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Displaying similar documents to “Quasi-modal algebras”

An algebraic and Kripke-style approach to a certain extension of intuitionistic logic

Cecylia Rauszer

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CONTENTSIntroduction............................................................................... 5Chapter I. Semi-Boolean algebras 1. Semi-Boolean algebras....................................... 8 2. Q-filters in semi-Boolean algebras............................ 11 3. Extensions of semi-Boolean algebras...................... 15Chapter II. Algebraic and semantic modelsfor Heyting-Brouwer logic 1. Preliminaries.......................................................... 17 2. Algebraic...

Topological representation for monadic implication algebras

Abad Manuel, Cimadamore Cecilia, Díaz Varela José (2009)

Open Mathematics

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In this paper, every monadic implication algebra is represented as a union of a unique family of monadic filters of a suitable monadic Boolean algebra. Inspired by this representation, we introduce the notion of a monadic implication space, we give a topological representation for monadic implication algebras and we prove a dual equivalence between the category of monadic implication algebras and the category of monadic implication spaces.

Modal Boolean Connexive Logics: Semantics and Tableau Approach

Tomasz Jarmużek, Jacek Malinowski (2019)

Bulletin of the Section of Logic

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In this paper we investigate Boolean connexive logics in a language with modal operators: □, ◊. In such logics, negation, conjunction, and disjunction behave in a classical, Boolean way. Only implication is non-classical. We construct these logics by mixing relating semantics with possible worlds. This way, we obtain connexive counterparts of basic normal modal logics. However, most of their traditional axioms formulated in terms of modalities and implication do not hold anymore without...