Referentiality and Matrix Semantics

Studia Logica 97 (2):297 - 312 (2011)

Abstract
Referential semantics importantly subscribes to the programme of theory of logical calculi. Defined by Wójcicki in [8], it has been subsequently studied in a series of papers of the author, till the full exposition of the framework in [9] and its intuitive characterisation in [10]. The aim of the article is to present several generalizations of referential semantics as compared and related to the matrix semantics for propositional logics. We show, in a uniform way, some own generalizations of referentiality: the first, directed to unrestricted cluster referential semantics, [4], its "discrete" version, a counterpart of algebraic semantics and a many-valued referentiality based on matrices, whose elements are functions from the set of indices to a finite n-element set of values, n≥2, [3]. Next to this we outline pragmatic matrices introduced by Tokarz in [6] as an alternative for cluster referential approach and discuss together all presented versions of referential semantics
Keywords referential algebra  referential semantics  referential matrix  cluster many-valuedness  pragmatic matrix  consequence operation  selfeextensionality
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DOI 10.1007/s11225-011-9307-5
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References found in this work BETA

Many-Valued Logics.J. Barkley Rosser - 1952 - Greenwood Press.
Referential Matrix Semantics for Propositional Calculi.Ryszard Wójcicki - 1979 - Bulletin of the Section of Logic 8 (4):170-176.
Pseudo-Referential Matrix Semantics for Propositional Logics.Grzegorz Malinowski - 1983 - Bulletin of the Section of Logic 12 (3):90-96.
Many-Valued Referential Matrices.Grzegorz Malinowski - 1995 - Bulletin of the Section of Logic 24 (3):140-146.

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Citations of this work BETA

Identity, Many-Valuedness and Referentiality.Grzegorz Malinowski - 2013 - Logic and Logical Philosophy 22 (4):375-387.
Possible Worlds in Use.Andrzej Indrzejczak - 2011 - Studia Logica 99 (1-3):229-248.
Professor Grzegorz Malinowski in Honorem.Andrzej Indrzejczak & Janusz Ciuciura - 2018 - Bulletin of the Section of Logic 46 (1/2).

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