# Rational Pavelka logic: the best among three worlds?

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 calibrate 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.

research
12/13/2018

### Comparing several calculi for first-order infinite-valued Łukasiewicz logic

From the viewpoint of provability, we compare some Gentzen-type hyperseq...
research
02/23/2018

### Implicit definability of truth constants in Łukasiewicz logic

In the framework of propositional Łukasiewicz logic, a suitable notion o...
research
08/08/2014

research
12/21/2019

### Logic and Rational Languages of Scattered and Countable Series-Parallel Posets

Let A be an alphabet and SP^(A) denote the class of all countable N-free...
research
07/15/2022

### First-order logic with self-reference

We consider an extension of first-order logic with a recursion operator ...
research
06/11/2009

### From formulas to cirquents in computability logic

Computability logic (CoL) (see http://www.cis.upenn.edu/ giorgi/cl.html)...
research
07/26/2000

### Ordering-based Representations of Rational Inference

Rational inference relations were introduced by Lehmann and Magidor as t...