23 found
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  1.  27
    Distinguished Algebraic Semantics for T -Norm Based Fuzzy Logics: Methods and Algebraic Equivalencies.Petr Cintula, Francesc Esteva, Joan Gispert, Lluís Godo, Franco Montagna & Carles Noguera - 2009 - Annals of Pure and Applied Logic 160 (1):53-81.
    This paper is a contribution to Mathematical fuzzy logic, in particular to the algebraic study of t-norm based fuzzy logics. In the general framework of propositional core and Δ-core fuzzy logics we consider three properties of completeness with respect to any semantics of linearly ordered algebras. Useful algebraic characterizations of these completeness properties are obtained and their relations are studied. Moreover, we concentrate on five kinds of distinguished semantics for these logics–namely the class of algebras defined over the real unit (...)
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  2.  22
    Residuated Fuzzy Logics with an Involutive Negation.Francesc Esteva, Lluís Godo, Petr Hájek & Mirko Navara - 2000 - Archive for Mathematical Logic 39 (2):103-124.
    Residuated fuzzy logic calculi are related to continuous t-norms, which are used as truth functions for conjunction, and their residua as truth functions for implication. In these logics, a negation is also definable from the implication and the truth constant $\overline{0}$ , namely $\neg \varphi$ is $\varphi \to \overline{0}$. However, this negation behaves quite differently depending on the t-norm. For a nilpotent t-norm (a t-norm which is isomorphic to Łukasiewicz t-norm), it turns out that $\neg$ is an involutive negation. However, (...)
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  3.  19
    A Complete Many-Valued Logic with Product-Conjunction.Petr Hájek, Lluis Godo & Francesc Esteva - 1996 - Archive for Mathematical Logic 35 (3):191-208.
    A simple complete axiomatic system is presented for the many-valued propositional logic based on the conjunction interpreted as product, the coresponding implication (Goguen's implication) and the corresponding negation (Gödel's negation). Algebraic proof methods are used. The meaning for fuzzy logic (in the narrow sense) is shortly discussed.
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  4.  79
    Maximality in Finite-Valued Lukasiewicz Logics Defined by Order Filters.Marcelo E. Coniglio, Francesc Esteva, Joan Gispert & Lluis Godo - forthcoming - Journal of Logic and Computation.
  5.  34
    On the Standard and Rational Completeness of Some Axiomatic Extensions of the Monoidal T-Norm Logic.Francesc Esteva, Joan Gispert, Lluís Godo & Franco Montagna - 2002 - Studia Logica 71 (2):199 - 226.
    The monoidal t-norm based logic MTL is obtained from Hájek''s Basic Fuzzy logic BL by dropping the divisibility condition for the strong (or monoidal) conjunction. Recently, Jenei and Montgana have shown MTL to be standard complete, i.e. complete with respect to the class of residuated lattices in the real unit interval [0,1] defined by left-continuous t-norms and their residua. Its corresponding algebraic semantics is given by pre-linear residuated lattices. In this paper we address the issue of standard and rational completeness (...)
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  6.  16
    The $L\Pi$ and $L\Pi\Frac{1}{2}$ Logics: Two Complete Fuzzy Systems Joining Łukasiewicz and Product Logics. [REVIEW]Francesc Esteva, Lluís Godo & Franco Montagna - 2001 - Archive for Mathematical Logic 40 (1):39-67.
    In this paper we provide a finite axiomatization (using two finitary rules only) for the propositional logic (called $L\Pi$ ) resulting from the combination of Lukasiewicz and Product Logics, together with the logic obtained by from $L \Pi$ by the adding of a constant symbol and of a defining axiom for $\frac{1}{2}$ , called $L \Pi\frac{1}{2}$ . We show that $L \Pi \frac{1}{2}$ contains all the most important propositional fuzzy logics: Lukasiewicz Logic, Product Logic, Gödel's Fuzzy Logic, Takeuti and Titani's (...)
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  7.  10
    On the Standard and Rational Completeness of Some Axiomatic Extensions of the Monoidal T-Norm Logic.Francesc Esteva, Joan Gispert, Lluís Godo & Franco Montagna - 2002 - Studia Logica 71 (2):199-226.
    The monoidal t-norm based logic MTL is obtained from Hájek's Basic Fuzzy logic BL by dropping the divisibility condition for the strong conjunction. Recently, Jenei and Montgana have shown MTL to be standard complete, i.e. complete with respect to the class of residuated lattices in the real unit interval [0, 1] defined by left-continuous t-norms and their residua. Its corresponding algebraic semantics is given by pre-linear residuated lattices. In this paper we address the issue of standard and rational completeness of (...)
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  8.  81
    On the Logical Structure of de Finetti's Notion of Event.Tommaso Flaminio, Lluis Godo & Hykel Hosni - 2014 - Journal of Applied Logic 12 (3):279-301.
    This paper sheds new light on the subtle relation between probability and logic by (i) providing a logical development of Bruno de Finetti's conception of events and (ii) suggesting that the subjective nature of de Finetti's interpretation of probability emerges in a clearer form against such a logical background. By making explicit the epistemic structure which underlies what we call Choice-based probability we show that whilst all rational degrees of belief must be probabilities, the converse doesn't hold: some probability values (...)
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  9.  22
    Logics of Formal Inconsistency Arising From Systems of Fuzzy Logic.Marcelo E. Coniglio, Francesc Esteva & Lluís Godo - 2014 - Logic Journal of the IGPL 22 (6):880-904.
    This article proposes the meeting of fuzzy logic with paraconsistency in a very precise and foundational way. Specifically, in this article we introduce expansions of the fuzzy logic MTL by means of primitive operators for consistency and inconsistency in the style of the so-called Logics of Formal Inconsistency (LFIs). The main novelty of the present approach is the definition of postulates for this type of operators over MTL-algebras, leading to the definition and axiomatization of a family of logics, expansions of (...)
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  10. Coherence in the Aggregate: A Betting Method for Belief Functions on Many-Valued Events.Tommaso Flaminio, Lluis Godo & Hykel Hosni - unknown
    Betting methods, of which de Finetti's Dutch Book is by far the most well-known, are uncertainty modelling devices which accomplish a twofold aim. Whilst providing an interpretation of the relevant measure of uncertainty, they also provide a formal definition of coherence. The main purpose of this paper is to put forward a betting method for belief functions on MV-algebras of many-valued events which allows us to isolate the corresponding coherence criterion, which we term coherence in the aggregate. Our framework generalises (...)
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  11.  21
    Equational Characterization of the Subvarieties of BL Generated by T-Norm Algebras.Fransesc Esteva, Lluís Godo & Franco Montagna - 2004 - Studia Logica 76 (2):161 - 200.
    In this paper we show that the subvarieties of BL, the variety of BL-algebras, generated by single BL-chains on [0, 1], determined by continous t-norms, are finitely axiomatizable. An algorithm to check the subsethood relation between these subvarieties is provided, as well as another procedure to effectively find the equations of each subvariety. From a logical point of view, the latter corresponds to find the axiomatization of every residuated many-valued calculus defined by a continuous t-norm and its residuum. Actually, the (...)
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  12.  7
    On the Set of Intermediate Logics Between the Truth- and Degree-Preserving Łukasiewicz Logics.Marcelo E. Coniglio, Francesc Esteva & Lluís Godo - 2016 - Logic Journal of the IGPL 24 (3):288-320.
  13.  40
    On the Relation Between Possibilistic Logic and Modal Logics of Belief and Knowledge.Mohua Banerjee, Didier Dubois, Lluis Godo & Henri Prade - 2017 - Journal of Applied Non-Classical Logics 27 (3-4):206-224.
    Possibilistic logic and modal logic are knowledge representation frameworks sharing some common features, such as the duality between possibility and necessity, and the decomposability of necessity for conjunctions, as well as some obvious differences since possibility theory is graded. At the semantic level, possibilistic logic relies on possibility distributions and modal logic on accessibility relations. In the last 30 years, there have been a series of attempts for bridging the two frameworks in one way or another. In this paper, we (...)
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  14.  7
    First-Order T-Norm Based Fuzzy Logics with Truth-Constants: Distinguished Semantics and Completeness Properties.Francesc Esteva, Lluís Godo & Carles Noguera - 2009 - Annals of Pure and Applied Logic 161 (2):185-202.
    This paper aims at being a systematic investigation of different completeness properties of first-order predicate logics with truth-constants based on a large class of left-continuous t-norms . We consider standard semantics over the real unit interval but also we explore alternative semantics based on the rational unit interval and on finite chains. We prove that expansions with truth-constants are conservative and we study their real, rational and finite chain completeness properties. Particularly interesting is the case of considering canonical real and (...)
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  15.  19
    Subvarieties of BL-Algebras Generated by Single-Component Chains.Antonio Di Nola, Francesc Esteva, Pere Garcia, Lluís Godo & Salvatore Sessa - 2002 - Archive for Mathematical Logic 41 (7):673-685.
    In this paper we study and equationally characterize the subvarieties of BL, the variety of BL-algebras, which are generated by families of single-component BL-chains, i.e. MV-chains, Product-chain or Gödel-chains. Moreover, it is proved that they form a segment of the lattice of subvarieties of BL which is bounded by the Boolean variety and the variety generated by all single-component chains, called ŁΠG.
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  16.  39
    On the Algebraic Structure of Conditional Events: 13th European Conference, ECSQARU 2015, Compiègne, France, July 15-17, 2015. [REVIEW]Tommaso Flaminio, Lluis Godo & Hykel Hosni - unknown
    This paper initiates an investigation of conditional measures as simple measures on conditional events. As a first step towards this end we investigate the construction of conditional algebras which allow us to distinguish between the logical properties of conditional events and those of the conditional measures which we can be attached to them. This distinction, we argue, helps us clarifying both concepts.
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  17.  22
    Extending a Temporal Defeasible Argumentation Framework with Possibilistic Weights.Lluís Godo, Enrico Marchioni & Pere Pardo - 2012 - In Luis Farinas del Cerro, Andreas Herzig & Jerome Mengin (eds.), Logics in Artificial Intelligence. Springer. pp. 242--254.
  18.  26
    Logical Approaches to Fuzzy Similarity-Based Reasoning: An Overview.Lluís Godo & Ricardo O. Rodríguez - 2008 - In Giacomo Della Riccia, Didier Dubois & Hans-Joachim Lenz (eds.), Preferences and Similarities. Springer. pp. 75--128.
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  19.  7
    Weighted Logics for Artificial Intelligence – 2.Lluis Godo, Henri Prade & Guilin Qi - 2015 - Journal of Applied Logic 13 (4):395-396.
  20.  6
    Fuzzy Inference as Deduction.Lluís Godo & Petr Hájek - 1999 - Journal of Applied Non-Classical Logics 9 (1):37-60.
    ABSTRACT The term fuzzy logic has two different meanings -broad and narrow. In Zadeh's opinion, fuzzy logic is an extension of many- valued logic but having a different agenda—as generalized modus ponens, max-min inference, linguistic quantifiers etc. The question we address in this paper is whether there is something in Zadeh's specific agenda which cannot be grasped by “classiceli”, “traditional” mathematical logic. We show that much of fuzzy logic can be understood as classical deduction in a many-sorted many-valued Pavelka- Lukasiewicz (...)
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  21. Logical Models of Reasoning with Vague Information.Petr Cintula, Chris Fermüller, Lluis Godo & Petr Hájek (eds.) - forthcoming
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  22. Reasoning Under Vagueness.Petr Cintula, Christian Fermuller, Lluis Godo & Petr Hajek (eds.) - forthcoming - College Publications.
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  23. Understanding Vagueness: Logical, Philosophical and Linguistic Perspectives.Petr Cintula, Christian G. Fermüller, Lluis Godo & Petr Hájek (eds.) - 2011 - College Publications.
     
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