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2002•Fundamenta InformaticaeRequires access

A study of interconnections between rough and 3-valued Lukasiewicz logics

Jayanta Sen, Mihir K. Chakraborty

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Abstract

Sequent calculi for topological quasi-Boolean algebras, topological quasi-Boolean algebras without distributivity, pre-rough algebras and Wajsberg algebras have been presented. It is shown that the calculi for the latter two classes of algebras are equivalent. A connection between some logics for the first class of algebras and the linear logic or linear logic with distributivity has been established.

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What this paper is about

Sequent calculi for topological quasi-Boolean algebras, topological quasi-Boolean algebras without distributivity, pre-rough algebras and Wajsberg algebras have been presented. It is shown that the calculi for the latter two classes of algebras are equivalent. A connection between some logics for the first class of algebras and the linear logic or linear logic with distributivity has been established.

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OpenAlex reports 11 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

Sequent calculi for topological quasi-Boolean algebras, topological quasi-Boolean algebras without distributivity, pre-rough algebras and Wajsberg algebras have been presented. It is shown that the calculi for the latter two classes of algebras are equivalent. A connection between some logics for the first class of algebras and the linear logic or linear logic with distributivity has been established.

Key concepts: Distributivity, Mathematics, Interior algebra, Heyting algebra, Boolean algebras canonically defined, Class (philosophy), Connection (principal bundle), Free Boolean algebra

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