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arXiv · 1812.04861

A repetition-free hypersequent calculus for first-order rational Pavelka logic

Alexander S. Gerasimov
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Abstract

We present a hypersequent calculus $\text{G}^3\textŁ\forall$ for first-order infinite-valued Łukasiewicz logic and for an extension of it, first-order rational Pavelka logic; the calculus is intended for bottom-up proof search. In $\text{G}^3\textŁ\forall$, there are no structural rules, all the rules are invertible, and designations of multisets of formulas are not repeated in any premise of the rules. The calculus $\text{G}^3\textŁ\forall$ proves any sentence that is provable in at least one of the previously known hypersequent calculi for the given logics. We study proof-theoretic properties of $\text{G}^3\textŁ\forall$ and thereby provide foundations for proof search algorithms.

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Alexander S. Gerasimov. 2019-01-28. A repetition-free hypersequent calculus for first-order rational Pavelka logic. https://doi.org/10.33048/semi.2020.17.127

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