Agents as Reasoners, Observers, or Arbitrary Believers

The work described in this paper aims at the definition of a general framework for the formal specification of agents’ beliefs in a multiagent environment. The basic idea is to model both agents’ beliefs and the view that each agent has of other agents’ beliefs as logical theories. Consider an agent as having beliefs only about the world. At a very abstract level, ai’s beliefs can be modeled by a reasoner defined as a pair (Li, ~): L~ is the language of the reasoner and 7~ are the be/iefs of the reasoner (in the following, we abbreviate s reasoner (Li, 2~) with R~). assume that a~ has beliefs about an agent aj and that aj has only beliefs about the world. This situation can be easily modeled introducing two other reasoners Rj, R~j --modeling aj’s beliefs and at’s beliefs about aj respectively m and extending R~ signature with a unary predicate tP, used to express a~’s beliefs about aj. R0 thus plays the role of as’s (mental) representation of aj. R4, R0 and i~ characterize a badc belief system, defined as (R4, Rij)w: R~ is the observer, R4j is the observed reasoner and the parameter B$ is the belief predicate of the basic belief system. Suppose that also aj has beliefs about another agent at. We model ai’s beliefs as a reasoner /~, ai’s beliefs about aj as a reasoner R0 and ai’s beliefs about aj’s beliefs about at as a reasoner Rijk. R~ observes P~j and/~j observes Rijh. From this example, it is easy to see how to represent an agent with arbitrary beliefs with a family of reasoners, in which each reasoner is possibly observing other reasoners. Such configurations of reasoners are described with "belief systems". Formally, if I is a set of indices (each corresponding to a reasoner), a belief system is a pair ({R~Jiel, B) where {Ri)j~! a family of reasoners and B is an n-tuple of binary relatious over I. If (i, j) is an element of the k-th binary relation then/~ observes Rj and expresses its beliefs about Rj using a Bk predicate (we thus assume that to the k-th binary relation there corresponds a unary predicate Bi). Following (Giunchiglia etal. 1993), say that R~ is an ideal reasoner if 2~ is closed under logical consequence. Analogously, we say that P~ is a B’-ideal observer of Rj if 2~ {A I B’("A") E 2~}. Notice that the two notions of ideal reasoner and ideal observer are independent. For instance, an ideal observer may be at the same time a real reasoner. Consider a belief system ({P~}iel, B). Both the language L~ and the beliefs 2} (i E I) of each reasoner can be eztenaionally characterized as sets of formulae satisfying certain conditions. However, a belief system can be also intensionally characterized by multi context systems (Giunchiglia & Serafini 1994). multi context system or MCsystem is a pair ({C~}~GI, BR), where {Ci}iGI is a family of axiomatic formal systems (that we call contexts) and BR is a set of bridge rules, i.e. inference rules having premises and conclnsion in distinct contexts. Notationally, we write (A, C~) indicate the formula A in the context C,.