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Specifying and reasoning about uncertain agents Nivea de Carvalho Ferreira, Michael Fisher *, Wiebe van der Hoek Department of Computer Science, University of Liverpool, Liverpool L69 3BX, UK Available online

7 September

2007 Abstract Logical formalisation of agent behaviour is desirable, not only in order to provide a clear semantics of agent-based sys- tems, but also to provide the foundation for sophisticated reasoning techniques to be used on, and by, the agents them- selves.

The possible worlds semantics o?ered by modal logic has proved to be a successful framework in which to model mental attitudes of agents such as beliefs, desires and intentions. The most popular choices for modeling the informational attitudes involves annotating the agent with an S5-like logic for knowledge, or a KD45-like logic for belief. However, using these logics in their standard form, an agent cannot distinguish situations in which the evidence for a certain fact is '

equally distributed'

over its alternatives, from situations in which there is only one, almost negligible, counterexample to a '

fact'

. Probabilistic modal logics are a way to address this, but they easily end up being both computationally and conceptually complex, for example often lacking the property of compactness. In this paper, we propose a probabilistic modal logic PFKD45, in which the probabilities of the possible worlds range over a ?nite domain of values, while still allowing the agent to reason about in?nitely many options. In this way, the logic remains compact, implying that the agent still has to consider only ?nitely many possibilities for probability distributions during a reasoning task. We demonstrate a sound, compact and complete axiomatization for PFKD45 and show that it has several appealing features. Then, we discuss an implemented decision procedure for the logic, and provide a small example. ?

2007 Elsevier Inc. All rights reserved. Keywords: Agents;

Knowledge and belief;

Probabilistic modal logic;

Decision procedure 1. Introduction Agent technology is increasingly used in contemporary systems. The overall idea is that an agent aims at maximizing its performance, based on environmental evidence and its knowledge, or beliefs. In this context, the representation of beliefs plays an important role in the agent description. This is the reason why, when considering the agent'

s representation, the chosen formalism often characterises the agent'

s state of '

'

mind'

'

. 0888-613X/$ - see front matter ?

2007 Elsevier Inc. All rights reserved. doi:10.1016/j.ijar.2007.08.003 * Corresponding author. E-mail addresses: niveacf@yahoo.com (N. de Carvalho Ferreira), MFisher@liverpool.ac.uk (M. Fisher), Wiebe.Van-Der-Hoek@ liverpool.ac.uk (W. van der Hoek). URLs: http://www.csc.liv.ac.uk/~michael (M. Fisher), http://www.csc.liv.ac.uk/~wiebe (W. van der Hoek). Available online at www.sciencedirect.com International Journal of Approximate Reasoning

49 (2008) 35C51 www.elsevier.com/locate/ijar And as a consequence, reasoning with beliefs (within that representation) becomes a crucial aspect for success- ful agent design. One possible approach to an agent'

s representation of knowledge (or belief) is the use of a formal language, whose syntax and semantics are precisely de?ned. In this way, a logical agent description and its associated semantics are consequently strongly linked. As information about the world may be vague, imperfect, uncer- tain, or ambiguous, agents should be able to represent and reason under uncertainty in order to operate in such an environment. By considering interaction with the '