1,721,127 research outputs found
Three complexity problems in quantified fuzzy logic
No full textWe prove that the sets of standard tautologies of predicate Product Logic and of predicate Basic Logic, as well as the set of standard-satisfiable formulas of predicate Basic Logic are not arithmetical, thus finding a rather satisfactory solution to three problems proposed by Hájek in [H01]. © 2001 Kluwer Academic Publishers
Subreducts of MV-algebras with product and product residuation
No full textRecently, MV-algebras with product have been investigated from different points of view. In particular, in [EGM01], a variety resulting from the combination of MV-algebras and product algebras (see [H98]) has been introduced. The elements of this variety are called L Pi-algebras. In this paper we treat subreducts of L Pi-algebras, with emphasis on quasivarieties of subreducts whose basic operations are continuous in the order topology. We give axiomatizations of the most interesting classes of subreducts, and we connect them with other algebraic classes of algebras, like f-rings and Wajsberg hoops, as well as to structures of co-infinitesimals of L Pi-algebras. In some cases, connections are given by means of equivalences of categories
On the predicate logic of continuous t-norm BL-algebras
No full textGiven a class C of t-norm BL-algebras, one may wonder which is the complexity of the set T aut (CFor All) of predicate formulas which are valid in any algebra in C. We first characterize the classes C for which T aut (CFor All) is recursively axiomatizable, and we show that this is the case iff C only consists of the Godel algebra on [0, 1]. We then prove that in all cases except from a finite number T aut (CFor All) is not even arithmetical. Finally we consider predicate monadic logics T aut(M)(CFor All) of classes C of t-norm BL-algebras, and we prove that ( possibly with finitely many exceptions) they are undecidable
Interpolation and Beth's property in many-valued logic: an algebraic investigation
No full textIn this paper we give a rather detailed algebraic investigation of interpolation and Beth’s property in propositional manyvalued
logics extending H ́ajek’s Basic Logic BL [P. H ́ajek, Metamathematics of Fuzzy Logic, Kluwer, 1998], and we connect such
properties with amalgamation and strong amalgamation in the corresponding varieties of algebras. It turns out that, while the most
interesting extensions of BL in the language of BL have deductive interpolation, very few of them have Beth’s property or Craig
interpolation. Thus in the last part of the paper we look for conservative extensions of BL having such properties
An algebraic treatment of imprecise probabilities
No full textThis is a survey paper about an algebraic approach to imprecise probabilities. In the first part of it, we outline the work by Walley on imprecise probabilities and the more algebraic approach of Fedel et al. Then, in the second part we will present some work in progress about a general treatment of upper and lower probabilities over many-valued events and of upper and lower previsions of gambles, by means of Universal Algebra
How Should Requirements be Defined to Have Real Innovation?
Full text linkAbstractPeople are generally influenced in their purchasing choices by diverse stakeholders and these influences are often not related only to “use situations”. Learning processes, product diffusion dynamics and externalities in fact frequently complicate innovation processes. “Design for Innovation” means considering that design cannot focus only on buyer's preferences and on “product use” because this could limit diffusion of products, besides bounding in general innovation opportunities. The “Design for Innovation” approach drives to study “beyond use situations” and the influences among the actors involved in the innovation processes. This paper describes through two different case studies how a more original list of needs that would have not emerged with more traditional approaches for the requirement management, can be generated with this approach
Substructural Fuzzy Logics
No full textSubstructural fuzzy logics are substructural logics that are complete with respect to algebras whose lattice reduct is the real unit interval [0. 1]. In this paper, we introduce Uninorm logic UL as Multi plicative additive intuitionistic linear logic MAILL extended with the prelinearity axiom. Axiomatic extensions of UL include known fuzzy logics such as Monoidal i-norm logic MTL and Goedel logic G and new weakening-free logics. Algebraic semantics for these logics are provided by subvarieties of (representable) pointed bounded commutative residuated lattices. Gentzen systems admitting cut-elimination are given in the framework of hypersequents. Completeness with respect to algebras with lattice reduct [0,1] is established for UL and several extensions using a two-part strategy. First, completeness is proved for the logic extended with Takeuti and Titani's density rule. A syntactic elimination of the rule is then given using a hypersequent calculus. As an algebraic corollary, it follows that certain varieties of residuated lattices are generated by their members with lattice reduct [0. 1]
Archimedean classes in integral, commutative residuated lattices
No full textThis paper investigates a quasi-variety of representable integral commutative residuated lattices axiomatized by the quasi-identity resulting from the well-known Wajsberg identity (p → q) → q ≤ (q → p) → p if it is written as a quasi-identity, i. e., (p → q) → q ≈ 1 ⇒ (q → p) → p ≈ 1. We prove that this quasi-identity is strictly weaker than the corresponding identity. On the other hand, we show that the resulting quasi-variety is in fact a variety and provide an axiomatization. The obtained results shed some light on the structure of Archimedean integral commutative residuated chains. Further, they can be applied to various subvarieties of MTL-algebras, for instance we answer negatively Hájek's question asking whether the variety of ΠMTL-algebras is generated by its Archimedean members. © 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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