DIGITAL.CSIChttps://digital.csic.esThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Thu, 09 Apr 2020 14:32:47 GMT2020-04-09T14:32:47Z50831- First order SMTL logic and quasi-witnessed modelshttp://hdl.handle.net/10261/39469Title: First order SMTL logic and quasi-witnessed models
Authors: Cerami, Marco; Esteva, Francesc
Abstract: In this paper we prove strong completeness
of axiomatic extensions of First Order SMTL
logic adding the so-called quasi-witnessed axioms
with respect to quasi-witnessed Models.
In order to achieve this result, we make use of
methods that are typical of Classical Predicate
Logic, and have been later generalized
by P. H ajek to cope with Predicate Fuzzy
Logic. At the end of the paper, we obtain,
as a particular case, the result of strong completeness,
already proven by M.C. Laskowski
and S. Malekpour, for Product Predicate
Logic with respect to quasi-witnessed Models.
Description: 6 páginas.-- Trabajo presentado al XV Congreso Español sobre Tecnologías y Lógica Fuzzy.
Tue, 13 Sep 2011 09:47:19 GMThttp://hdl.handle.net/10261/394692011-09-13T09:47:19Z
- On elementary extensions in Fuzzy Predicate Logicshttp://hdl.handle.net/10261/42507Title: On elementary extensions in Fuzzy Predicate Logics
Authors: Dellunde, Pilar; Esteva, Francesc
Abstract: Our work is a contribution to the model-theoretic study of
equality-free fuzzy predicate logics. We give a characterization of ele-
mentary equivalence in fuzzy predicate logics using elementary exten-
sions and introduce an strengthening of this notion, the so-called strong
elementary equivalence. Using the method of diagrams developed in [5]
and elementary extensions we present a counterexample to Conjectures
1 and 2 of [8].
Description: 10 páginas.-- Comunicación presentada a la International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU) celebrada en Dortmund (Alemania) del 28 de Junio al 2 de Julio de 2010.
Wed, 16 Nov 2011 13:25:17 GMThttp://hdl.handle.net/10261/425072011-11-16T13:25:17Z
- Putting together Lukasiewicz and product logicshttp://hdl.handle.net/10261/2247Title: Putting together Lukasiewicz and product logics
Authors: Esteva, Francesc; Godo, Lluis
Abstract: In this paper we investigate a propositional fuzzy logical system LΠ which contains the well-known Lukasiewicz, Product and Gödel fuzzy logics as sublogics. We define the corresponding algebraic structures, called LΠ-algebras and prove the following completeness result: a formula φ is provable in the LΠ logic iff it is a tautology for all linear LΠ-algebras. Moreover, linear LΠ-algebras are shown to be embeddable in linearly ordered abelian rings with a strong unit and cancellation law.
Description: This is a revised version of the paper with the same title appeared in the Proc. of the Estylf'98 Conference, September 8-10, 1998, Pamplona (Spain).
Tue, 20 Nov 2007 13:24:50 GMThttp://hdl.handle.net/10261/22472007-11-20T13:24:50Z
- On defining multiple-valued logics for knowledge-based systems communicationhttp://hdl.handle.net/10261/2236Title: On defining multiple-valued logics for knowledge-based systems communication
Authors: Reyes, José Antonio; Puyol-Gruart, Josep; Esteva, Francesc
Abstract: Multiple-valued logics are useful for dealing with uncertainty and imprecision in Knowledge-Based Systems. Different problems can require different logics. Then we need mechanisms to translate the information exchanged between two problems with different logics. In this paper, we introduce the logical foundations of such logics and the communication mechanisms that preserve some deductive properties. We also describe a tool to assist users in the declaration of logics and their communication mechanisms.
Tue, 20 Nov 2007 11:29:57 GMThttp://hdl.handle.net/10261/22362007-11-20T11:29:57Z
- On the structure of intuitionistic algebras with relational probabiliteshttp://hdl.handle.net/10261/2253Title: On the structure of intuitionistic algebras with relational probabilites
Authors: Esteva, Francesc
Abstract: Trillas has defined a relational probability on an intuitionistic algebra and has given its basic properties. The main results of this paper are two. The first one says that a relational probability on a intuitionistic algebra defines a congruence such that the quotient is a Boolean algebra. The second one shows that relational probabilities are, in most cases, extensions of conditional probabilities on Boolean algebras.
Tue, 20 Nov 2007 15:31:40 GMThttp://hdl.handle.net/10261/22532007-11-20T15:31:40Z
- Map Generation by Cooperative Low-Cost Robots in Structured Unknown Environmentshttp://hdl.handle.net/10261/60910Title: Map Generation by Cooperative Low-Cost Robots in Structured Unknown Environments
Authors: López-Sánchez, Maite; Esteva, Francesc; López de Mántaras, Ramón; Sierra, Carles; Amat, Josep
Abstract: In this paper we present some results obtained with a troupe of low-cost robots designed to cooperatively explore unknown structured orthogonal environments. In order to improve the covering of the explored zone the robots show different behaviours (routine, normal and anxious) and cooperate by transferring each other the perceived environment when they meet; therefore, not all the information of the non-returning robots is lost provided that they had encountered robots that safely returned. The returning robots deliver to a host their perceived and communicated (by other robots) partial maps and the host incrementally generates the most plausible map of the environment. To perform the map generation, a fusion, completion and alignment process of the partial maps, based on fuzzy techniques, has been developed.
Thu, 22 Nov 2012 15:17:32 GMThttp://hdl.handle.net/10261/609102012-11-22T15:17:32Z
- A logical approach to case-based reasoning using fuzzy similarity relationshttp://hdl.handle.net/10261/60486Title: A logical approach to case-based reasoning using fuzzy similarity relations
Authors: Plaza, Enric; Esteva, Francesc; García-Calvés, Pere; Godo, Lluis; López de Mántaras, Ramón
Abstract: This article approaches the formalization of inference in Case-based Reasoning (CBR) systems. CBR systems infer solutions of new problems on the basis of a precedent case that is, to some extent, similar to the current problem. Using the logics developed for similarity-based inference we characterize CBR systems defining what we call the Precedent-based Plausible Reasoning (PPR) model. This model is based on the graded consequence relations named approximation entailment and proximity entailment. A modal interpretation is provided for the precedent-based inference where the plausibility is given by the graded possibility operator ◇α-The PPR model shows that both knowledge-intensive CBR systems and the nearest neighbor algorithms share a common core formalism and that their difference is on whether or not (respectively) they use a general theory in addition to the precedent cases. © 1998 Elsevier Science Inc. All rights reserved.
Fri, 16 Nov 2012 12:39:08 GMThttp://hdl.handle.net/10261/604862012-11-16T12:39:08Z
- Strict core fuzzy logics and quasi-witnessed modelshttp://hdl.handle.net/10261/139264Title: Strict core fuzzy logics and quasi-witnessed models
Authors: Cerami, Marco; Esteva, Francesc
Abstract: In this paper we prove strong completeness of axiomatic extensions of first-order strict core fuzzy logics with the so-called quasi-witnessed axioms with respect to quasi-witnessed models. As a consequence we obtain strong completeness of Product Predicate Logic with respect to quasi-witnessed models, already proven by M. C. Laskowski and S. Malekpour in [19]. Finally we study similar problems for expansions with Δ, define Δ-quasi-witnessed axioms and prove that any axiomatic extension of a first-order strict core fuzzy logic, expanded with Δ, and Δ-quasi-witnessed axioms are complete with respect to Δ-quasi-witnessed models. © 2011 Springer-Verlag.
Mon, 24 Oct 2016 14:03:35 GMThttp://hdl.handle.net/10261/1392642016-10-24T14:03:35Z
- On the Minimum Many-Valued Modal Logic over a Finite Residuated Latticehttp://hdl.handle.net/10261/138239Title: On the Minimum Many-Valued Modal Logic over a Finite Residuated Lattice
Authors: Bou, Felix; Esteva, Francesc; Godo, Lluis; Rodriguez, Ricardo O.
Abstract: This article deals with many-valued modal logics, based only on the necessity operator, over a residuated lattice. We focus on three basic classes, according to the accessibility relation, of Kripke frames: the full class of frames evaluated in the residuated lattice (and so defining the minimum modal logic), the ones evaluated in the idempotent elements and the ones only evaluated in 0 and 1. We show how to expand an axiomatization, with canonical truth-constants in the language, of a finite residuated lattice into one of the modal logic, for each one of the three basic classes of Kripke frames. We also provide axiomatizations for the case of a finite MV chain but this time without canonical truth-constants in the language. © 2009 The Author.
Wed, 19 Oct 2016 16:27:32 GMThttp://hdl.handle.net/10261/1382392016-10-19T16:27:32Z
- A probabilistic author-centered model for Twitter discussionshttp://hdl.handle.net/10261/163022Title: A probabilistic author-centered model for Twitter discussions
Authors: Alsinet, Teresa; Argelich, Josep; Bejar, Ramon; Esteva, Francesc; Godo, Lluis
Abstract: In a recent work some of the authors have developed an argumentative approach for discovering relevant opinions in Twitter discussions with probabilistic valued relationships. Given a Twitter discussion, the system builds an argument graph where each node denotes a tweet and each edge denotes a criticism relationship between a pair of tweets of the discussion. Relationships between tweets are associated with a probability value, indicating the uncertainty that the relationships hold. In this work we introduce and investigate a natural extension of the representation model, referred as probabilistic author-centered model, in which tweets within a discussion are grouped by authors, in such a way that tweets of a same author describe his/her opinion in the discussion and are rep- resented with a single node in the graph, and criticism relationships denote controversies between opinions of Twitter users in the discussion. In this new model, the interactions between authors can give rise to circular criticism relationships, and the probability of one opinion criticizing another has to be evaluated from the probabilities of criticism among the tweets that compose both opinions.
Wed, 28 Mar 2018 12:03:07 GMThttp://hdl.handle.net/10261/1630222018-03-28T12:03:07Z
- A product modal logichttp://hdl.handle.net/10261/131208Title: A product modal logic
Authors: Esteva, Francesc; Godo, Lluis; Vidal, Amanda
Abstract: Fuzzy modal logics are a family of logics that are still under research for their under- standing. Several papers have been published on this issue, treating different problems about the fuzzy modal logics (see for instance [CR10], [CR11], [BEGR11], [HT06], [HT13], or [CMRR13]). However, the study of the product moda l logics, which we understand as logics that arise from Kripke structures whos e relation and universes are evaluated over the product standard algebra, has remained undone. We present here some results to partially fill that gap for Kripke semantics with crisp accessibility relations, together with a characterization of a strongly complete infinitary product logic with truth-constants. We consider that the characterization and understanding of the product modal logics could open the possibility of studying the more general case of BL modal logics
Mon, 18 Apr 2016 17:52:44 GMThttp://hdl.handle.net/10261/1312082016-04-18T17:52:44Z
- Logics of formal inconsistency arising from systems of fuzzy logichttp://hdl.handle.net/10261/131548Title: Logics of formal inconsistency arising from systems of fuzzy logic
Authors: Coniglio, Marcelo E.; Esteva, Francesc; Godo, Lluis
Abstract: 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 MTL, whose degree-preserving counterpart are paraconsistent and moreover LFIs.
Thu, 28 Apr 2016 17:34:01 GMThttp://hdl.handle.net/10261/1315482016-04-28T17:34:01Z
- On strong standard completeness in some MTL Δ expansionshttp://hdl.handle.net/10261/155338Title: On strong standard completeness in some MTL Δ expansions
Authors: Vidal, Amanda; Bou, Felix; Esteva, Francesc; Godo, Lluis
Abstract: In this paper, inspired by the previous work of Franco Montagna on infinitary axiomatizations for standard BL-algebras, we focus on a uniform approach to the following problem: given a left-continuous t-norm ∗ , find an axiomatic system (possibly with infinitary rules) which is strongly complete with respect to the standard algebra [InlineEquation not available: see fulltext.] This system will be an expansion of Monoidal t-norm-based logic. First, we introduce an infinitary axiomatic system L∗∞, expanding the language with Δ and countably many truth constants, and with only one infinitary inference rule, that is inspired in Takeuti–Titani density rule. Then we show that L∗∞ is indeed strongly complete with respect to the standard algebra [InlineEquation not available: see fulltext.]. Moreover, the approach is generalized to axiomatize expansions of these logics with additional operators whose intended semantics over [0, 1] satisfy some regularity conditions. © 2016, Springer-Verlag Berlin Heidelberg.
Wed, 20 Sep 2017 09:40:52 GMThttp://hdl.handle.net/10261/1553382017-09-20T09:40:52Z
- On Conjectures in t-Norm Based Fuzzy Logicshttp://hdl.handle.net/10261/130758Title: On Conjectures in t-Norm Based Fuzzy Logics
Authors: Esteva, Francesc; García-Honrado, Itziar; Godo, Lluis
Abstract: This paper is a humble homage to EnricTrillas. Following his foundational contributions on models of ordinary reasoning in an algebraic setting, we study here elements of thesemodels, like conjectures and hypothesis, in the logical framework of continuous t-norm based fuzzy logics.We consider notions of consistency, conjecture and hypothesis arising from two natural families of consequence operators definable in these logics, namely the ones corresponding to the so-called truth-preserving and degree-preserving consequence relations. We pay special attention to the particular cases of three prominent fuzzy logics: Gödel, Product and Łukasiewicz logics © 2015 Springer International Publishing Switzerland.
Fri, 01 Apr 2016 15:39:44 GMThttp://hdl.handle.net/10261/1307582016-04-01T15:39:44Z
- Enric Trillas: A Passion for Fuzzy Setshttp://hdl.handle.net/10261/159306Title: Enric Trillas: A Passion for Fuzzy Sets
Authors: Magdalena, Luis; Verdegay, Jose Luis; Esteva, Francesc
Abstract: The book is a comprehensive collection of the most recent and significant research and applications in the field of fuzzy logic. It covers fuzzy structures, systems, rules, operations as well as important applications, e.g in decision making, environmental prediction and prevention, and communication. It is dedicated to Enric Trillas as an acknowledgement for his pioneering research in the field. The book include a foreword by Lotfi A. Zadeh.
Fri, 19 Jan 2018 10:39:43 GMThttp://hdl.handle.net/10261/1593062018-01-19T10:39:43Z
- Distinguished algebraic semantics for t-norm based fuzzy logics: Methods and algebraic equivalencieshttp://hdl.handle.net/10261/160341Title: Distinguished algebraic semantics for t-norm based fuzzy logics: Methods and algebraic equivalencies
Authors: Cintula, Petr; Esteva, Francesc; Gispert, Joan; Godo, Lluis; Montagna, Franco; Noguera, Carles
Abstract: 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 interval, the rational unit interval, the hyperreals (all ultrapowers of the real unit interval), the strict hyperreals (only ultrapowers giving a proper extension of the real unit interval) and finite chains, respectively-and we survey the known completeness methods and results for prominent logics. We also obtain new interesting relations between the real, rational and (strict) hyperreal semantics, and good characterizations for the completeness with respect to the semantics of finite chains. Finally, all completeness properties and distinguished semantics are also considered for the first-order versions of the logics where a number of new results are proved. © 2009 Elsevier B.V. All rights reserved.
Thu, 08 Feb 2018 13:09:32 GMThttp://hdl.handle.net/10261/1603412018-02-08T13:09:32Z
- Commutative integral bounded residuated lattices with an added involutionhttp://hdl.handle.net/10261/160167Title: Commutative integral bounded residuated lattices with an added involution
Authors: Cignoli, Roberto; Esteva, Francesc
Abstract: A symmetric residuated lattice is an algebra A = (A, ∨, ∧, *, →, ∼, 1, 0) such that (A, ∨, ∧, *, →, 1, 0) is a commutative integral bounded residuated lattice and the equations ∼ ∼ x = x and ∼ (x ∨ y) = ∼ x ∧ ∼ y are satisfied. The aim of the paper is to investigate the properties of the unary operation ε defined by the prescription ε x = ∼ x → 0. We give necessary and sufficient conditions for ε being an interior operator. Since these conditions are rather restrictive (for instance, on a symmetric Heyting algebra ε is an interior operator if and only the equation (x → 0) ∨ ((x → 0) → 0) = 1 is satisfied) we consider when an iteration of ε is an interior operator. In particular we consider the chain of varieties of symmetric residuated lattices such that the n iteration of ε is a boolean interior operator. For instance, we show that these varieties are semisimple. When n = 1, we obtain the variety of symmetric stonean residuated lattices. We also characterize the subvarieties admitting representations as subdirect products of chains. These results generalize and in many cases also simplify, results existing in the literature. © 2009 Elsevier B.V. All rights reserved.
Mon, 05 Feb 2018 15:33:52 GMThttp://hdl.handle.net/10261/1601672018-02-05T15:33:52Z
- Fuzzy Description Logics and t-norm based Fuzzy Logicshttp://hdl.handle.net/10261/160549Title: Fuzzy Description Logics and t-norm based Fuzzy Logics
Authors: García-Cerdaña, Àngel; Armengol, Eva; Esteva, Francesc
Abstract: Description Logics (DLs) are knowledge representation languages built on the basis of classical logic. DLs allow the creation of knowledge bases and provide ways to reason on the contents of these bases. Fuzzy Description Logics (FDLs) are natural extensions of DLs for dealing with vague concepts, commonly present in real applications. Hájek proposed to deal with FDLs taking as basis t-norm based fuzzy logics with the aim of enriching the expressive possibilities in FDLs and to capitalize on recent developments in the field of Mathematical Fuzzy Logic. From this perspective we define a family of description languages, denoted by ALC*(S), which includes truth constants for representing truth degrees. Having truth constants in the language allows us to define the axioms of the knowledge bases as sentences of a predicate language in much the same way as in classical DLs. On the other hand, taking advantage of the expressive power provided by these truth constants, we define a graded notion of satisfiability, validity and subsumption of DL concepts as the satisfiability, validity and subsumption of evaluated formulas. In the last section we summarize some results concerning fuzzy logics associated with these new description languages, we analyze aspects relative to general and canonical semantics, and we prove some results relative to canonical standard completeness for some FDLs considered in the paper. © 2010 Elsevier Inc. All rights reserved.
Tue, 13 Feb 2018 11:27:34 GMThttp://hdl.handle.net/10261/1605492018-02-13T11:27:34Z
- Forewordhttp://hdl.handle.net/10261/160429Title: Foreword
Authors: Esteva, Francesc; Godo, Lluis
Fri, 09 Feb 2018 15:40:56 GMThttp://hdl.handle.net/10261/1604292018-02-09T15:40:56Z
- On product logic with truth-constantshttp://hdl.handle.net/10261/160967Title: On product logic with truth-constants
Authors: Savicky, Petr; Cignoli, Roberto; Esteva, Francesc; Godo, Lluis; Noguera, Carles
Abstract: Product Logic Π is an axiomatic extension of Hájek's Basic Fuzzy Logic BL coping with the 1-tautologies when the strong conjunction & and implication → are interpreted by the product of reals in [0, 1] and its residuum respectively. In this paper we investigate expansions of Product Logic by adding into the language a countable set of truth-constants (one truth-constant <rmacr> for each r in a countable Π-subalgebra <Cscr> of [0, 1]) and by adding the corresponding book-keeping axioms for the truthconstants. We first show that the corresponding logics Π(<Cscr>) are algebraizable, and hence complete with respect to the variety of Π(<Cscr>)-algebras. The main result of the paper is the canonical standard completeness of these logics, that is, theorems of Π(<Cscr>) are exactly the 1-tautologies of the algebra defined over the real unit interval where the truth-constants are interpreted as their own values. It is also shown that they do not enjoy the canonical strong standard completeness, but they enjoy it for finite theories when restricted to evaluated Π-formulas of the kind <rmacr> → φ, where <rmacr> is a truth-constant and φ a formula not containing truth-constants. Finally we consider the logics Π(Δ)(<Cscr>), the expansion of Π(<Cscr>) with the well-known Baaz's projection connective Δ, and we show canonical finite strong standard completeness for them.
Mon, 19 Feb 2018 18:10:25 GMThttp://hdl.handle.net/10261/1609672018-02-19T18:10:25Z
- On expansions of WNM t-norm based logics with truth-constantshttp://hdl.handle.net/10261/160963Title: On expansions of WNM t-norm based logics with truth-constants
Authors: Esteva, Francesc; Godo, Lluis; Noguera, Carles
Abstract: This paper focuses on completeness results about generic expansions of propositional weak nilpotent minimum (WNM) logics with truth-constants. Indeed, we consider algebraic semantics for expansions of these logics with a set of truth-constants { over(r, -) | r ∈ C }, for a suitable countable C ⊆ [0, 1], and provide a full description of completeness results when: (i) the t-norm is a weak nilpotent minimum satisfying the finite partition property and (ii) the set of truth-constants covers all the unit interval in the sense that each interval of the partition contains values of C in its interior. © 2009 Elsevier B.V. All rights reserved.
Mon, 19 Feb 2018 16:50:52 GMThttp://hdl.handle.net/10261/1609632018-02-19T16:50:52Z
- On implicative closure operators in approximate reasoninghttp://hdl.handle.net/10261/160965Title: On implicative closure operators in approximate reasoning
Authors: Rodriguez, Ricardo O.; Esteva, Francesc; García-Calvés, Pere; Godo, Lluis
Abstract: This paper introduces a new class of fuzzy closure operators called implicative closure operators, which generalize some notions of fuzzy closure operators already introduced by different authors. We show that implicative closure operators capture some usual consequence relations used in Approximate Reasoning, like Chakraborty's graded consequence relation, Castro et al.'s fuzzy consequence relation, similarity-based consequence operators introduced by Dubois et al. and Gerla's canonical extension of classical closure operators. We also study the relation of the implicative closure operators to other existing fuzzy inference operators as the Natural Inference Operators defined by Boixader and Jacas and the fuzzy operators defined by Biacino, Gerla and Ying. © 2003 Elsevier Science Inc. All rights reserved.
Mon, 19 Feb 2018 17:08:44 GMThttp://hdl.handle.net/10261/1609652018-02-19T17:08:44Z
- Local multi-valued logics in modular expert systemshttp://hdl.handle.net/10261/160864Title: Local multi-valued logics in modular expert systems
Authors: Agusti, Jaume; Esteva, Francesc; García-Calvés, Pere; Godo, Lluis; López de Mántaras, Ramón; Sierra, Carles
Abstract: In this paper we describe an approach to the problem of dealing with uncertainty by means of finite multi-valued logics in modular expert systems, and the results obtained. The modularity of the systems allows us to address two main characteristics of human problem-solving: the adaptation of general knowledge to particular problems and the dependency of the management of uncertainty on the different subtasks being implemented in the modules of the system, i.e. different modules can have different local multiple-valued logics as part of their local deductive mechanisms. Although the results obtained are general, we use, throughout the paper, examples of a medical expert system that has been designed using a modular language called MILORD-II, that implements them showing the practical interest of the theoretical concepts involved. © 1994 Taylor & Francis.
Fri, 16 Feb 2018 13:00:15 GMThttp://hdl.handle.net/10261/1608642018-02-16T13:00:15Z
- On triangular norm based axiomatic extensions of the weak nilpotent minimum logichttp://hdl.handle.net/10261/161161Title: On triangular norm based axiomatic extensions of the weak nilpotent minimum logic
Authors: Noguera, Carles; Esteva, Francesc; Gispert, Joan
Abstract: In this paper we carry out an algebraic investigation of the weak nilpotent minimum logic (WNM) and its t-norm based axiomatic extensions. We consider the algebraic counterpart of WNM, the variety of WNM-algebras (double-struck Wdouble-struck Ndouble-struck M) and prove that it is locally finite, so all its subvarieties are generated by finite chains. We give criteria to compare varieties generated by finite families of WNM-chains, in particular varieties generated by standard WNM-chains, or equivalently t-norm based axiomatic extensions of WNM, and we study their standard completeness properties. We also characterize the generic WNM-chains, i. e. those that generate the variety double-struck Wdouble-struck Ndouble-struck M, and we give finite axiomatizations for some t-norm based extensions of WNM. © 2008 Wiley-VCH Verlag GmbH & Co. KGaA.
Wed, 21 Feb 2018 18:40:43 GMThttp://hdl.handle.net/10261/1611612018-02-21T18:40:43Z
- On the scope of some formulas defining additive connectives in fuzzy logicshttp://hdl.handle.net/10261/161157Title: On the scope of some formulas defining additive connectives in fuzzy logics
Authors: García-Cerdaña, Àngel; Noguera, Carles; Esteva, Francesc
Abstract: In (Fuzzy Sets and Systems 149 (2005) 297) Wang et al. defined a new fuzzy logic called NMG. They also introduced new formulas to define the additive connectives from multiplicative conjunction, residuated implication and bottom in NMG. However, they did not study the scope of these formulas in the general framework of fuzzy logics. This is the aim of this paper. Therefore, we add the definability formulas to known fuzzy logics as new axioms, following the method used in (Beyond Two: Theory and Applications of Multiple-Valued Logic, 2003, 251.), and we obtain some families of logics presented in a simpler language. Finally, we discuss the standard completeness of these new logics. © 2005 Elsevier B.V. All rights reserved.
Wed, 21 Feb 2018 17:38:15 GMThttp://hdl.handle.net/10261/1611572018-02-21T17:38:15Z
- On the Equational Characterization of Continuous t-Normshttp://hdl.handle.net/10261/157266Title: On the Equational Characterization of Continuous t-Norms
Authors: Esteva, Francesc; Godo, Lluis
Abstract: A (continuous) t-norm is called equationally definable when the corresponding standard BL-algebra [0,1]∗ defined by ∗ and its residuum is the only (up to isomorphism) standard BL-algebra that generates the same variety Var([0,1]∗). In this chapter we check that a continuous t-norm ∗ is equationally definable if and only if the t-norm is a finite ordinal sum of copies of the three basic continuous t-norms, i.e. Łukasiewicz, Gödel and Product t-norms.
Mon, 13 Nov 2017 14:30:35 GMThttp://hdl.handle.net/10261/1572662017-11-13T14:30:35Z
- Smooth Finite T-norms and Their Equational Axiomatizationhttp://hdl.handle.net/10261/157268Title: Smooth Finite T-norms and Their Equational Axiomatization
Authors: Esteva, Francesc; García-Cerdaña, Àngel; Godo, Lluis
Abstract: In this paper, as homage to Professor Gaspar Mayor in his 70 anniversary, we present a summary of results on BL-algebras and related structures that, using the one-to-one correspondence between divisible finite t-norms and finite BL-chains, allows us to provide an equational characterization of any divisible finite t-norm.
Mon, 13 Nov 2017 15:26:46 GMThttp://hdl.handle.net/10261/1572682017-11-13T15:26:46Z
- Generalized continuous and left-continuous t-norms arising from algebraic semantics for fuzzy logicshttp://hdl.handle.net/10261/160556Title: Generalized continuous and left-continuous t-norms arising from algebraic semantics for fuzzy logics
Authors: Noguera, Carles; Esteva, Francesc; Godo, Lluis
Abstract: This paper focuses on the issue of how generalizations of continuous and left-continuous t-norms over linearly ordered sets should be from a logical point of view. Taking into account recent results in the scope of algebraic semantics for fuzzy logics over chains with a monoidal residuated operation, we advocate linearly ordered BL-algebras and MTL-algebras as adequate generalizations of continuous and left-continuous t-norms respectively. In both cases, the underlying basic structure is that of linearly ordered residuated lattices. Although the residuation property is equivalent to left-continuity in t-norms, continuous t-norms have received much more attention due to their simpler structure. We review their complete description in terms of ordinal sums and discuss the problem of describing the structure of their generalization to BL-chains. In particular we show the good behavior of BL-algebras over a finite or complete chain, and discuss the partial knowledge of rational BL-chains. Then we move to the general non-continuous case corresponding to left-continuous t-norms and MTL-chains. The unsolved problem of describing the structure of left-continuous t-norms is presented together with a fistful of construction-decomposition techniques that apply to some distinguished families of t-norms and, finally, we discuss the situation in the general study of MTL-chains as a natural generalization of left-continuous t-norms. © 2009 Elsevier Inc. All rights reserved.
Tue, 13 Feb 2018 11:49:44 GMThttp://hdl.handle.net/10261/1605562018-02-13T11:49:44Z
- Hoops and fuzzy logichttp://hdl.handle.net/10261/160601Title: Hoops and fuzzy logic
Authors: Esteva, Francesc; Godo, Lluis; Hajek, Petr; Montagna, Franco
Abstract: In this paper we investigate the falsehood-free fragments of main residuated fuzzy logics related to continuous t-norms (HaÌ?jek's Basic fuzzy logic BL and some well-known axiomatic extensions), and we relate them to the varieties of 0-free subreducts of the corresponding algebras. These turn out to be classes of algebraic structures known as hoops. We provide axiomatizations of all these fragments and we call them hoop logics; we prove they are strongly complete with respect to their corresponding classes of hoops, and that each fuzzy logic is a conservative extension of the corresponding hoop logic. Analogously, we also study the falsehood-free fragment of a weaker logic than BL, called MTL, which is the logic of left-continuous t-norms and their residua, and we introduce the related algebraic structures which are called semihoops. Moreover, we also consider the falsehood-free fragments of the fuzzy predicate calculi of the above logics and show completeness and conservativeness results. The role of axiom (âˆ€3) in these predicate logics is studied. Finally, computational complexity issues of the prepositional logics are also addressed.
Tue, 13 Feb 2018 14:25:50 GMThttp://hdl.handle.net/10261/1606012018-02-13T14:25:50Z
- On a Graded Modal Logic Approach to Reason with Fuzzy Preferenceshttp://hdl.handle.net/10261/164743Title: On a Graded Modal Logic Approach to Reason with Fuzzy Preferences
Authors: Esteva, Francesc; Godo, Lluis; Vidal, Amanda
Abstract: In this paper we first consider the problem of extending a fuzzy preference relation on a set, represented by a fuzzy preorder, to a fuzzy preference rela- tion on subsets, and we characterise different possibilities. Based on their properties, we then semantically define and axiomatize a two-tiered graded modal logic to reason about a notion of fuzzy preferences.
Fri, 11 May 2018 11:30:02 GMThttp://hdl.handle.net/10261/1647432018-05-11T11:30:02Z
- Possibilistic Semantics for a Modal KD45 Extension of Gödel Fuzzy Logichttp://hdl.handle.net/10261/157269Title: Possibilistic Semantics for a Modal KD45 Extension of Gödel Fuzzy Logic
Authors: Bou, Felix; Esteva, Francesc; Godo, Lluis; Rodriguez, Ricardo O.
Abstract: In this paper we provide a simplified semantics for the logic $KD45(\mathbf{G})$, i.e. the many-valued G\>odel counterpart of the classical modal logic $KD45$. More precisely, we characterize $KD45(\mathbf{G})$ as the set of valid formulae of the class of possibilistic G\>odel Kripke Frames $\langle W, \pi \rangle$, where $W$ is a non-empty set of worlds and $\pi: W \to [0, 1]$ is a normalized possibility distribution on $W$.
Mon, 13 Nov 2017 16:10:44 GMThttp://hdl.handle.net/10261/1572692017-11-13T16:10:44Z
- On Finite-Valued Bimodal Logics with an Application to Reasoning About Preferenceshttp://hdl.handle.net/10261/164660Title: On Finite-Valued Bimodal Logics with an Application to Reasoning About Preferences
Authors: Vidal, Amanda; Esteva, Francesc; Godo, Lluis
Abstract: In a previous paper by Bou et al., the minimal modal logic over a finite residuated lattice with a necessity operator was characterized under different semantics. In the general context of a residuated lattice, the residual negation ¬ is not necessarily involutive, and hence a corresponding possibility operator cannot be introduced by duality. In the first part of this paper we address the problem of extending such a minimal modal logic with a suitable possibility operator Q. In the second part of the paper, we introduce suitable axiomatic extensions of the resulting bimodal logic and define a logic to reason about fuzzy preferences, generalising to the many-valued case a basic preference modal logic considered by van Benthem et al. © Springer International Publishing AG 2018
Thu, 10 May 2018 09:48:25 GMThttp://hdl.handle.net/10261/1646602018-05-10T09:48:25Z
- Expanding FL e w with a Boolean connectivehttp://hdl.handle.net/10261/154750Title: Expanding FL e w with a Boolean connective
Authors: Ertola-Biraben, Rodolfo C.; Esteva, Francesc; Godo, Lluis
Abstract: We expand FL e w with a unary connective whose algebraic counterpart is the operation that gives the greatest complemented element below a given argument. We prove that the expanded logic is conservative and has the Finite Model Property. We also prove that the corresponding expansion of the class of residuated lattices is an equational class. © 2016, Springer-Verlag Berlin Heidelberg.
Tue, 05 Sep 2017 10:21:13 GMThttp://hdl.handle.net/10261/1547502017-09-05T10:21:13Z
- On the relationship between fuzzy description logics and many-valued modal logicshttp://hdl.handle.net/10261/161156Title: On the relationship between fuzzy description logics and many-valued modal logics
Authors: Cerami, Marco; Esteva, Francesc; García-Cerdaña, Àngel
Abstract: In this paper we study the relationships between a family of ALC-like fuzzy description logics (FDLs) defined over left-continuous t-norms and some many-valued multi-modal logics (MMLs). We analyze these relationships in both directions, that is, how to merge FDLs into MMLs and vice-versa. The analysis starts from the relationships between the languages to reach systematically the deeper level of reasoning tasks. At this level we are able to truly investigate both formalisms from each other point of view. Finally, the results concerning translations between reasoning tasks are applied in order to get decidability and complexity bounds.
Wed, 21 Feb 2018 17:25:09 GMThttp://hdl.handle.net/10261/1611562018-02-21T17:25:09Z
- On a class of left-continuous t-normshttp://hdl.handle.net/10261/160962Title: On a class of left-continuous t-norms
Authors: Cignoli, Roberto; Esteva, Francesc; Godo, Lluis; Montagna, Franco
Abstract: In this paper we study the subclass of left-continuous t-norms *n which are definable by an arbitrary continuous t-norm * and a weak (i.e. non necessarily involutive) negation n by putting x *n y = 0 if x ≤ n(y), x *n y = x * y otherwise, thus generalizing the construction of the so-called nilpotent minimum t-norms. We provide the characterization of weak negations compatible with a given continuous t-norm and conversely which are the continuous t-norms compatible with a given weak negation function. © 2002 Elsevier Science B.V. All rights reserved.
Mon, 19 Feb 2018 16:43:36 GMThttp://hdl.handle.net/10261/1609622018-02-19T16:43:36Z
- On Learning similarity relations in fuzzy case-based reasoninghttp://hdl.handle.net/10261/160966Title: On Learning similarity relations in fuzzy case-based reasoning
Authors: Armengol, Eva; Esteva, Francesc; Godo, Lluis; Torra, Vicenç
Abstract: Case-based reasoning (CBR) is a problem solving technique that puts at work the general principle that similar problems have similar solutions. In particular, it has been proved effective for classification problems. Fuzzy set-based approaches to CBR rely on the existence of a fuzzy similarity functions on the problem description and problem solution domains. In this paper, we study the problem of learning a global similarity measure in the problem description domain as a weighted average of the attribute - based similarities and, therefore, the learning problem consists in finding the weighting vector that minimizes mis - classification. The approach is validated by comparing results with an application of case-based reasoning in a medical domain that uses a different model. © Springer-Verlag 2004.
Mon, 19 Feb 2018 17:50:17 GMThttp://hdl.handle.net/10261/1609662018-02-19T17:50:17Z
- On rational weak Nilpotent Minimum logicshttp://hdl.handle.net/10261/160968Title: On rational weak Nilpotent Minimum logics
Authors: Esteva, Francesc; Godo, Lluis; Noguera, Carles
Abstract: In this paper we investigate extensions of Gödel and Nilpotent Minimum logics by adding rational truth-values as truth constants in the language and by adding corresponding book-keeping axioms for the truth-constants. We also investigate the rational extensions of some parametric families of Weak Nilpotent Minimum logics, weaker than both Gödel and Nilpotent Minimum logics. Weak and strong standard completeness of these logics are studied in general and in particular when we restrict ourselves to formulas of the kind r̄ → φ, where r is a rational in [0, 1] and φ is a formula without rational truth-constants. © 2006 Old City Publishing, Inc.
Mon, 19 Feb 2018 18:20:16 GMThttp://hdl.handle.net/10261/1609682018-02-19T18:20:16Z
- Residuated fuzzy logics with an involutive negationhttp://hdl.handle.net/10261/162444Title: Residuated fuzzy logics with an involutive negation
Authors: Esteva, Francesc; Godo, Lluis; Hajek, Petr; Navara, Mirko
Abstract: 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 0̄, namely ¬φ is φ → 0̄. However, this negation behaves quite differently depending on the t-norm. For a nilpotent t-norm (a t-norm which is isomorphic to LŁukasiewicz t-norm), it turns out that ¬ is an involutive negation. However, for t-norms without non-trivial zero divisors, ¬ is Gödel negation. In this paper we investigate the residuated fuzzy logics arising from continuous t-norms without non-trivial zero divisors and extended with an involutive negation.
Mon, 19 Mar 2018 12:21:21 GMThttp://hdl.handle.net/10261/1624442018-03-19T12:21:21Z
- A Logical Approach to Interpolation Based on Similarity Relationshttp://hdl.handle.net/10261/159954Title: A Logical Approach to Interpolation Based on Similarity Relations
Authors: Dubois, Didier; Prade, Henri; Esteva, Francesc; García-Calvés, Pere; Godo, Lluis
Abstract: One of the possible semantics of fuzzy sets is in terms of similarity; namely, a grade of membership of an item in a fuzzy set can be viewed as the degree of resemblance between this item and prototypes of the fuzzy set. In such a framework, an interesting question is how to devise a logic of similarity, where inference rules can account for the proximity between interpretations. The aim is to capture the notion of interpolation inside a logical setting. In this paper, we investigate how a logic of similarity dedicated to interpolation can be defined, by considering different natural consequence relations induced by the presence of a similarity relation on the set of interpretations. These consequence relations are axiomatically characterized in a way that parallels the characterization of nonmonotonic consequence relationships. It is shown how to reconstruct the similarity relation underlying a given family of consequence relations that obey the axioms. Our approach strikingly differs from the logics of indiscernibility, such as the rough-set logics, because emphasis is put on interpolation capabilities. Potential applications are fuzzy rule-based systems and fuzzy case-based reasoning, where notions of similarity play a crucial role. © 1997 Elsevier Science Inc.
Wed, 31 Jan 2018 13:49:27 GMThttp://hdl.handle.net/10261/1599542018-01-31T13:49:27Z
- On modal extensions of Product fuzzy logichttp://hdl.handle.net/10261/155299Title: On modal extensions of Product fuzzy logic
Authors: Vidal, Amanda; Esteva, Francesc; Godo, Lluis
Abstract: In this article, we study modal extensions of Product fuzzy logic with both algebraic semantics and relational semantics based on Kripke structures with crisp accessibility relations, when the underlying product fuzzy logic is expanded with truth-constants, the Δ operator and with two infinitary inference rules. We provide completeness results for both kinds of semantics. Finally, we also consider a generalization of possibilistic logic evaluated over product algebras. © The Author, 2015. Published by Oxford University Press. All rights reserved.
Tue, 19 Sep 2017 14:46:03 GMThttp://hdl.handle.net/10261/1552992017-09-19T14:46:03Z
- On strong standard completeness of MTL*(Q) expansionshttp://hdl.handle.net/10261/159892Title: On strong standard completeness of MTL*(Q) expansions
Authors: Vidal, Amanda; Godo, Lluis; Esteva, Francesc
Abstract: Within the mathematical logic field, much effort has been devoted to prove completeness of different axiomatizations with respect to classes of algebras defined on the real unit interval [0, 1], but in general, what has been mainly achieved are axiomatizations and results concerning finitary completeness, that is, for deductions from a finite number of premises. In this work we are concerned with the problem of strong completeness, i.e., completeness for deductions from an arbitrary number of premises. In particular, we will focus on presenting axiomatic systems strongly complete with respect to the logic of some left-continuous t-norm expanded with rational constants and Delta operator. Moreover, we show how this system can be extended in order to be strongly complete with respect to the previous algebra further expanded with arbitrary functions fulfulling some regularity conditions.
Wed, 31 Jan 2018 09:37:27 GMThttp://hdl.handle.net/10261/1598922018-01-31T09:37:27Z
- Perfect and bipartite IMTL-algebras and disconnected rotations of prelinear semihoopshttp://hdl.handle.net/10261/162114Title: Perfect and bipartite IMTL-algebras and disconnected rotations of prelinear semihoops
Authors: Noguera, Carles; Esteva, Francesc; Gispert, Joan
Abstract: IMTL logic was introduced in [12] as a generalization of the infinitely-valued logic of Lukasiewicz, and in [11] it was proved to be the logic of left-continuous t-norms with an involutive negation and their residua. The structure of such t-norms is still not known. Nevertheless, Jenei introduced in [20] a new way to obtain rotation-invariant semigroups and, in particular, IMTL-algebras and left-continuous t-norm with an involutive negation, by means of the disconnected rotation method. In order to give an algebraic interpretation to this construction, we generalize the concepts of perfect, bipartite and local algebra used in the classification of MV-algebras to the wider variety of IMTL-algebras and we prove that perfect algebras are exactly those algebras obtained from a prelinear semihoop by Jenei's disconnected rotation. We also prove that the variety generated by all perfect IMTL-algebras is the variety of the IMTL-algebras that are bipartite by every maximal filter and we give equational axiomatizations for it. © Springer-Verlag 2005.
Tue, 13 Mar 2018 10:22:07 GMThttp://hdl.handle.net/10261/1621142018-03-13T10:22:07Z
- Commutative integral bounded residuated lattices with an added involutionhttp://hdl.handle.net/10261/160166Title: Commutative integral bounded residuated lattices with an added involution
Authors: Cignoli, Roberto; Esteva, Francesc
Abstract: A symmetric residuated lattice is an algebra A = (A, ∨, ∧, *, →, ∼, 1, 0) such that (A, ∨, ∧, *, →, 1, 0) is a commutative integral bounded residuated lattice and the equations ∼ ∼ x = x and ∼ (x ∨ y) = ∼ x ∧ ∼ y are satisfied. The aim of the paper is to investigate the properties of the unary operation ε defined by the prescription ε x = ∼ x → 0. We give necessary and sufficient conditions for ε being an interior operator. Since these conditions are rather restrictive (for instance, on a symmetric Heyting algebra ε is an interior operator if and only the equation (x → 0) ∨ ((x → 0) → 0) = 1 is satisfied) we consider when an iteration of ε is an interior operator. In particular we consider the chain of varieties of symmetric residuated lattices such that the n iteration of ε is a boolean interior operator. For instance, we show that these varieties are semisimple. When n = 1, we obtain the variety of symmetric stonean residuated lattices. We also characterize the subvarieties admitting representations as subdirect products of chains. These results generalize and in many cases also simplify, results existing in the literature. © 2009 Elsevier B.V. All rights reserved.
Mon, 05 Feb 2018 15:09:13 GMThttp://hdl.handle.net/10261/1601662018-02-05T15:09:13Z
- Adding truth-constants to logics of continuous t-norms: Axiomatization and completeness resultshttp://hdl.handle.net/10261/159904Title: Adding truth-constants to logics of continuous t-norms: Axiomatization and completeness results
Authors: Esteva, Francesc; Gispert, Joan; Godo, Lluis; Noguera, Carles
Abstract: In this paper we study generic expansions of logics of continuous t-norms with truth-constants, taking advantage of previous results for Łukasiewicz logic and more recent results for Gödel and Product logics. Indeed, we consider algebraic semantics for expansions of logics of continuous t-norms with a set of truth-constants { over(r, -) | r ∈ C }, for a suitable countable C ⊆ [0, 1], and provide a full description of completeness results when (i) the t-norm is a finite ordinal sum of Łukasiewicz, Gödel and Product components, (ii) the set of truth-constants covers all the unit interval in the sense that each component of the t-norm contains at least one value of C different from the bounds of the component, and (iii) the truth-constants in Łukasiewicz components behave as rational numbers. © 2007 Elsevier B.V. All rights reserved.
Wed, 31 Jan 2018 10:34:37 GMThttp://hdl.handle.net/10261/1599042018-01-31T10:34:37Z
- First-order t-norm based fuzzy logics with truth-constants: Distinguished semantics and completeness propertieshttp://hdl.handle.net/10261/160427Title: First-order t-norm based fuzzy logics with truth-constants: Distinguished semantics and completeness properties
Authors: Esteva, Francesc; Godo, Lluis; Noguera, Carles
Abstract: 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 (mainly continuous and weak nilpotent minimum 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 rational semantics provided by the algebras where the truth-constants are interpreted as the numbers they actually name. Finally, we study completeness properties restricted to evaluated formulae of the kind over(r, -) → φ, where φ has no additional truth-constants. © 2009 Elsevier B.V. All rights reserved.
Fri, 09 Feb 2018 15:29:25 GMThttp://hdl.handle.net/10261/1604272018-02-09T15:29:25Z
- Expanding the propositional logic of a t-norm with truth-constants: completeness results for rational semanticshttp://hdl.handle.net/10261/160412Title: Expanding the propositional logic of a t-norm with truth-constants: completeness results for rational semantics
Authors: Esteva, Francesc; Godo, Lluis; Noguera, Carles
Abstract: In this paper we consider the expansions of logics of a left-continuous t-norm with truth-constants from a subalgebra of the rational unit interval. From known results on standard semantics, we study completeness for these propositional logics with respect to chains deined over the rational unit interval with a special attention to the completeness with respect to the canonical chain, i.e. the algebra over $[0, 1] \cap Q$ where each truth-constant is interpreted in its corresponding rational truth-value. Finally, we study rational completeness results when we restrict ourselves to deductions between the so-called evaluated formulae.
Fri, 09 Feb 2018 13:44:20 GMThttp://hdl.handle.net/10261/1604122018-02-09T13:44:20Z
- Relating and extending semantical approaches to possibilistic reasoninghttp://hdl.handle.net/10261/162432Title: Relating and extending semantical approaches to possibilistic reasoning
Authors: Esteva, Francesc; García-Calvés, Pere; Godo, Lluis
Abstract: Two main semantical approaches to possibilistic reasoning with classical propositions have been proposed in the literature. Namely, Dubois-Prade's approach known as possibilistic logic, whose semantics is based on a preference ordering in the set of possible worlds, and Ruspini's approach that we redefine and call similarity logic, which relies on the notion of similarity or resemblance between worlds. In this article we put into relation both approaches, and it is shown that the monotonic fragment of possibilistic logic can be semantically embedded into similarity logic. Furthermore, to extend possibilistic reasoning to deal with fuzzy propositions, a semantical reasoning framework, called fuzzy truth-valued logic, is also introduced and proved to capture the semantics of both possibilistic and similarity logics. © 1994.
Mon, 19 Mar 2018 11:47:04 GMThttp://hdl.handle.net/10261/1624322018-03-19T11:47:04Z
- Reasoning about probability using fuzzy logichttp://hdl.handle.net/10261/162416Title: Reasoning about probability using fuzzy logic
Authors: Godo, Lluis; Esteva, Francesc; Hajek, Petr
Abstract: In this paper we deal with an approach to reasoning about numerical beliefs in a logical framework. Among the different models of numerical belief, probability theory is the most relevant. Nearly all logics of probability that have been proposed in the literature are based on classical two-valued logic. After making clear the differences between fuzzy logic and probability theory, that apply also to uncertainty measures in general, here we propose two different theories in a fuzzy logic to cope with probability and belief functions respectively. Completeness results are provided for them. The main idea behind this approach is that uncertainty measures of crisp propositions can be understood as truth-values of some suitable fuzzy propositions associated to the crisp ones.
Mon, 19 Mar 2018 11:16:16 GMThttp://hdl.handle.net/10261/1624162018-03-19T11:16:16Z
- On elementary equivalences in Fuzzy Predicate logicshttp://hdl.handle.net/10261/133719Title: On elementary equivalences in Fuzzy Predicate logics
Authors: Dellunde, Pilar; Esteva, Francesc
Abstract: Our work is a contribution to the model theory of fuzzy predicate logics. In this paper we characterize elementary equivalence between models of fuzzy predicate logic using elementary mappings. Refining the method of diagrams we give a solution to an open problem of Hájek and Cintula (J Symb Log 71(3):863-880, 2006, Conjectures 1 and 2). We investigate also the properties of elementary extensions in witnessed and quasi-witnessed theories, generalizing some results of Section 7 of Hájek and Cintula (J Symb Log 71(3):863-880, 2006) and of Section 4 of Cerami and Esteva (Arch Math Log 50(5/6):625-641, 2011) to non-exhaustive models. © 2012 Springer-Verlag.
Fri, 17 Jun 2016 13:09:55 GMThttp://hdl.handle.net/10261/1337192016-06-17T13:09:55Z
- About strong standard completeness of Product Logichttp://hdl.handle.net/10261/131173Title: About strong standard completeness of Product Logic
Authors: Vidal, Amanda; Esteva, Francesc; Godo, Lluis
Abstract: Propositional Product Logic is known to be standard finite-strong complete but not a strong complete, that is, it is complete for deductions only from finite sets of premises with respect to evaluations on the standard product chain over the real unit interval. On the other hand, Montagna has defined a logical system, an axiomatic extension of the Hájek’s Basic Fuzzy Logic BL with an storage operator and an infinitary rule, which was proved to be standard strong complete (i.e. for deductions from possibly infinite theories) with respect to the standard BL chains. In particular, the expansion of Product Logic with the infinitary rule and Monteiro-Baaz Delta operator is standard strong complete. In this paper we generalize this result to the case of having rational truth constants in the language, and provide alternative infinitary rules better adapted to the final goal of our ongoing research, that is to study modal extensions over product fuzzy logic.
Mon, 18 Apr 2016 10:43:11 GMThttp://hdl.handle.net/10261/1311732016-04-18T10:43:11Z