Contextual Deduction Theorems

Studia Logica 99 (1-3):279-319 (2011)
Abstract
Logics that do not have a deduction-detachment theorem (briefly, a DDT) may still possess a contextual DDT —a syntactic notion introduced here for arbitrary deductive systems, along with a local variant. Substructural logics without sentential constants are natural witnesses to these phenomena. In the presence of a contextual DDT, we can still upgrade many weak completeness results to strong ones, e.g., the finite model property implies the strong finite model property. It turns out that a finitary system has a contextual DDT iff it is protoalgebraic and gives rise to a dually Brouwerian semilattice of compact deductive filters in every finitely generated algebra of the corresponding type. Any such system is filter distributive, although it may lack the filter extension property. More generally, filter distributivity and modularity are characterized for all finitary systems with a local contextual DDT, and several examples are discussed. For algebraizable logics, the well-known correspondence between the DDT and the equational definability of principal congruences is adapted to the contextual case
Keywords Deductive system  deduction-detachment theorem  protoalgebraic  algebraizable  quasivariety  EDPC  distributive  modular  substructural logics
Categories (categorize this paper)
DOI 10.1007/s11225-011-9353-z
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history
Request removal from index
Download options
Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 26,162
Through your library
References found in this work BETA
A Survey of Abstract Algebraic Logic.J. M. Font, R. Jansana & D. Pigozzi - 2003 - Studia Logica 74 (1-2):13 - 97.
Protoalgebraic Logics.Janusz Czelakowski - 2001 - Kluwer Academic Publishers.
Protoalgebraic Logics.W. J. Blok & Don Pigozzi - 1986 - Studia Logica 45 (4):337 - 369.

View all 28 references / Add more references

Citations of this work BETA
The Simplest Protoalgebraic Logic.Josep Maria Font - 2013 - Mathematical Logic Quarterly 59 (6):435-451.
Almost Structural Completeness; an Algebraic Approach.Wojciech Dzik & Michał M. Stronkowski - 2016 - Annals of Pure and Applied Logic 167 (7):525-556.

Add more citations

Similar books and articles
Algebraic Aspects of Deduction Theorems.Janusz Czelakowski - 1985 - Studia Logica 44 (4):369 - 387.
Local Deductions Theorems.Janusz Czelakowski - 1986 - Studia Logica 45 (4):377 - 391.
Filter Distributive Logics.Janusz Czelakowski - 1984 - Studia Logica 43 (4):353 - 377.
Protoalgebraic Logics.W. J. Blok & Don Pigozzi - 1986 - Studia Logica 45 (4):337 - 369.
Deliberating with Critical Friends.Shane Ralston - 2011 - Teaching Philosophy 34 (4):393-410.
Deduction Theorems for Weak Implicational Logics.M. W. Bunder - 1982 - Studia Logica 41 (2-3):95 - 108.
Algebraic Semantics for Deductive Systems.W. J. Blok & J. Rebagliato - 2003 - Studia Logica 74 (1-2):153 - 180.
Contextual Hidden Variables Theories and Bell's Inequalities.Abner Shimony - 1984 - British Journal for the Philosophy of Science 35 (1):25-45.

Monthly downloads

Added to index

2011-08-27

Total downloads

7 ( #516,344 of 2,152,522 )

Recent downloads (6 months)

2 ( #281,162 of 2,152,522 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Order:
There  are no threads in this forum
Nothing in this forum yet.

Other forums