A Logic of Finite Syntactic Epistemic States
Thomas Ågotnes · 2004
The thesis presents a logic of the explicit knowledge of deliberative agents who represent their knowledge symbolically as sets of formulae – agents with finite syntactic epistemic states. It is well known that modal epistemic logic either describes implicit knowledge, including all logical consequences of the explicit knowledge, or describes the explicit knowledge of unrealistically intelligent and powerful agents, but does not describe the explicit knowledge of real agents. A source of this problem is the failure to separate the concepts of explicit knowledge and reasoning. The logic in this thesis consists of two parts. The first is a logic of explicit syntactic knowledge, with no closure conditions, which can be viewed as knowledge at a given point in time. Although this is a simple concept, the meta-language is expressive enough to allow the development of an interesting theory of static finite syntactic epistemic states. The second part is a logic of the evolving explicit syntactic knowledge of agents who have reasoning and communication mechanisms in addition to syntactical storage, i.e. about how the epistemic states can change over time as a result of reasoning and/or communication. The language introduces expressions for knowing a rule, analogue to knowing a formula. Instead of the usual closure conditions on knowledge it is possible to express the fact that if an agent knows some formulae and he knows a certain rule, then he may get to know a conclusion if he chooses to. This model is based on Alternating-time Temporal Logic (ATL). It differs from related epistemic logics based on ATL in that it models explicit instead of implicit knowledge and in the expressiveness of rule operators. It differs from related models of evolving explicit knowledge in that it allows reasoning in terms of possible futures, cooperation and strategies.