ISSN:1166-3081    

DOI:10.1080/11663081.1999.10510955

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

In this paper we study consequence relations on the set of many sided sequents over a propositional language. We deal with the consequence relations axiomatized by the sequent calculi defined in [2] and associated with arbitrary finite algebras. These consequence relations are examples of what we call Gentzen systems. We define a semantics for these systems and prove a Strong Completeness Theorem, which is an extension of the Completeness Theorem for provable sequents stated in [2]. For the special case of the finite linear MV-algebras, the Strong Completeness Theorem was proved in [10], as a consequence of McNaughton's Theorem. The main tool to prove this result for arbitrary algebras is the deduction-detachment theorem for Gentzen systems.

ISSN:1166-3081    

DOI:10.1080/11663081.1999.10510956

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

The termfuzzy logichas two different meanings -broad and narrow. In Zadeh's opinion ([19]), fuzzy logic (in the narrow sense) 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 (many-valued) logic. We show that much of fuzzy logic can be understood as classical deduction in a many-sorted many-valued Pavelka- Lukasiewicz style rational quantification logic. This means that, besides the linguistic or approximation aspects, the logical aspect (symbolic, deductive) is present too and can be made explicit.

ISSN:1166-3081    

DOI:10.1080/11663081.1999.10510957

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

In this paper we study 12 four-valued logics arisen from Belnap's truth and/or knowledge four-valued lattices, with or without constants, by adding one or both or none of two new non-regular operations—classical negation and natural implication. We prove that the secondary connectives of the bilattice four-valued logic with bilattice constants are exactly the regular four-valued operations. Moreover, we prove that its expansion by any non-regular connective (such as, e.g., classical negation or natural implication) is strictly functionally complete. Further, finding axiomatizations of the quasi varieties generated by the 12 logics involved (that prove to be varieties), we find naturell equational axiomatizations of these logics. Finally, applying Pynko's general theory of algebraizable sequential consequence operations, we also find equivalent natural sequentiell axiomatizations of the logics under consideration that expand either of two Pynko's sequential calculi for the constant-free truth-lattice four-valued logic.

ISSN:1166-3081    

DOI:10.1080/11663081.1999.10510958

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

In an unpublished paper(see [9]), we prove the equivalence between validity in 3L-models and algebraic validity in 3-valued Lukasiewicz algebras. R. Cignoli and M. Sagastume de Gallego present in [4] an intrinsic definition of the operators s, for i = 1,…,4 of a 5-valued Lukasiewicz algebra.

ISSN:1166-3081    

DOI:10.1080/11663081.1999.10510959

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

This work presents the concepts of translation and conservative translation between logics. By using algebraic semantics we introduce several conservative translations involving the classical propositional calculus and the many-valued calculi of Post and Lukasiewicz.

ISSN:1166-3081    

DOI:10.1080/11663081.1999.10510960

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

We characterize, for every subvariety V of the variety of all MV- algebras, the free objects in V. We use our results to compute coproducts in V and to provide simple single-axiom axiomatizations of all many-valued logics extending the Lukasiewicz one.

ISSN:1166-3081    

DOI:10.1080/11663081.1999.10510961

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

In this paper we shall prove thatl-rings are categorally equivalent to the MV*-algebras, a subcategory of perfect MV-algebras. We shall use this equivalence in order to characterizel-rings as quotients of certain semirings of matrices over MV*-algebras. We shall establish a relation betweenl-ideals inl-rings and some ideals in MV*-algebras. This edlows us to study the MV* f-algebras, a subclass of the MV*-algebras corresponding to thef-rings.

ISSN:1166-3081    

DOI:10.1080/11663081.1999.10510962

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

The variety O2of double Ockham algebras consists of the algebras (A∨, ∧,f,g0,1) of type (2,2,1,1,0,0) where (A; ∨, ∧,f, 0,1) and (A;∨, ∧,g0,1) are Ockham algebras. In [16], M. Sequeira introduced several subvarieties of O2. In this paper we give a construction of free double Ockham algebras on a partially ordered set. We also describe free objects for the subvarieties of O2considered in [16].

ISSN:1166-3081    

DOI:10.1080/11663081.1999.10510963

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

ISSN:1166-3081    

DOI:10.1080/11663081.1999.10510964

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor