexibility and more expressive power to model human reasoning and computing. In 2000-2010 a few results on describing of explicit bases for admissible inference rules for nonstandard logics (S4, K4, H etc.) appeared. The key property of these logics was weak co-cover property. Beside the improvement of deductive power in logic, an admissible rule are able to describe some semantic property of given logic. We describe a semantic property of modal logics in term of admissibility of given set of inference rules. We prove that modal logic over logic GL enjoys weak co-cover property iff all given rules are admissible for logic. © 2021 Irkutsk State University. All rights reserved.

Журнал: BULLETIN OF IRKUTSK STATE UNIVERSITY-SERIES MATHEMATICS

Выпуск журнала: Vol. 37

Номера страниц: 104-117

ISSN журнала: 19977670

Место издания: IRKUTSK

Издатель: IRKUTSK STATE UNIV

• Римацкий Виталий Валентинович (Сибирский федеральный университет)

• РИНЦ (eLIBRARY.RU)
• Web of Science Core Collection
• Scopus