J. Gispert - Profile on Academia.edu (original) (raw)

Papers by J. Gispert

Mejora de la actuación docente del profesorado de Matemáticas

Aquest article és fruit de la recerca duta a terme en el marc del projecte conjunt REDICE08, PID0... more Aquest article és fruit de la recerca duta a terme en el marc del projecte conjunt REDICE08, PID08, PID09 Com motivar, com adequar l’avaluació continuada i com mesurar el treball a les assignatures de Matemàtiques durant els cursos 2008 2009 i 2009-2010. El projecte aborda temes relacionats amb els resultats de les enquestes sobre l’actuació docent del professorat a l’ensenyament de Matemàtiques de la Universitat de Barcelona (UB), en què l’alumnat posa de manifest, en general, un baixa motivació del professorat i un elevat volum de feina en les assignatures. Com a resultat de l’estudi i de la pràctica docent en les assignatures involucrades en el projecte citat abans, es desprèn que la motivació de l’alumnat s’aconsegueix sumant esforços en diferents direccions: d’una banda, cal una tria adequada i una bona comunicació dels continguts, que fomenti el diàleg amb l’alumnat; d’altra banda, cal que l’avaluació continuada presenti un esglaonament progressiu en la dificultat de les activ...

arXiv (Cornell University), 1997

In this paper we show that every locally finite quasivariety of MV-algebras is finitely generated... more In this paper we show that every locally finite quasivariety of MV-algebras is finitely generated and finitely based. To see this result we study critical MV-algebras. We also give axiomatizations of some of these quasivarieties.

REIRE Revista d'Innovació i Recerca en Educació, Jul 4, 2012

Benseny, Cascante, Gispert i Verdú. Millora de l'actuació docent del professorat de Matemàtiques

Estudi algebraic de les extensions dels càlculs multivalorats de Lukasiewicz: = Estudio algebraico de las extensiones de los cálculos multivalentes de Lukasiewicz

Journal of Algebra, 1999

Up to categorical equivalence, abelian lattice-ordered groups with strong unit coincide with Chan... more Up to categorical equivalence, abelian lattice-ordered groups with strong unit coincide with Chang's MV-algebrasᎏthe Lindenbaum algebras of the infinite-valued Łukasiewicz calculus. While the property of being a strong unit is not definable even in first-order logic, MV-algebras form an equational class. On the other hand, the addition operation and the translation invariant lattice order of a lattice-ordered group are more amenable than the truncated addition operation of an MV-algebra. In this paper MV-algebraic and group-theoretical techniques are combined to classify and axiomatize all universal classes generated by an infinite totally ordered * Partially supported by Grants Nos. FIr94-1351 and SGRr96-00052 of DGR of Generalitat de Catalunya and by Grant No. PB97-0888 of DGICYT of Spain and by COST ACTION 15 on many-valued logics for computer science applications. † Partially supported by COST ACTION 15 on many-valued logics for computer science applications, and by the Italian MURST Project on Logic. ‡ Partially supported by Grant No. SGRr96-00052 of DGR of Generalitat de Catalunya and by Grant No. PB97-0888 of DGICYT of Spain and by COST ACTION 15 on many-valued logics for computer science applications.

Algebraic Expansions of Logics

The Journal of Symbolic Logic

ISMVL 2010 Organizing Committee

Searching... Advanced Search. Google Search Engine. ...

The logics RŁ, RP, and RG have been obtained by expanding Łukasiewicz logic Ł, product logic P, a... more The logics RŁ, RP, and RG have been obtained by expanding Łukasiewicz logic Ł, product logic P, and Gödel–Dummett logic G with rational constants. We study the lattices of extensions and structural completeness of these three expansions, obtaining results that stand in contrast to the known situation in Ł, P, and G. Namely, RŁ is hereditarily structurally complete. RP is algebraized by the variety of rational product algebras that we show to be Q-universal. We provide a base of admissible rules in RP, show their decidability, and characterize passive structural completeness for extensions of RP. Furthermore, structural completeness, hereditary structural completeness, and active structural completeness coincide for extensions of RP, and this is also the case for extensions of RG, where in turn passive structural completeness is characterized by the equivalent algebraic semantics having the joint embedding property. For nontrivial axiomatic extensions of RG we provide a base of admis...

Axiomatic extensions of the nilpotent minimum logic

Reports on Mathematical Logic, 2003

... 2 From (WNM) it is easy to see that given a totally ordered set A with upper bound 1 and lowe... more ... 2 From (WNM) it is easy to see that given a totally ordered set A with upper bound 1 and lower bound 0 equipped with an involutive negation ¬ dually order preserving, if we define ∧, ∨ asmeet and join and for every a, b ∈ A, a ∗ b = { 0, if b ≤ ¬a; a ∧ b, otherwise. ...

Uncertainty and Intelligent information Systems, 2008

In order to reach a deeper understanding of the structure of fuzzy logics, some very general new ... more In order to reach a deeper understanding of the structure of fuzzy logics, some very general new logics are defined. Namely, we consider the extensions of MTL by adding the generalized contraction and excludded middle laws introduced in [4], and we enrich this family by means of the axiom of weak cancellation and the Ω operator defined in [18]. The algebraic counterpart of these logics is studied characterizing the subdirectly irreducible, the semisimple and the simple algebras. Finally, some important algebraic and logical properties of the considered logics are discussed: local finiteness, finite embedding property, finite model property, decidability and standard completeness.

Fuzzy Sets and Systems, 2014

This paper is a contribution to the study of the lattice of all quasivarieties of MV-algebras. Gi... more This paper is a contribution to the study of the lattice of all quasivarieties of MV-algebras. Given a variety V of MV-algebras, we say that a quasivariety is a V-quasivariety provided that it generates V as a variety. It turns out that every variety has a least V-quasivariety denoted by Q V. Moreover, it is generated as a quasivariety by its free algebra over an infinite set of generators. We obtain a Komori's type characterization of Q V for every proper subvariety of MV-algebras. We investigate the order structure of the poset of least V-quasivarieties and we find all minimal quasivarieties among all quasivarieties of MV-algebras different from the class of boolean algebras. Finally, we make some remarks on the logical interpretation of least V-quasivarieties of MV-algebras as structurally complete extensions of the infinite valued Łukasiewicz logic.

Logic Journal of the Igpl, 2005

The study of perfect, local and bipartite IMTL-algebras presented in [29] is generalized in this ... more The study of perfect, local and bipartite IMTL-algebras presented in [29] is generalized in this paper to the general non-involutive case, i. e. to MTL-algebras. To this end we describe the radical of MTL-algebras and characterize perfect MTL-algebras as those for which the quotient by the radical is isomorphic to the two-element Boolean algebra, and a special class of bipartite MTL-algebras, BP 0 , as those for which the quotient by the radical is a Boolean algebra. We prove that BP 0 is the variety generated by all perfect MTL-algebras and give some equational bases for it. We also introduce a new way to build MTL-algebras by adding a negation fixpoint to a perfect algebra and also by adding some set of points whose negation is the fixpoint. Finally, we consider the varieties generated by those algebras, giving equational bases for them, and we study which of them define a fuzzy logic with standard completeness theorem.

On the standard and rational completeness of some axiomatic extensions of the monoidal t-norm logic

Studia Logica, 2002

The monoidal t-norm based logic MTL is obtained from Hájek's Basic Fuzzy logic BL by droppin... more 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, ie complete with respect to the ...

Archive for Mathematical Logic, 2005

IMTL logic was introduced in [12] as a generalization of the infinitely-valued logic of Lukasiewi... more 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.

sn this pper we study ek xilpotent winimum tEnorms nd their ssoited lgeri struturesD the stndrd x... more sn this pper we study ek xilpotent winimum tEnorms nd their ssoited lgeri struturesD the stndrd xwEhinsF e lssify ll the vrieties generted y one stndrd xwEhinD otining ll the xiomti extensions of xw logi tht re omplete with respet to the semnE tis given y leftEontinuous tEnormF o this endD we dene set of nonil stndrd xwE hins nd we prove tht they generte pirwise dierent vrieties nd there re no other vrieties generted y stndrd xwEhinF Keywords: puzzy logisD veftEontinuous tE normsD xilpotent winimum vogiD wvElgersD xwElgersD esiduted lttiesD rietiesD ek xilpotent winimum vogiD xonElssil logisD xwElgersF

Real, rational and finite chain semantics for t-norm based logics: methods and algebraic equivalencies

Algebraic characterization of completeness properties for core fuzzy logics I: propositional logics

In this paper we carry out an algebraic investigation of the Weak Nilpotent Minimum logic (WNM) a... more 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 this logic, the variety of WNMalgebras (WNM) and we 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 study their standard completeness properties. We also characterize the generic WNM-chains, i.e. those that generate the variety WNM, and we give finite axiomatizations for some t-norm based extensions of WNM.

Annals of Pure and Applied Logic, 2009

This paper is a contribution to the algebraic study of t-norm based fuzzy logics. In the general ... more This paper is a contribution to the algebraic study of t-norm based fuzzy logics. In the general framework of propositional core and ∆-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 propose 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 ultraproducts of the real unit interval), the strict hyperreals (only ultraproducts 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. §1. Introduction. In his famous book [31], Hájek considers the problem of finding a basic fuzzy logic which is a common fragment of the most important fuzzy logics, namely Lukasiewicz, Gödel and product logics. There, he introduced a logic, named BL, and he proposed it for the role of basic fuzzy logic. Hájek's proposal was greatly supported by , where it was shown that BL is the logic of all continuous t-norms 1 and of their residua. But in the authors observed that the minimal condition for a t-norm to have a residuum, and therefore to determine a logic, is left-continuity (continuity is not necessary). There, they proposed a weaker logic, called MTL (monoidal t-norm based logic), and conjectured that MTL is the logic of left-continuous t-norms and of their residuals. This conjecture was shown to be true in . Thus, it makes sense to propose it (instead of BL) as the real 'basic fuzzy logic' (this claim is also supported by an interesting methodological paper [4]). Another feature of MTL, which adds interest to it, is constituted by its relationship with substructural logics. Indeed, MTL is a logic without contraction (see ) and it can be characterized as FL ew (i.e. Full Lambek calculus plus exchange and weakening, see [55]) plus prelinearity. As the most important substructural logics, MTL can be formulated in a hypersequent calculus which enjoys cut-elimination (see [3]) by adding to the calculus for FL ew Avron's communication rule [1], a rule which yields completeness with respect to linearly ordered (commutative, integral, bounded) residuated lattices. Further generalizations are also possible, (e.g. by removing exchange or weakening), but MTL seems general enough.

ALGEBRAIC AND TOPOLOGICAL METHODS IN NON-CLASSICAL LOGICS III (TANCL'07)

atlas-conferences.com, 2007

Atlas home || Conferences | Abstracts | about Atlas ALGEBRAIC AND TOPOLOGICAL METHODS IN NON-CLAS... more Atlas home || Conferences | Abstracts | about Atlas ALGEBRAIC AND TOPOLOGICAL METHODS IN NON-CLASSICAL LOGICS III (TANCL'07) August 5-9, 2007 St Anne's College, University of Oxford Oxford, England. Organizers Mai Gehrke and Hilary Priestley. Conference Homepage. Abstracts. SAMSON ABRAMSKY Domain Theory in Logical Form Revisited: a 20-year Retrospective Stefano Aguzzoli Goedel algebras free over finite distributive ...