A Strong Completeness Theorem for the Gentzen systems associated with finite algebras

Journal of Applied Non-Classical Logics 9 (1):9-36 (1999)
  Copy   BIBTEX


ABSTRACT In this paper we study consequence relations on the set of many sided sequents over a propositional language. We deal with the consequence relations axiomatized by the sequent calculi defined in [2] and associated with arbitrary finite algebras. These consequence relations are examples of what we call Gentzen systems. We define a semantics for these systems and prove a Strong Completeness Theorem, which is an extension of the Completeness Theorem for provable sequents stated in [2]. For the special case of the finite linear MV-algebras, the Strong Completeness Theorem was proved in [10], as a consequence of McNaughton's Theorem. The main tool to prove this result for arbitrary algebras is the deduction-detachment theorem for Gentzen systems.



    Upload a copy of this work     Papers currently archived: 74,429

External links

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

Through your library

Similar books and articles

On Weak and Strong Interpolation in Algebraic Logics.Gábor Sági & Saharon Shelah - 2006 - Journal of Symbolic Logic 71 (1):104 - 118.
The Abstract Variable-Binding Calculus.Don Pigozzi & Antonino Salibra - 1995 - Studia Logica 55 (1):129 - 179.
On Finite-Valued Propositional Logical Calculi.O. Anshakov & S. Rychkov - 1995 - Notre Dame Journal of Formal Logic 36 (4):606-629.
Interpretability Over Peano Arithmetic.Claes Strannegård - 1999 - Journal of Symbolic Logic 64 (4):1407-1425.
Cylindric Modal Logic.Yde Venema - 1995 - Journal of Symbolic Logic 60 (2):591-623.
A Completeness Theorem for Higher Order Logics.Gábor Sági - 2000 - Journal of Symbolic Logic 65 (2):857-884.


Added to PP

23 (#495,906)

6 months
1 (#417,143)

Historical graph of downloads
How can I increase my downloads?

References found in this work

Theory of Logical Calculi: Basic Theory of Consequence Operations.Ryszard Wójcicki - 1988 - Dordrecht, Boston and London: Kluwer Academic Publishers.
A Theorem About Infinite-Valued Sentential Logic.Robert McNaughton - 1951 - Journal of Symbolic Logic 16 (1):1-13.
Algebraic Aspects of Deduction Theorems.Janusz Czelakowski - 1985 - Studia Logica 44 (4):369 - 387.
Elimination of Cuts in First-Order Finite-Valued Logics.Matthias Baaz, Christian G. Fermüller & Richard Zach - 1993 - Journal of Information Processing and Cybernetics EIK 29 (6):333-355.
A Theorem About Infinite-Valued Sentential Logic.Robert Mcnaughton - 1951 - Journal of Symbolic Logic 16 (3):227-228.

View all 7 references / Add more references