Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-27T02:23:00.671Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected]
Giancarlo Meloni
Affiliation:
Dipartimento di Matematica, Universita' Degli Studi di Milano, Via C. Saldini 50, 20133 Milano, Italy, E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Ghilardi, S. and Meloni, G., Relative and absolute topological semantics for modal and basic predicate logic, in preparation.Google Scholar
[2]Ghilardi, S., Modal and temporal predicate logic: models in presheaves and categorical conceptualization, Categorical algebra and its applications (Borceux, F., editor), Springer LNM 1348, 1988, pp. 130–142.CrossRefGoogle Scholar
[3]Ghilardi, S., Relational and topological semantics for temporal and modal predicative logic, Atti del congresso ‘Nuovi problemi delta logica e delta filosofia delta scienza’ Viareggio, Gennaio 1990, vol. II - Logica, CLUEB Bologna, 1991, pp. 59–77.Google Scholar
[4]Gödel, K., Eine Interpretation des intuitionistischen Aussagenkalkiils, Ergebnisse eines mathematischen Kolloquiums, vol. 4 (1933), pp. 34–40.Google Scholar
[5]Lawvere, F. W., Equality in hyperdoctrines and the comprehension schema as an adjoint functor, Applications of categorical algebra, Proceedings of Symp. in Pure Math., XVII, 1970, pp. 1–14.Google Scholar