O produktové logice s pravdivostními konstantami

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F06%3A00045161" target="_blank" >RIV/67985807:_____/06:00045161 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

On Product Logic with Truth-Constants

Popis výsledku v původním jazyce

Product Logic is an axiomatic extension of Hájek's Basic Fuzzy Logic BL coping with the 1-tautologies when the strong conjunction and implication are interpreted by the product of reals in [0, 1] and its residuum respectively. In this paper we investigate expansions of Product Logic by adding into the language a countable set of truth-constants, for example one truth-constant for each rational number in [0, 1], and by adding the corresponding book-keeping axioms for the truth-constants. We first show that the corresponding logics are algebraizable, and hence complete with respect to the variety of corresponding algebras. The main result of the paper is the canonical standard completeness of these logics, that is, theorems of them are exactly the 1-tautologies of the algebra defined over the real unit interval where the truth-constants are interpreted as their own values.

Název v anglickém jazyce

On Product Logic with Truth-Constants

Popis výsledku anglicky

Product Logic is an axiomatic extension of Hájek's Basic Fuzzy Logic BL coping with the 1-tautologies when the strong conjunction and implication are interpreted by the product of reals in [0, 1] and its residuum respectively. In this paper we investigate expansions of Product Logic by adding into the language a countable set of truth-constants, for example one truth-constant for each rational number in [0, 1], and by adding the corresponding book-keeping axioms for the truth-constants. We first show that the corresponding logics are algebraizable, and hence complete with respect to the variety of corresponding algebras. The main result of the paper is the canonical standard completeness of these logics, that is, theorems of them are exactly the 1-tautologies of the algebra defined over the real unit interval where the truth-constants are interpreted as their own values.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/1M0545" target="_blank" >1M0545: Institut Teoretické Informatiky</a><br>

Návaznosti

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

Rok uplatnění

2006

Kód důvěrnosti údajů

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

Název periodika

Journal of Logic and Computation

ISSN

0955-792X

e-ISSN

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Svazek periodika

16

Číslo periodika v rámci svazku

-

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

21

Strana od-do

205-225

Kód UT WoS článku

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EID výsledku v databázi Scopus

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