Axiomatic classes in propositional modal logic

Goldblatt, Robert; Thomason, S. K.

doi:10.1007/bfb0062855

Cited by 75 publications

(62 citation statements)

References 2 publications

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“…They explored the fact that the union of two accessibility relations is definable in the basic modal language in the sense that the formula T p ↔ R p ∨ S p is valid on a frame precisely if R T , the relation that interprets T , is the union of R R and R S , respectively the relation that interprets R and the relation that interprets S . Yet, and it came as a surprise, the intersection of two accessibility relations does not work in the same way [55]. Later, Gargov,…”

Section: History Of Hybrid Logicsmentioning

confidence: 99%

Paraconsistency in hybrid logic

Costa

Martins

2016

J Logic Computation

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palavras-chaveParaconsistência, lógica híbrida, lógica quase-híbrida, bistrutura, frame de Kripke, satisfação dissociada, satisfação forte, modelo, medida de inconsistência. However, the information we collect is subject to inconsistencies, namely, the search for different information sources can lead us to pick up contradictions. Nowadays, by having so many means of dissemination available, that happens frequently.The aim of this work is to develop tools capable of dealing with contradictory information that can be described as hybrid logics' formulas. To build models, to compare inconsistency in different databases, and to see the applicability of this method in day-to-day life are the basis for the development of this dissertation.

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Section: History Of Hybrid Logicsmentioning

confidence: 99%

Paraconsistency in hybrid logic

Costa

Martins

2016

J Logic Computation

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“…Theorem 5.40 below, due to GOLDBLATT & THOMASON [47], can be read as a modal dual of Birkhoff's theorem identifying varieties with equational classes. For a definition of Birkhoff's theorem from a coalgebraic perspective, the reader is referred to section 14.…”

Section: Proofmentioning

confidence: 99%

6 Algebras and coalgebras

Venema

2007

Handbook of Modal Logic

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This chapter1 sketches some of the mathematical surroundings of modal logic. First, we discuss the algebraic perspective on the field, showing how the theory of universal algebra, and more specifically, that of Boolean algebras with operators, can be used to prove significant results in modal logic. In the second and last part of the chapter we describe how modal logic, and its model theory, provides many natural manifestations of the more general theory of universal coalgebra.

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“…posets) [25,21]; that is, of a class K of the form {X : X + ∈ V} for some variety V of closure algebras (resp. Heyting algebras).…”

Section: Definabilitymentioning

confidence: 99%

Topo-canonical completions of closure algebras and Heyting algebras

2007

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We introduce and investigate topo-canonical completions of closure algebras and Heyting algebras. We develop a duality theory that is an alternative to Esakia's duality, describe duals of topo-canonical completions in terms of the Salbany and Banaschewski compactifications, and characterize topo-canonical varieties of closure algebras and Heyting algebras. Consequently, we show that ideal completions preserve no identities of Heyting algebras. We also characterize definable classes of topological spaces.

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Axiomatic classes in propositional modal logic

Abstract: In his review (Kaplan [1966] A first-order frame is a triple (W,R,P), where W is a non-empty set, R is a binary relation on W, and P is a non-empty collection of subsets of W closed under the Boolean operations and the unary operation M R

Cited by 75 publications

References 2 publications

Paraconsistency in hybrid logic

Paraconsistency in hybrid logic

6 Algebras and coalgebras

Topo-canonical completions of closure algebras and Heyting algebras

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