Rational Pavelka logic: The best among three worlds?

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F23%3A00563350" target="_blank" >RIV/67985807:_____/23:00563350 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1016/j.fss.2022.08.010" target="_blank" >https://doi.org/10.1016/j.fss.2022.08.010</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.fss.2022.08.010" target="_blank" >10.1016/j.fss.2022.08.010</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Rational Pavelka logic: The best among three worlds?

Popis výsledku v původním jazyce

This comparative survey explores three formal approaches to reasoning with partly true statements and degrees of truth, within the family of Łukasiewicz logic. These approaches are represented by infinite-valued Łukasiewicz logic (Ł), Rational Pavelka logic (RPL) and a logic with graded formulas that we refer to as Graded Rational Pavelka logic (GRPL). Truth constants for all rationals between 0 and 1 are used as a technical means to represent degrees of truth. Łukasiewicz logic ostensibly features no truth constants except 0 and 1, Rational Pavelka logic includes constants in the basic language, with suitable axioms, Graded Rational Pavelka logic works with graded formulas and proofs, following the original intent of Pavelka, inspired by Goguen's work. Historically, Pavelka's papers precede the definition of GRPL, which in turn precedes RPL. Retrieving these steps, we discuss how these formal systems naturally evolve from each other, and we also recall how this process has been a somewhat contentious issue in the realm of Łukasiewicz logic. This work can also be read as a case study in logics, their fragments, and the relationship of the fragments to a logic.

Název v anglickém jazyce

Rational Pavelka logic: The best among three worlds?

Popis výsledku anglicky

This comparative survey explores three formal approaches to reasoning with partly true statements and degrees of truth, within the family of Łukasiewicz logic. These approaches are represented by infinite-valued Łukasiewicz logic (Ł), Rational Pavelka logic (RPL) and a logic with graded formulas that we refer to as Graded Rational Pavelka logic (GRPL). Truth constants for all rationals between 0 and 1 are used as a technical means to represent degrees of truth. Łukasiewicz logic ostensibly features no truth constants except 0 and 1, Rational Pavelka logic includes constants in the basic language, with suitable axioms, Graded Rational Pavelka logic works with graded formulas and proofs, following the original intent of Pavelka, inspired by Goguen's work. Historically, Pavelka's papers precede the definition of GRPL, which in turn precedes RPL. Retrieving these steps, we discuss how these formal systems naturally evolve from each other, and we also recall how this process has been a somewhat contentious issue in the realm of Łukasiewicz logic. This work can also be read as a case study in logics, their fragments, and the relationship of the fragments to a logic.

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/GA18-00113S" target="_blank" >GA18-00113S: Usuzování se stupňovanými vlastnostmi</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název periodika

Fuzzy Sets and Systems

ISSN

0165-0114

e-ISSN

1872-6801

Svazek periodika

456

Číslo periodika v rámci svazku

March 2023

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

15

Strana od-do

92-106

Kód UT WoS článku

000939550700001

EID výsledku v databázi Scopus

2-s2.0-85137060216