A Study of Truth Predicates in Matrix Semantics

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F18%3A00491283" target="_blank" >RIV/67985807:_____/18:00491283 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1017/S175502031800014X" target="_blank" >http://dx.doi.org/10.1017/S175502031800014X</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/S175502031800014X" target="_blank" >10.1017/S175502031800014X</a>

Result language
angličtina
Original language name
A Study of Truth Predicates in Matrix Semantics
Original language description
Abstract algebraic logic is a theory that provides general tools for the algebraic study of arbitrary propositional logics. According to this theory, every logic L is associated with a matrix semantics Mod*L. This article is a contribution to the systematic study of the so-called truth sets of the matrices in Mod*L. In particular, we show that the fact that the truth sets of Mod*L can be defined by means of equations with universally quantified parameters is captured by an order-theoretic property of the Leibniz operator restricted to deductive filters of L. This result was previously known for equational definability without parameters. Similarly, it was known that the truth sets of Mod*L are implicitly definable if and only if the Leibniz operator is injective on deductive filters of L over every algebra. However, it was an open problem whether the injectivity of the Leibniz operator transfers from the theories of L to its deductive filters over arbitrary algebras. We show that this is the case for logics expressed in a countable language, and that it need not be true in general. Finally we consider an intermediate condition on the truth sets in Mod∗L that corresponds to the order-reflection of the Leibniz operator.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA17-04630S" target="_blank" >GA17-04630S: Predicate graded logics and their applications to computer science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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