A Qualitative Theory of Cognitive Attitudes and their Change
This work addresses the problem of formalizing cognitive attitudes for qualitative decision theory, which is incremental as it builds on existing logical frameworks.
The authors developed a general logical framework to model agents' cognitive attitudes, such as knowledge, belief, and desire, and extended it with dynamic operators for belief and desire change, applying it to analyze single-stage games under incomplete information. They provided sound and complete axiomatizations for the basic logic and its extensions.
We present a general logical framework for reasoning about agents' cognitive attitudes of both epistemic type and motivational type. We show that it allows us to express a variety of relevant concepts for qualitative decision theory including the concepts of knowledge, belief, strong belief, conditional belief, desire, conditional desire, strong desire and preference. We also present two extensions of the logic, one by the notion of choice and the other by dynamic operators for belief change and desire change, and we apply the former to the analysis of single-stage games under incomplete information. We provide sound and complete axiomatizations for the basic logic and for its two extensions. The paper is under consideration in Theory and Practice of Logic Programming (TPLP).