An Algebraic View of Super-Belnap Logics

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F17%3A00477279" target="_blank" >RIV/67985807:_____/17:00477279 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s11225-017-9739-7" target="_blank" >http://dx.doi.org/10.1007/s11225-017-9739-7</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11225-017-9739-7" target="_blank" >10.1007/s11225-017-9739-7</a>

Jazyk výsledku

angličtina

Název v původním jazyce

An Algebraic View of Super-Belnap Logics

Popis výsledku v původním jazyce

The Belnap–Dunn logic (also known as First Degree Entailment, or FDE) is a well-known and well-studied four-valued logic, but until recently little has been known about its extensions, i.e. stronger logics in the same language, called super-Belnap logics here. We give an overview of several results on these logics which have been proved in recent works by Přenosil and Rivieccio. We present Hilbert-style axiomatizations, describe reduced matrix models, and give a description of the lattice of super-Belnap logics and its connections with graph theory. We adopt the point of view of Abstract Algebraic Logic, exploring applications of the general theory of algebraization of logics to the super-Belnap family. In this respect we establish a number of new results, including a description of the algebraic counterparts, Leibniz filters, and strong versions of super-Belnap logics, as well as the classification of these logics within the Leibniz and Frege hierarchies.

Název v anglickém jazyce

An Algebraic View of Super-Belnap Logics

Popis výsledku anglicky

The Belnap–Dunn logic (also known as First Degree Entailment, or FDE) is a well-known and well-studied four-valued logic, but until recently little has been known about its extensions, i.e. stronger logics in the same language, called super-Belnap logics here. We give an overview of several results on these logics which have been proved in recent works by Přenosil and Rivieccio. We present Hilbert-style axiomatizations, describe reduced matrix models, and give a description of the lattice of super-Belnap logics and its connections with graph theory. We adopt the point of view of Abstract Algebraic Logic, exploring applications of the general theory of algebraization of logics to the super-Belnap family. In this respect we establish a number of new results, including a description of the algebraic counterparts, Leibniz filters, and strong versions of super-Belnap logics, as well as the classification of these logics within the Leibniz and Frege hierarchies.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

<a href="/cs/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Centrum excelence - Institut teoretické informatiky (CE-ITI)</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Studia Logica

ISSN

0039-3215

e-ISSN

—

Svazek periodika

105

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

36

Strana od-do

1051-1086

Kód UT WoS článku

000415716400002

EID výsledku v databázi Scopus

2-s2.0-85026908823