David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jonathan Jenkins Ichikawa
Jack Alan Reynolds
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Studia Logica 59 (3):359-386 (1997)
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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Citations of this work BETA
Josep Maria Font, Ramon Jansana & Don Pigozzi (2009). Update to “A Survey of Abstract Algebraic Logic”. Studia Logica 91 (1):125-130.
Eduardo Hirsh & Renato A. Lewin (2008). Algebraization of Logics Defined by Literal-Paraconsistent or Literal-Paracomplete Matrices. Mathematical Logic Quarterly 54 (2):153-166.
A. Lewin Renato, F. Mikenberg Irene & G. Schwarze Marı́a (2001). On Free Annotated Algebras. Annals of Pure and Applied Logic 108 (1-3):249-259.
Carlos Augusto Di Prisco (1999). XI Latin American Symposium on Mathematical Logic. Bulletin of Symbolic Logic 5 (4):495-524.
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