You can manage bookmarks using lists, please log in to your user account for this.
Media type:
E-Article
Title:
Cylindric Modal Logic
Contributor:
Venema, Yde
imprint:
Association for Symbolic Logic, Inc., 1995
Published in:The Journal of Symbolic Logic
Language:
English
ISSN:
0022-4812
Origination:
Footnote:
Description:
<p>Treating the existential quantification ∃ν<sub>i</sub> as a diamond <tex-math>$\diamond_i$</tex-math> and the identity ν<sub>i</sub> = ν<sub>j</sub> as a constant δ<sub>ij</sub>, 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].</p>