Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-26T20:55:25.039Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected], [email protected]
Get access Rights & Permissions [Opens in a new window]

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 

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

BIBLIOGRAPHY

Blackburn, P., De Rijke, M., & Venema, Y. (2001). Modal Logic. Cambridge University Press. Cambridge, UK.CrossRefGoogle Scholar
Ebbinghaus, H.-D., Flum, J., & Thomas, W. (1984). Mathematical Logic (first edition). Springer. New York, NY.Google Scholar
van Benthem, J. (2010). Modal Logic for Open Minds. CSLI Publications. Stanford.Google Scholar
Visser, A., van Benthem, J., de Jongh, D., & Renardel de Lavalette, G. R. (1995). NNIL, a study in intuitionistic propositional logic. In Ponse, A., de Rijke, M., and Venemapp, Y., editors. Modal Logic and Process Algebra (Amsterdam, 1994), Vol. 53 of CSLI Lecture Notes. Stanford, CA: CSLI Publications, pp. 289–326.Google Scholar