Rational Pavelka logic: The best among three worlds?

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Rational Pavelka logic: The best among three worlds?
Original language description
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.
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
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project
<a href="/en/project/GA18-00113S" target="_blank" >GA18-00113S: Reasoning with graded properties</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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