Cylindric modal logic

Journal of Symbolic Logic 60 (2):591-623 (1995)
  Copy   BIBTEX

Abstract

Treating the existential quantification ∃ν i as a diamond $\diamond_i$ and the identity ν i = ν j as a constant δ ij , we study restricted versions of first order logic as if they were modal formalisms. This approach is closely related to algebraic logic, as the Kripke frames of our system have the type of the atom structures of cylindric algebras; the full cylindric set algebras are the complex algebras of the intended multidimensional frames called cubes. The main contribution of the paper is a characterization of these cube frames for the finite-dimensional case and, as a consequence of the special form of this characterization, a completeness theorem for this class. These results lead to finite, though unorthodox, derivation systems for several related formalisms, e.g. for the valid n-variable first order formulas, for type-free valid formulas and for the equational theory of representable cylindric algebras. The result for type-free valid formulas indicates a positive solution to Problem 4.16 of Henkin, Monk and Tarski [16]

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 89,764

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
247 (#72,937)

6 months
7 (#174,092)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Yde Venema
University of Amsterdam

Citations of this work

Multi-dimensional modal logic.Maarten Marx - 1997 - Boston, Mass.: Kluwer Academic Publishers. Edited by Yde Venema.
A Simple Logic of Functional Dependence.Alexandru Baltag & Johan van Benthem - 2021 - Journal of Philosophical Logic 50 (5):939-1005.
Non-finite-axiomatizability results in algebraic logic.Balázs Biró - 1992 - Journal of Symbolic Logic 57 (3):832 - 843.

View all 24 citations / Add more citations

References found in this work

Algebraizable Logics.W. J. Blok & Don Pigozzi - 2022 - Advanced Reasoning Forum.
Modal Logic.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2001 - Studia Logica 76 (1):142-148.
Varieties of complex algebras.Robert Goldblatt - 1989 - Annals of Pure and Applied Logic 44 (3):173-242.
The modal logic of inequality.Maarten de Rijke - 1992 - Journal of Symbolic Logic 57 (2):566-584.

View all 13 references / Add more references