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Referentiality and Matrix Semantics

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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.

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References

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  1. Department of Logic, University of Łódź, Lodz, Poland

    Grzegorz Malinowski

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  1. Grzegorz Malinowski
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Correspondence to Grzegorz Malinowski.

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Malinowski, G. Referentiality and Matrix Semantics. Stud Logica 97, 297–312 (2011). https://doi.org/10.1007/s11225-011-9307-5

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