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2011 | 46 | 109-132
Tytuł artykułu

ON SEMILATTICE-BASED LOGICS WITH AN ALGEBRAIZABLE ASSERTIONAL COMPANION

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Języki publikacji
EN
Abstrakty
EN
This paper studies some properties of the so-called semilattice-based logics (which are defined in a standard way using only the order relation from a variety of algebras that have a semilattice reduct with maximum) under the assumption that its companion assertional logic (defined from the same variety of algebras using the top element as representing truth) is algebraizable. This describes a very common situation, and the conclusion of the paper is that these semilattice-based logics exhibit some of the good behaviour of protoalgebraic logics, without being necessarily so. The main result is that all these logics have enough Leibniz filters, a fact previously known in the literature to occur only for protoalgebraic logics. Another significant result is that the two companion logics coincide if and only if one of them enjoys the characteristic property of the other, that is, if and only if the semilattice-based logic is algebraizable, and if and only if its assertional companion is selfextensional. When these conditions are met, then the (unique) logic is finitely, regularly and strongly algebraizable and fully Fregean, this places it at some of the highest ranks in both the Leibniz hierarchy and the Frege hierarchy.
Rocznik
Numer
46
Strony
109-132
Opis fizyczny
Rodzaj publikacji
ARTICLE
Twórcy
  • Josep Maria Font, Department of Probability, Logic and Statistics, Faculty of Mathematics, University of Barcelona, Barcelona, Spain
Bibliografia
Typ dokumentu
Bibliografia
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11PLAAAA10196
Identyfikator YADDA
bwmeta1.element.1a467f5c-51d2-3016-8c1f-c962ed71c7f1
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