Annals of Pure and Applied Logic 127 (1-3):17-76 (2004)

Authors
Abstract
According to Frege's principle the denotation of a sentence coincides with its truth-value. The principle is investigated within the context of abstract algebraic logic, and it is shown that taken together with the deduction theorem it characterizes intuitionistic logic in a certain strong sense.A 2nd-order matrix is an algebra together with an algebraic closed set system on its universe. A deductive system is a second-order matrix over the formula algebra of some fixed but arbitrary language. A second-order matrix A is Fregean if, for any subset X of A, the set of all pairs a,b such that X{a} and X{b} have the same closure is a congruence relation on A. Hence a deductive system is Fregean if interderivability is compositional. The logics intermediate between the classical and intuitionistic propositional calculi are the paradigms for Fregean logics. Normal modal logics are non-Fregean while quasi-normal modal logics are generally Fregean.The main results of the paper: Fregean deductive systems that either have the deduction theorem, or are protoalgebraic and have conjunction, are completely characterized. They are essentially the intermediate logics, possibly with additional connectives. All the full matrix models of a protoalgebraic Fregean deductive system are Fregean, and, conversely, the deductive system determined by any class of Fregean second-order matrices is Fregean. The latter result is used to construct an example of a protoalgebraic Fregean deductive system that is not strongly algebraizable
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1016/j.apal.2003.11.008
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Translate to english
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 63,319
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

Protoalgebraic Logics.W. J. Blok & Don Pigozzi - 1986 - Studia Logica 45 (4):337 - 369.
Ontology in the Tractatus of L. Wittgenstein.Roman Suszko - 1968 - Notre Dame Journal of Formal Logic 9 (1):7-33.
Equivalential Logics (I).Janusz Czelakowski - 1981 - Studia Logica 40 (3):227 - 236.
Weakly Algebraizable Logics.Janusz Czelakowski & Ramon Jansana - 2000 - Journal of Symbolic Logic 65 (2):641-668.

View all 19 references / Add more references

Citations of this work BETA

Selfextensional Logics with a Conjunction.Ramon Jansana - 2006 - Studia Logica 84 (1):63-104.

View all 20 citations / Add more citations

Similar books and articles

Rasiowa-Sikorski Proof System for the Non-Fregean Sentential Logic SCI.Joanna Golinska-Pilarek - 2007 - Journal of Applied Non-Classical Logics 17 (4):509–517.
New Rhetorics and Non-Fregean Logics.Fernand Vandamme - 1991 - Communication and Cognition: An Interdisciplinary Quarterly Journal 24 (3-4):389-401.
Identity, Many-Valuedness and Referentiality.Grzegorz Malinowski - 2013 - Logic and Logical Philosophy 22 (4):375-387.
Fregean Extensions of First‐Order Theories.John L. Bell - 1994 - Mathematical Logic Quarterly 40 (1):27-30.
Weakly Algebraizable Logics.Janusz Czelakowski & Ramon Jansana - 2000 - Journal of Symbolic Logic 65 (2):641-668.
Advances in the ŁΠ and Logics.Petr Cintula - 2003 - Archive for Mathematical Logic 42 (5):449-468.

Analytics

Added to PP index
2014-01-16

Total views
16 ( #642,886 of 2,448,697 )

Recent downloads (6 months)
4 ( #178,140 of 2,448,697 )

How can I increase my downloads?

Downloads

My notes