Neighborhood Semantics for Basic and Intuitionistic Logic

• Authors: Moniri Morteza , Maleki Fatemeh Shirmohammadzadeh
• Languages of publication: EN

Abstracts

EN

In this paper we present a neighborhood semantics for Intuitionistic Propositional Logic (IPL). We show that for each Kripke model of the logic there is a pointwise equivalent neighborhood model and vice versa. In this way, we establish soundness and completeness of IPL with respect to the neighborhood semantics. The relation between neighborhood and topological semantics are also investigated. Moreover, the notions of bisimulation and n-bisimulation between neighborhood models of IPL are defined naturally and some of their basic properties are proved. We also consider Basic Propositional Logic (BPL), a logic weaker than IPL introduced by Albert Visser, and introduce and study its neighborhood models in the same manner.

Keywords

EN

Intuitionistic Logic; Basic Logic; Kripke models; neighborhood models; bisimulation; modal logic; topological semantics

• Publisher: Uniwersytet Mikołaja Kopernika (Nicolaus Copernicus University in Toruń)
• Journal: Logic and Logical Philosophy
• Year: 2015
• Volume: 24
• Issue: 3
• Pages: 339–355

Dates

published

2015-09-01

online

2015-08-20

Contributors

author

Moniri Morteza

• Department of Mathematics, Shahid Beheshti University G. C., Evin, Tehran, Iran

author

Maleki Fatemeh Shirmohammadzadeh

• Department of Mathematics, Shahid Beheshti University G. C., Evin, Tehran, Iran

References

• Bezhanishvili, N., and W. Hoek, “Structures for epistemic logic”, Chapter 12 in Johan van Benthem on Logic and Information Dynamics, Springer. DOI: 10.1007/978-3-319-06025-5_12
• Chellas, B., Modal Logic: An Introduction, Cambridge University Press, Cambridge, 1980.
• Johnstone, P., Stone Spaces, Cambridge University Press, 1982.
• Hansen, H.H., “Monotonic modal logics”, Master thesis, University of Amsterdam, 2003.
• Kruszelnicka, M., “A note on bisimulations of finite Kripke models”, Bulletin of the Section of Logic, 41 (2012): 185–198.
• Montague, R., “Universal grammar”, Theoria, 36, 3 (1970): 373–398. DOI: 10.1111/j.1755-2567.1970.tb00434.x
• Ruitenburg, W., “Constructive logic and the paradoxes”, Modern Logic, 1, 4 (1991): 271–301.
• Scott, D.S., “Advice on modal logic”, Chapter 7 in Philosophical Problems in Logic, K. Lambert (ed.), D. Reidel Publishing Company, 1970. DOI: 10.1007/978-94-010-3272-8_7
• van Dalen, D., Logic and Structure, Fourth Edition, Springer, 2004. DOI: 10.1007/978-3-540-85108-0
• Visser, A., “A propositional logic with explicit fixed points”, Studia Logica, 40, 2 (1981): 155–175. DOI: 10.1007/BF01874706

Identifiers

DOI

10.12775/LLP.2015.015