Protoalgebraic logics

Studia Logica 45 (4):337 - 369 (1986)
  Copy   BIBTEX

Abstract

There exist important deductive systems, such as the non-normal modal logics, that are not proper subjects of classical algebraic logic in the sense that their metatheory cannot be reduced to the equational metatheory of any particular class of algebras. Nevertheless, most of these systems are amenable to the methods of universal algebra when applied to the matrix models of the system. In the present paper we consider a wide class of deductive systems of this kind called protoalgebraic logics. These include almost all (non-pathological) systems of prepositional logic that have occurred in the literature. The relationship between the metatheory of a protoalgebraic logic and its matrix models is studied. The following results are obtained for any finite matrix model U of a filter-distributive protoalgebraic logic : (I) The extension U of is finitely axiomatized (provided has only finitely many inference rules); (II) U has only finitely many extensions.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 74,662

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
47 (#247,308)

6 months
1 (#419,921)

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.
Explicating Logical Independence.Lloyd Humberstone - 2020 - Journal of Philosophical Logic 49 (1):135-218.
Weakly Algebraizable Logics.Janusz Czelakowski & Ramon Jansana - 2000 - Journal of Symbolic Logic 65 (2):641-668.

View all 73 citations / Add more citations

References found in this work

Multiple Conclusion Logic.D. J. Shoesmith & Timothy Smiley - 1978 - Cambridge, England / New York London Melbourne: Cambridge University Press.
Equivalential Logics (I).Janusz Czelakowski - 1981 - Studia Logica 40 (3):227 - 236.
Investigations Into the Sentential Calculus with Identity.Roman Suszko & Stephen L. Bloom - 1972 - Notre Dame Journal of Formal Logic 13 (3):289-308.

View all 11 references / Add more references