A repetition-free hypersequent calculus for first-order rational Pavelka logic
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.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2018
- DOI:
- 10.48550/arXiv.1812.04861
- arXiv:
- arXiv:1812.04861
- Bibcode:
- 2018arXiv181204861G
- Keywords:
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- Computer Science - Logic in Computer Science;
- F.4.1;
- I.2.3
- E-Print:
- 21 pages