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Relational and partial variable sets and basic predicate logic

Published online by Cambridge University Press:  12 March 2014

Silvio Ghilardi  and
Giancarlo Meloni
Silvio Ghilardi
Affiliation:
Dipartimento di Matematica, Universita' Degli Studi di Milano, Via C. Saldini 50, 20133 Milano, Italy, E-mail: ghilardi@vmimat.mat.unimi.it
Giancarlo Meloni
Affiliation:
Dipartimento di Matematica, Universita' Degli Studi di Milano, Via C. Saldini 50, 20133 Milano, Italy, E-mail: meloni@vmimat.mat.unimi.it
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 61 , Issue 3 , September 1996 , pp. 843 - 872
Copyright
Copyright © Association for Symbolic Logic 1996

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References

REFERENCES

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