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MODEL-THEORETIC CHARACTERIZATION OF INTUITIONISTIC PROPOSITIONAL FORMULAS

Published online by Cambridge University Press:  19 March 2013

GRIGORY K. OLKHOVIKOV
GRIGORY K. OLKHOVIKOV*
Affiliation:
Department of Philosophy, Ural Federal University
*
*DEPARTMENT OF PHILOSOPHY URAL FEDERAL UNIVERSITY 51 LENIN AVENUE, OFF 332 YEKATERINBURG RUSSIA 620083 E-mail: grigory.olkhovikov@usu.ru, grigory.olkhovikov@gmail.com
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Abstract

Notions of k-asimulation and asimulation are introduced as asymmetric counterparts to k-bisimulation and bisimulation, respectively. It is proved that a first-order formula is equivalent to a standard translation of an intuitionistic propositional formula iff it is invariant with respect to k-asimulations for some k, and then that a first-order formula is equivalent to a standard translation of an intuitionistic propositional formula iff it is invariant with respect to asimulations. Finally, it is proved that a first-order formula is equivalent to a standard translation of an intuitionistic propositional formula over the class of intuitionistic Kripke models iff it is invariant with respect to asimulations between intuitionistic models.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 6 , Issue 2 , June 2013 , pp. 348 - 365
Copyright
Copyright © Association for Symbolic Logic 2013 

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References

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