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Changing and using beliefs under incomplete information

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Jamroga W.

Prace Instytutu Podstaw Informatyki Polskiej Akademii Nauk

2001

tom Nr 928

31-36

The concept being proposed here is to use prototype semantics to represent an agent's belief state. Prototype semantics is a linguistic theory that emerged in the 1980s - the key idea is to describe the meaning of an utterance, or a notion, by defining the prototype (the most typical example to which the notion refers) and the extension rules describing 'family resemblances' between various entities and, in consequence, allowing to derive less typical instances from more typical ones. The intuition behind this paper is that in situations of incomplete information such a representation of the agent's knowledge may be easier to deal with than a straightforward probabilistic representation - especially when belief changes are not necessarily monotonic, and informations being acquired by the agent may be vague themselves. Moreover, when an exhaustive search through all the possibilities is impossible the agent may benefit from analyzing the typical situations instead of random ones. This property was tested for a family of games with incomplete information on binary trees.

Agents that Know How to Play

100%

Jamroga W. , Van der Hoek W.

Fundamenta Informaticae

2004

tom Vol. 63, nr 2,3

185--219

We look at ways to enrich Alternating-time Temporal Logic (ATL) - a logic for specification and verification of multi-agent systems - with a notion of knowledge. Starting point of our study is a recent proposal for a system called Alternating-time Temporal Epistemic Logic (ATEL). We show that, assuming that agents act under uncertainty in some states of the system, the notion of allowable strategy should be defined with some caution. Moreover, we demonstrate a subtle difference between an agent knowing that he has a suitable strategy and knowing the strategy itself. We also point out that the agents should be assumed similar epistemic capabilities in the semantics of both strategic and epistemic operators. Trying to implement these ideas, we propose two different modifications of ATEL. The first one, dubbed Alternating-time Temporal Observational Logic (ATOL), is a logic for agents with bounded recall of the past. With the second, ATEL-R*, we present a framework to reason about both perfect and imperfect recall, in which we also incorporate operators for reasoning about the past. We identify some feasible subsystems of this expressive system.