On the algebraizability of annotated logics

Studia Logica 59 (3):359-386 (1997)

Abstract
Annotated logics were introduced by V.S. Subrahmanian as logical foundations for computer programming. One of the difficulties of these systems from the logical point of view is that they are not structural, i.e., their consequence relations are not closed under substitutions. In this paper we give systems of annotated logics that are equivalent to those of Subrahmanian in the sense that everything provable in one type of system has a translation that is provable in the other. Moreover these new systems are structural. We prove that these systems are weakly congruential, namely, they have an infinite system of congruence 1-formulas. Moreover, we prove that an annotated logic is algebraizable (i.e., it has a finite system of congruence formulas,) if and only if the lattice of annotation constants is finite.
Keywords Philosophy   Logic   Mathematical Logic and Foundations   Computational Linguistics
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DOI 10.1023/A:1005036412368
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Correspondences Between Gentzen and Hilbert Systems.J. G. Raftery - 2006 - Journal of Symbolic Logic 71 (3):903 - 957.
On Recent Applications of Paraconsistent Logic: An Exploratory Literature Review.A. Zamansky - 2019 - Journal of Applied Non-Classical Logics 29 (4):382-391.
On Free Annotated Algebras.Renato A. Lewin, Irene F. Mikenberg & Marı́a G. Schwarze - 2001 - Annals of Pure and Applied Logic 108 (1-3):249-259.

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