Equivalential and algebraizable logics

Studia Logica 57 (2-3):419 - 436 (1996)
  Copy   BIBTEX

Abstract

The notion of an algebraizable logic in the sense of Blok and Pigozzi [3] is generalized to that of a possibly infinitely algebraizable, for short, p.i.-algebraizable logic by admitting infinite sets of equivalence formulas and defining equations. An example of the new class is given. Many ideas of this paper have been present in [3] and [4]. By a consequent matrix semantics approach the theory of algebraizable and p.i.-algebraizable logics is developed in a different way. It is related to the theory of equivalential logics in the sense of Prucnal and Wroski [18], and it is extended to nonfinitary logics. The main result states that a logic is algebraizable (p.i.-algebraizable) iff it is finitely equivalential (equivalential) and the truth predicate in the reduced matrix models is equationally definable.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 90,221

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Analytics

Added to PP
2009-01-28

Downloads
34 (#405,202)

6 months
7 (#174,572)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

A survey of abstract algebraic logic.J. M. Font, R. Jansana & D. Pigozzi - 2003 - Studia Logica 74 (1-2):13 - 97.
Fregean logics.J. Czelakowski & D. Pigozzi - 2004 - Annals of Pure and Applied Logic 127 (1-3):17-76.
Weakly algebraizable logics.Janusz Czelakowski & Ramon Jansana - 2000 - Journal of Symbolic Logic 65 (2):641-668.
Correspondences between Gentzen and Hilbert Systems.J. G. Raftery - 2006 - Journal of Symbolic Logic 71 (3):903 - 957.

View all 26 citations / Add more citations

References found in this work

Algebraizable Logics.W. J. Blok & Don Pigozzi - 2022 - Advanced Reasoning Forum.
An algebraic approach to non-classical logics.Helena Rasiowa - 1974 - Warszawa,: PWN - Polish Scientific Publishers.
On the theory of inconsistent formal systems.Newton C. A. Costa - 1972 - Recife,: Universidade Federal de Pernambuco, Instituto de Matemática.
Theory of Logical Calculi: Basic Theory of Consequence Operations.Ryszard Wójcicki - 1988 - Dordrecht, Boston and London: Kluwer Academic Publishers.
On the theory of inconsistent formal systems.Newton C. A. da Costa - 1974 - Notre Dame Journal of Formal Logic 15 (4):497-510.

View all 20 references / Add more references