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2016 Modal Consequence Relations Extending S4.3: An Application of Projective Unification
Wojciech Dzik, Piotr Wojtylak
Notre Dame J. Formal Logic 57(4): 523-549 (2016). DOI: 10.1215/00294527-3636512


We characterize all finitary consequence relations over S4.3, both syntactically, by exhibiting so-called (admissible) passive rules that extend the given logic, and semantically, by providing suitable strongly adequate classes of algebras. This is achieved by applying an earlier result stating that a modal logic L extending S4 has projective unification if and only if L contains S4.3. In particular, we show that these consequence relations enjoy the strong finite model property, and are finitely based. In this way, we extend the known results by Bull and Fine, from logics, to consequence relations. We also show that the lattice of consequence relations over S4.3 (the lattice of quasivarieties of S4.3-algebras) is countable and distributive and it forms a Heyting algebra.


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Wojciech Dzik. Piotr Wojtylak. "Modal Consequence Relations Extending S4.3: An Application of Projective Unification." Notre Dame J. Formal Logic 57 (4) 523 - 549, 2016.


Received: 30 November 2012; Accepted: 11 November 2013; Published: 2016
First available in Project Euclid: 19 July 2016

zbMATH: 06663939
MathSciNet: MR3565536
Digital Object Identifier: 10.1215/00294527-3636512

Primary: 03B45 , 08C15 , 68T15
Secondary: 03B35 , 06E25

Keywords: $\mathbf{S4.3}$ , admissible rules , consequence relations , projective unification , quasivarieties , structural completeness

Rights: Copyright © 2016 University of Notre Dame


Vol.57 • No. 4 • 2016
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