Creator: Gerla, Brunella - LINDAT/CLARIAH-CZ Catalog Search Results

Creator:: Gerla, Brunella
Format:: bez média and svazek
Type:: model:article and TEXT
Subject:: BL-algebras, MV-algebras, semirings, and MV-automata
Language:: English
Description:: In this paper we describe the relationship between many-valued logics (in particular Basic logic and Lukasiewicz logic) and semirings. We will also give definitions of antomata on BL-algebras and MV-algebras.
Rights:: http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

Creator:: Aguzzoli, Stefano and Gerla, Brunella
Format:: bez média and svazek
Type:: model:article and TEXT
Subject:: continuous t-norms, triangular logics, Basic Logic, and bounds on the cardinality of countermodels
Language:: English
Description:: In [3] the tautology problém for Hájek’s Basic Logic BL is proved to be co-NP-cornplete by showing that if a formula ϕ is not a tautology of BL then there exists an integer m > 0, polynomially bounded by the length of ϕ, such that ϕ fails to be a tautology in the infinite-valued logic mŁ corresponding to the ordinal sum of m copies of the Łukasiewicz t-norrn. In this paper we state that if ϕ is not a tautology of BL then it already fails to be a tautology of a finite set of finite-valued logics, defined by taking the ordinal sum of m copies of k-valued Łukasiewicz logics, for effectively determined integers m, k > 0 only depending on polynomial-time computable features of ϕ. This result allows the definition of a calculus for mŁ along the lines of [1], [2], while the analysis of the features of functions associated with formulas of mŁ constitutes a step toward the characterization of finitely generated free BL-algebras as algebras of [0, 1]-valued functions.
Rights:: http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

Creator:: Gerla, Brunella
Format:: bez média and svazek
Type:: model:article and TEXT
Subject:: many-valued logic, fuzzy logic, Rational Łukasiewicz logic, DMV-algebras, completeness, and computational complexity
Language:: English
Description:: In this paper we present some results concerning the variety of divisible MV-algebras. Any free divisible MV-algebra is an algebra of continuous piecewise linear functions with rational coefficients. Correspondingly, the Rational Łukasiewicz logic is defined and its tautology problem is shown to be co-NP-complete.
Rights:: http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

Limit your search