Abstract
A soundness proof for an axiomatization of common belief in minimal neighbourhood semantics is provided, thereby leaving aside all assumptions of monotonicity in agents’ reasoning. ‘Minimality’ properties of common belief are thus emphasized, in contrast to the more usual ‘fixed point’ properties. The proof relies on the existence of transfinite fixed points of sequences of neighbourhood systems even when they are not closed under supersets. Obvious shortcoming of the note is the lack of a completeness proof.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Lismont, L.: 1993, ‘La connaisance commune en logique modal’,Mathematical Logic Quarterly,39, 115–130.
Lismont, L. and Mongin, P.: 1994a, ‘On the logic of common belief and common knowledge’,Theory and Decision,37, 75–106.
Lismont, L. and Mongin, P.: 1994b, ‘A non-minimal but very weak axiomatization of common belief’,Artificial Intelligence,70, 363–374.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ferrante, V. A sound interpretation of minimality properties of common belief in minimal semantics. Theor Decis 41, 179–185 (1996). https://doi.org/10.1007/BF00134643
Issue Date:
DOI: https://doi.org/10.1007/BF00134643