Geodesic
Free-variable semantic tableaux for the logic of fuzzy inequalities
Algebra i logika, Tome 55 (2016) no. 2, pp. 156-191

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We present a free-variable tableau calculus for the logic of fuzzy inequalities F$\forall$, which is an extension of infinite-valued first-order Lukasiewicz logic Ł$\forall$. The set of all Ł$\forall$-sentences provable in the hypersequent calculus of Baaz and Metcalfe for Ł$\forall$ is embedded into the set of all F$\forall$-sentences provable in the given tableau calculus. We prove NP-completeness of the problem of checking tableau closability and propose an algorithm, which is based on unification, for solving the problem.
Keywords: fuzzy logic, infinite-valued first-order Lukasiewicz logic, automatic proof search, hypersequent calculus, NP-complete problem.
Mots-clés : tableau calculus, tableau closability 
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     author = {A. S. Gerasimov},
     title = {Free-variable semantic tableaux for the logic of fuzzy inequalities},
     journal = {Algebra i logika},
     pages = {156--191},
     publisher = {mathdoc},
     volume = {55},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2016_55_2_a1/}
}
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A. S. Gerasimov. Free-variable semantic tableaux for the logic of fuzzy inequalities. Algebra i logika, Tome 55 (2016) no. 2, pp. 156-191. http://geodesic.mathdoc.fr/item/AL_2016_55_2_a1/