Logical matrices and non-structural consequence operators

Studia Logica 42 (1):33 - 42 (1983)
In the present paper, we study some properties of matrices for non-structural consequence operators. These matrices were introduced in a former work (see [3]). In sections 1. and 2., general definitions and theorems are recalled; in section 3. a correspondence is studied, among our matrices and Wójcicki's ones for structural operators. In section 4. a theorem is given about operators, induced by submatrices or epimorphic images, or quotient matrices of a given one.Such matrices are used to characterize lattices of non-structural consequence operators, by constructing lattices, antiisomorphic to them (see section 5.). In the last section, a sufficient condition is given for a non-structural operator to be finite.
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DOI 10.1007/BF01418757
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Selected Works.Jan Łukasiewicz - 1970 - Amsterdam: North-Holland Pub. Co..
Deducibility and Many-Valuedness.D. J. Shoesmith & T. J. Smiley - 1971 - Journal of Symbolic Logic 36 (4):610-622.

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Nonmonotonic Theories and Their Axiomatic Varieties.Zbigniew Stachniak - 1995 - Journal of Logic, Language and Information 4 (4):317-334.
Many-Valued Computational Logics.Zbigniew Stachniak - 1989 - Journal of Philosophical Logic 18 (3):257 - 274.

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