A logic for suspicious players : epistemic actions and belief-update in games
In this paper, we introduce a notion of ``epistemic action'' to describe changes in the information states of the players in a game. For this, we use ideas that we have developed in our previous papers [BMS], [BMS2] and [B], enriching them to cover, not just purely epistemic actions, but also fact-changing actions (``real moves'', e.g. choosing a card, exchanging cards etc.) and nondeterministic actions and strategies (conditional actions having knowledge tests as conditions). We consider natural operations with epistemic actions and we use them to describe significant aspects of the interaction between beliefs and actions in a game. For this, we use a logic that combines in a specific way a multi-agent epistemic logic with a dynamic logic of ``epistemic actions''. We give (without proof) a complete and decidable proof system for this logic. As an application, we analyze a specific example of a dialogue game (a version of the Muddy Children Puzzle, in which some of the children can ``cheat'' by engaging in secret communication moves, while others may be punished for their credulity). We also present a sketch of a ``rule-based'' approach to games with imperfect information(allowing ``sneaky'' possibilities, such as: cheating, being deceived and suspecting the others to be cheating).
|Distributed Systems (acm C.2.4), CODING AND INFORMATION THEORY (acm E.4), Mathematical Logic (acm F.4.1), Knowledge Representation Formalisms and Methods (acm I.2.4)|
|Philosophical and critical (msc 03A05), Logics of knowledge and belief (including belief change) (msc 03B42), Modal logic (including the logic of norms) (msc 03B45), Logic in computer science (msc 03B70), Logic in artificial intelligence (msc 68T27), Knowledge representation (msc 68T30), Reasoning under uncertainty (msc 68T37), Rationality, learning (msc 91A26), Signaling, communication (msc 91A28), Game-theoretic models (msc 91A40)|
|Software Engineering [SEN]|
Baltag, A. (2000). A logic for suspicious players : epistemic actions and belief-update in games. Software Engineering [SEN]. CWI.