We investigate an axiomatization of the notion of common belief (knowledge) that makes use of no rules of inference (apart from Modus Ponens and Necessitation) and highlight the property of the set of accessibility relations that characterizes each axiom.
On the logic of conscious belief
β Scribed by Marek Tokarz
- Publisher
- Springer Netherlands
- Year
- 1990
- Tongue
- English
- Weight
- 581 KB
- Volume
- 49
- Category
- Article
- ISSN
- 0039-3215
No coin nor oath required. For personal study only.
β¦ Synopsis
In this paper we are discussing a version of propositional belief logic, denoted by LB, in which so-called axioms of introspection (Be =-BBc~ and ~ Be = B ~ Be) are added to the usual ones. LB is proved to be sound and complete with,respect to Boolean algebras equipped with proper filters (Theorem 5). Interpretations in classical theories (Theorem 4) are also considered. A few modifications of LB are ,further dealt with, one of which turns out to be $5.
π SIMILAR VOLUMES
The logic of common belief does not always reflect that of individual beliefs. In particular, even when the individual belief operators satisfy the KD45 logic, the common belief operator may fail to satisfy axiom 5. That is, it can happen that neither is A commonly believed nor is it common belief t
In this paper we survey formal techniques for the study of reasoning about knowledge and belief, and consider their application in the areas of distributed computing and nonmonotonic reasoning.