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Modal Equivalence and Bisimilarity in Many-valued Modal Logics with Many-valued Accessibility Relations

100%

Diaconescu D.

tom Vol. 173, nr 2-3

177--189

In this paper we investigate the Hennessy-Milner property for models of many-valued modal logics defined based on complete MTL-chains having many-valued accessibility relations. Our main result gives a necessary and sufficient algebraic condition for the class of image-finite models for such modal logics to admit the Hennessy-Milner property.

Relational semantics for the 4-valued relevant logics BN4 and E4

100%

Robles G. , Blanco J. M. , López S. M. , Paradela J. R. , Recio M. M.

nr 2

173-201

The logic BN4 was defined by R.T. Brady in 1982. It can be considered as the 4-valued logic of the relevant conditional. E4 is a variant of BN4 that can be considered as the 4-valued logic of (relevant) entailment. The aim of this paper is to define reduced general Routley-Meyer semantics for BN4 and E4. It is proved that BN4 and E4 are strongly sound and complete w.r.t. their respective semantics.

A 2-set-up Routley-Meyer Semantics for the 4-valued Relevant Logic E4

100%

Robles G. , López S. M. , Blanco J. M. , Recio M. M. , Paradela J. R.

tom 45

nr 2

The logic BN4 can be considered as the 4-valued logic of the relevant conditional and the logic E4, as the 4-valued logic of (relevant) entailment. The aim of this paper is to endow E4 with a 2-set-up Routley-Meyer semantics. It is proved that E4 is strongly sound and complete w.r.t. this semantics.

Finite-valued Logics for Information Processing

75%

Avron A. , Konikowska B.

tom Vol. 114, nr 1

1-30

We examine the issue of collecting and processing information from various sources, which involves handling incomplete and inconsistent information. Inspired by the framework first proposed by Belnap, we consider structures consisting of information sources which provide information about the values of formulas of classical propositional logic, and a processor which collects that information and extends it by deriving conclusions following from it according to the truth tables of classical logic, applied forward and backward. Our model extends Belnap’s in allowing the sources to provide information also about complex formulas. As that framework cannot be captured using finite ordinary logical matrices, if we want to represent each of the relevant logics with a single matrix, we employ Nmatrices for that purpose. In opposition to the approach proposed in our earlier work, we assume that the information sources are reasonable, i.e. that they provide information consistent with certain coherence rules. We provide sound and complete sequent calculi admitting strong cut elimination for the logic of a single information source, and (several variants of) the logic generated by the source and processor structures described above. In doing this, we also provide new characterizations for some known logics. We prove that, in opposition to the variantwith unconstrained information sources considered earlier, the latter logic cannot be generated by structures with any bounded number of sources.