Journal of Symbolic Logic

Relational and Partial Variable Sets and Basic Predicate Logic

Silvio Ghilardi and Giancarlo Meloni

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Abstract

In this paper we study the logic of relational and partial variable sets, seen as a generalization of set-valued presheaves, allowing transition functions to be arbitrary relations or arbitrary partial functions. We find that such a logic is the usual intuitionistic and co-intuitionistic first order logic without Beck and Frobenius conditions relative to quantifiers along arbitrary terms. The important case of partial variable sets is axiomatizable by means of the substitutivity schema for equality. Furthermore, completeness, incompleteness and independence results are obtained for different kinds of Beck and Frobenius conditions.

Article information

Source
J. Symbolic Logic, Volume 61, Issue 3 (1996), 843-872.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183745080

Mathematical Reviews number (MathSciNet)
MR1412513

Zentralblatt MATH identifier
0860.03043

JSTOR
links.jstor.org

Citation

Ghilardi, Silvio; Meloni, Giancarlo. Relational and Partial Variable Sets and Basic Predicate Logic. J. Symbolic Logic 61 (1996), no. 3, 843--872. https://projecteuclid.org/euclid.jsl/1183745080


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