Many-valued Logic: Foundations and Applications to Satisfiability, Argumentation and Ontologies Many-valued Logic: Foundations and Applications to Satisfiability, Argumentation and Ontologies

A Project coordinated by IIIA.

Principal investigator:

Francesc Esteva Francesc Esteva

Collaborating organisations:

Funding entity:

TIN2007-68005-C04-01 TIN2007-68005-C04-01

Funding call:

Project #:


Funding amount:

0,00€ 0,00€


2007-10-15 2007-10-15


2010-10-15 2010-10-15
Irina PerfilievaDidier DuboisHenri PradeFrancesc EstevaLluís GodoPetra Hodáková; Interpolation of fuzzy data: Analytical approach and overview. Fuzzy Sets and Systems; 2012.  [PDF]  [BibTeX]
Tommaso FlaminioLluís GodoEnrico Marchioni; On the Logical Formalization of Possibilistic Counterparts of States over n-Valued Lukasiewicz Events. Journal of Logic and Computation; 2011.  [PDF]  [BibTeX]
Fèlix BouFrancesc EstevaLluís GodoRicardo Oscar Rodriguez; On the Minimum Many-Valued Modal Logic over a Finite Residuated Lattice. Journal of Logic and Computation; 2011.  [PDF]  [BibTeX]
Petr CintulaCarles Noguera; A general approach to non-classical first-order logics. 2010.  [BibTeX]
Jordi LevyMateu Villaret; An Efficient Nominal Unification Algorithm. 2010.  [PDF]  [BibTeX]
Carlos AnsóteguiMaría Luisa BonetJordi Levy; A New Algorithm for Weighted Partial MaxSAT. 2010.  [PDF]  [BibTeX]
Maliha S.Muhammad A.Ana María Martínez-EnriquezGonzalo Escalada-Imaz; A rule based system for reliability centered maintenance. 2010.  [BibTeX]
Francesc EstevaLluís GodoCarles Noguera; Expanding the propositional logic of a t-norm with truth-constants: completeness results for rational semantics. Soft Computing - A Fusion of Foundations, Methodologies and Applications; 2010.  [PDF]  [BibTeX]
Carles Noguera; From fuzzy set theory to mathematical fuzzy logic. 2010.  [BibTeX]
Angel García-CerdañaEva ArmengolFrancesc Esteva; Fuzzy Description Logics and t-norm based Fuzzy Logics. International Journal of Approximate reasoning; 2010.  [PDF]  [BibTeX]
Carles NogueraFrancesc EstevaLluís Godo; Generalized continuous and left-continuous t-norms arising from algebraic semantics for fuzzy logics. Information Sciences; 2010.  [PDF]  [BibTeX]
Petr CintulaCarles Noguera; Implicational logics vs. order algebraizable logics. 2010.  [BibTeX]
Petr CintulaCarles Noguera; Implicational (semilinear) logics I: a new hierarchy. Archive for Mathematical Logic; 2010.  [PDF]  [BibTeX]
Eva ArmengolAngel García-Cerdaña; Lazy induction of descriptions using two fuzzy versions of the Rand index. 2010.  [PDF]  [BibTeX]
Fi92a, Fi92b}of Fitting where the author defines a modal system over a logic of a finite Heyting algebragive a complete axiomatization of them. In its late paper Fitting justify it in a very nice an elegant semantics based on a multi-agent system each one using classical logichaving a preference relation. He defined the modal operators based on semanticshis definitions is the ones used in later papers on the topic as generalizations modal operators on many-valued systems based on Kripke semantics (with many-valued worldsmany-valued accessibility relations). In these approaches Modal many-valued language is built taking the language of the many-valued logic $(\land, \lor, &, \to_&, \neg_&, 0, 1)$ plus at least one the usual modal operators (necessity $\Box$possibility $\Diamond$)its semantic is defined by generalized Kripke models taking many-valued evaluation in each world $w \in W$many-valued accessibility relations $S: W \times W \to [0,1]$. The evaluation of modal operators are given (following Fitting \cite {Fi92a, Fi92b}) by \begin{itemize}\item $V ( \Box \varphi, w ) = {\displaystyle \bigwedge}\{ R(w,w') \to V(\varphi,w'): w' \in W \}$. \item $V ( \Diamond \varphi, w ) = {\displaystyle \bigvee}\{ R(w,w') & V(\varphi,w'): w' \in W \}$. \end{itemize}There are different attemptsapproaches to motivatestudy modal logic formalisms based on Kripke semantics to the many-valued setting. Roughly speaking we can classify the approaches in three groups depending how the corresponding Kripke frames look like, in the sense of how many-valuedness affects the worldsthe accesibility relations. Next we describe these three groupscomment about our work in each of them. A first group (see e.g. \cite{ChFr92, EsGaGoRo97,Su97}) is formed by those logical systems whose class of Kripke frames are such that their {\em worlds are classical}(i.e. they follow the rules of classical logic) but their {\em accessibility relations are many-valued; Modalities and many-valued: modeling uncertainty measures and similarity-based reasoning and application to Fuzzy description Logics .. 2010.  [PDF]  [BibTeX]
Francesc EstevaLluís GodoCarles Noguera; On expansions of WNM t-norm based logics with truth-constants. Fuzzy Sets and Systems; 2010.  [PDF]  [BibTeX]
Temur KutsiaJordi LevyMateu Villaret; On the Relation Between Context and Sequence Unification. Journal of Symbolic Computation; 2010.  [PDF]  [BibTeX]
L.P. BelluceAntonio Di NolaEnrico Marchioni; Rings and Godel Algebras. Algebra Universalis; 2010.  [BibTeX]
Yannis KalfoglouMarco Schorlemmer; The Information-Flow Approach to Ontology-Based Semantic Integration. 2010.  [BibTeX]
Fèlix BouF. PaoliA. LeddaM. SpinksR. Giuntini; The logic of quasi-MV algebras. Journal of Logic and Computation; 2010.  [BibTeX]
Petr CintulaCarles Noguera; An abstract approach to fuzzy logics: implicational semilinear logics. 2009.  [BibTeX]
978-989-95079-6-8; Characterizing Fuzzy Modal Semantics by fuzzy multimodal systems with crisp accessibility relations. IFSA - EUSFLAT 2009; 2009.  [PDF]  [BibTeX]
Roberto CignoliFrancesc Esteva; Commutative, integral bounded residuated lattices with an added involution. Annals of Pure and Applied Logic; 2009.  [PDF]  [BibTeX]
Petr CintulaFrancesc EstevaJoan GispertLluís GodoFranco MontagnaCarles Noguera; Distinguished algebraic semantics for t-norm based fuzzy logics: Methods and algebraic equivalences. Annals of Pure and Applied Logic; 2009.  [PDF]  [BibTeX]
Francesc EstevaLluís GodoCarles Noguera; First-order t-norm based fuzzy logics with truth-constants: distinguished semantics and completeness properties. Annals of Pure and Applied Logic; 2009.  [PDF]  [BibTeX]
Fèlix BouFrancesc EstevaJosep Maria FontAngel GilLluís GodoAntoni TorrensVentura Verdú; Logics preserving degrees of truth from varieties of residuated lattices. Journal of Logic and Computation (doi:10.1093/logcom/exp030); 2009.  [PDF]  [BibTeX]
Francesc EstevaLluís GodoCarles Noguera; On generalized continuous and left-continuous t-norms over chains: a survey. 30th Linz Seminar on Fuzzy Set Theory "The legacy of 30 seminars - where do we stand and where do we go?"; 2009.  [PDF]  [BibTeX]
Jordi LevyManfred Schmidt-SchaussMateu Villaret; On the Complexity of Bounded Second-order Unification and Stratified Context Unification. Journal of Algorithms in Cognition, Informatics, and Logic; 2009.  [BibTeX]
Carlos AnsóteguiMaría Luisa BonetJordi Levy; On the Structure of Industrial SAT Instances. 2009.  [PDF]  [BibTeX]
Enrico Marchioni; Ordered fields and LPi1/2 algebras. Soft Computing - A Fusion of Foundations, Methodologies and Applications; 2009.  [BibTeX]
Manuel Atencia ArcasMarco Schorlemmer; Reaching semantic agreements through interaction. 2009.  [PDF]  [BibTeX]
Carlos AnsóteguiMaría Luisa BonetJordi Levy; Solving (Weighted) Partial MaxSAT Through Satisfiability Testing. 2009.  [PDF]  [BibTeX]
Carlos AnsóteguiMaría Luisa BonetJordi Levy; Towards Industrial-Like Random SAT Instances. 2009.  [PDF]  [BibTeX]
Fèlix Bou; A first approach to the Deduction-Detachment Theorem in logics preserving degrees of truth. 2008.  [PDF]  [BibTeX]
Teresa AlsinetC. ChesñevarLluís Godo; Computation of Skeptical Outputs in P-DeLP Satisfying Indirect Consistency: a Level-based Approach. IPMU 2008; 2008.  [PDF]  [BibTeX]
Fèlix BouFrancesc EstevaLluís Godo; Exploring a Syntactic Notion of Modal Many-Valued Logics. Mathware & Soft Computing; 2008.  [PDF]  [BibTeX]
Lluís GodoRicardo Oscar Rodriguez; Logical approaches to fuzzy similarity-based reasoning: an overview. 2008.  [PDF]  [BibTeX]
Carlos AnsóteguiMaría Luisa BonetJordi LevyFelip Manyà; Measuring the Hardness of SAT Instances. 2008.  [PDF]  [BibTeX]
Jordi LevyMateu Villaret; Nominal Unification from a Higher-Order Perspective. 2008.  [PDF]  [BibTeX]
Enrico Marchioni; On computational complexity of semilinear varietes. Journal of Logic and Computation; 2008.  [BibTeX]
Enrico Marchioni; On computational complexity of semilinear varieties. Journal of Logic and Computation; 2008.  [BibTeX]
Angel García-CerdañaFrancesc Esteva; On Fuzzy Description Logics. 2008.  [BibTeX]
Francesc EstevaCarles NogueraJoan Gispert; On n-contractive Fuzzy Logics. First results. 2008.  [BibTeX]
Angel García-Cerdaña; On Some Implication-free Fragments of Substructural and Fuzzy Logics. 2008.  [PDF]  [BibTeX]
Fèlix BouFrancesco PaoliAntonio LeddaHector Freytes; On some properties of quasi-MV algebras and square root quasi-MV algebras. Part II. Soft Computing; 2008.  [PDF]  [BibTeX]
Enrico MarchioniFranco Montagna; On triangular norms and uninorms definable in LPi1/2. International Journal of Approximate Reasoning; 2008.  [BibTeX]
Carlos AnsóteguiMaría Luisa BonetJordi Levy; Random SAT Instances à la Carte. 2008.  [PDF]  [BibTeX]
Jordi LevyManfred Schmidt-SchaussMateu Villaret; The Complexity of Monadic Second-Order Unification. SIAM Journal on Computing; 2008.  [PDF]  [BibTeX]
Carles Noguera; Un apropament matemàtic al problema de vaguetat. Butlletí de la Societat Catalana de Matemàtiques; 2008.  [PDF]  [BibTeX]
Francesc EstevaLluís GodoCarles Noguera; On Completeness Results for Predicate Lukasiewicz, Product, Goedel and Nilpotent Minimum Logics Expanded with Truth-constantsc. Mathware and Soft Computing; 2007.  [PDF]  [BibTeX]