Rational Pavelka logic: The best among three worlds?

0563350 - ÚI 2024 RIV NL eng J - Journal Article
Haniková, Zuzana
Rational Pavelka logic: The best among three worlds?
Fuzzy Sets and Systems. Roč. 456, March 2023 (2023), s. 92-106. ISSN 0165-0114. E-ISSN 1872-6801
R&D Projects: GA ČR(CZ) GA18-00113S
Institutional support: RVO:67985807
Keywords : fuzzy logic * Łukasiewicz logic * Rational Pavelka logic * rational truth constants * graded formula
OECD category: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Impact factor: 3.9, year: 2022
Method of publishing: Limited access
https://doi.org/10.1016/j.fss.2022.08.010

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.
Permanent Link: https://hdl.handle.net/11104/0335337