## Duality and Canonical Extensions of Bounded Distributive Lattices with Operators, and Applications to the Semantics of Non-Classical Logics I (1998)

Venue: | Studia Logica |

Citations: | 12 - 6 self |

### BibTeX

@ARTICLE{Sofronie-stokkermans98dualityand,

author = {Viorica Sofronie-stokkermans},

title = {Duality and Canonical Extensions of Bounded Distributive Lattices with Operators, and Applications to the Semantics of Non-Classical Logics I},

journal = {Studia Logica},

year = {1998},

volume = {64},

pages = {2000}

}

### OpenURL

### Abstract

The main goal of this paper is to explain the link between the algebraic and the Kripke-style models for certain classes of propositional logics. We start by presenting a Priestley-type duality for distributive lattices endowed with a general class of well-behaved operators. We then show that finitely-generated varieties of distributive lattices with operators are closed under canonical embedding algebras. The results are used in the second part of the paper to construct topological and non-topological Kripke-style models for logics that are sound and complete with respect to varieties of distributive lattices with operators in the above-mentioned classes. Introduction In the study of non-classical propositional logics (and especially of modal logics) there are two main ways of defining interpretations or models. One possibility is to use algebras -- usually lattices with operators -- as models. Propositional variables are interpreted over elements of these algebraic models, an...

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Citation Context ...ul for instance in the study of the semantics of program languages, where the topology provides additional information about properties of states (e.g. verifiability, refutability, observability, cf. =-=[RB98]-=-). However, the use of topological models is not fully satisfactory in all situations, especially when one of the ultimate goals is automated theorem proving. Non-topological Kripke models are the typ... |

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