Full-text resources of PSJD and other databases are now available in the new Library of Science.
Visit https://bibliotekanauki.pl

PL EN


Preferences help
enabled [disable] Abstract
Number of results
2011 | 46 |

Article title

On Semilattice-based Logics with an Algebraizable Assertional Companion

Content

Title variants

Languages of publication

PL

Abstracts

PL
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.

Publisher

Year

Volume

46

Physical description

Dates

published
2011
online
07 - 07 - 2015

Contributors

References

Document Type

Publication order reference

Identifiers

YADDA identifier

bwmeta1.element.ojs-issn-2084-2589-year-2011-volume-46-article-2883
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.