PL EN


2011 | 46 | 109-132
Article title

ON SEMILATTICE-BASED LOGICS WITH AN ALGEBRAIZABLE ASSERTIONAL COMPANION

Selected contents from this journal
Title variants
Languages of publication
EN
Abstracts
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.
Year
Issue
46
Pages
109-132
Physical description
Document type
ARTICLE
Contributors
  • Josep Maria Font, Department of Probability, Logic and Statistics, Faculty of Mathematics, University of Barcelona, Barcelona, Spain
References
Document Type
Publication order reference
Identifiers
CEJSH db identifier
11PLAAAA10196
YADDA identifier
bwmeta1.element.1a467f5c-51d2-3016-8c1f-c962ed71c7f1
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.