A General Approach to Multi-agent Minimal Knowledge

  • Authors:

  • Wiebe van der Hoek;Jan Jaspars;Elias Thijsse

  • Affiliations:

  • -;-;-

  • Venue:
  • JELIA '00 Proceedings of the European Workshop on Logics in Artificial Intelligence
  • Year:
  • 2000

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Abstract

We extend our general approach to characterizing information to multi-agent systems. In particular, we provide a formal description of an agent's knowledge containing exactly the information conveyed by some (honest) formula ϕ. Only knowing is important for dynamic agent systems in two ways. First of all, one wants to compare different states of knowledge of an agent and, secondly, for agent a's decisions, it may be relevant that (he knows that) agent b does not know more than ϕ. There are three ways to study the question whether a formula ϕ can be interpreted as minimal information. The first method is semantic and inspects 'minimal' models for ϕ (with respect to some order ≤ on states). The second one is syntactic and searches for stable expansions, minimal with respect to some language L*. The third method is a deductive test, known as the disjunction property. We present a condition under which the three methods are equivalent. Then, we show how to construct the order ≤ by collecting 'layered orders'. We then focus on the multi-agent case and identify languages L* for several orders ≤, and show how they yield different notions of honesty for different multi-modal systems. Finally, some consequences of the different notions are discussed.