Journal of Symbolic Logic

Relational and Partial Variable Sets and Basic Predicate Logic

Silvio Ghilardi and Giancarlo Meloni

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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.

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

First available in Project Euclid: 6 July 2007

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Ghilardi, Silvio; Meloni, Giancarlo. Relational and Partial Variable Sets and Basic Predicate Logic. J. Symbolic Logic 61 (1996), no. 3, 843--872.

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