2-element matrices

Studia Logica 40 (4):315 - 353 (1981)

Abstract
Sections 1, 2 and 3 contain the main result, the strong finite axiomatizability of all 2-valued matrices. Since non-strongly finitely axiomatizable 3-element matrices are easily constructed the result reveals once again the gap between 2-valued and multiple-valued logic. Sec. 2 deals with the basic cases which include the important F i from Post's classification. The procedure in Sec. 3 reduces the general problem to these cases. Sec. 4 is a study of basic algebraic properties of 2-element algebras. In particular, we show that equational completeness is equivalent to the Stone-property and that each 2-element algebra generates a minimal quasivariety. The results of Sec. 4 will be applied in Sec. 5 to maximality questions and to a matrix free characterization of 2-valued consequences in the lattice of structural consequences in any language. Sec. 6 takes a look at related axiomatization. problems for finite algebras and matrices. We study the notion of a propositional consequence with equality and, among other things, present explicit axiomatizations of 2-valued consequences with equality.
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DOI 10.1007/BF00401653
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References found in this work BETA

Klassische und nichtklassische Aussagenlogik.Wolfgang Rautenberg - 1980 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 11 (2):405-407.
Fragments of the Propositional Calculus.Leon Henkin - 1949 - Journal of Symbolic Logic 14 (1):42-48.

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Juxtaposition: A New Way to Combine Logics.Joshua Schechter - 2011 - Review of Symbolic Logic 4 (4):560-606.
Singulary Extensional Connectives: A Closer Look. [REVIEW]I. L. Humberstone - 1997 - Journal of Philosophical Logic 26 (3):341-356.

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