A Framework for Uncertain Agents
Nivea de C. Ferreira∗, Michael Fisher and Wiebe van der Hoek
Department of Computer Science, University of Liverpool
Peach Street, Chadwick Building, L69 3BX, Liverpool - UK
{niveacf, michael, wiebe}@csc.liv.ac.uk
Our work focuses on the formal representation and verification of agent systems. In those, representation of information and knowledge of the agents is crucial. One of the leading logical approaches to do this is using a modal epistemic logic (cf. [Meyer and van der Hoek 95]), which has
a well-defined and clear semantics, suitable for modeling various other attitudes of agents as well
as time ([Rao and Georgeff 95]). It also permits logical verification tools to be used for analysing
a specification. Furthermore, direct execution of logical statements provides an implementation of
an agent’s behaviour, which is a means of bridging the gap between an agent’s theory and its implementation, something that is not always present in contemporary agent programming frameworks
[Bradshaw et al. 99].
In real world applications however, it is not enough to just specify whether or not the agent knows
something: often, an agent has to make a decision under circumstances where he is not absolutely sure
about the pre-conditions for his actions. It is then necessary to have a more fine-tuned mechanism to
deal with uncertain information. This allows one to express that, although the agent is not sure about a
particular condition, he has a bias to assume certain states of affairs, if only to decide he has to obtain
more information. Environments are usually unpredictable, and an agent may also interact with other
unpredictable entities, like other agents [Halpern 03]. Therefore, it is important to have formalisms
that incorporate uncertainty.
It is in the context of executable frameworks for agents that deal with uncertain information in
which our project is situated. In short, our aim is to develop a powerful, although simple, logical
language that allow agents to represent uncertainty with respect to their beliefs. More specifically, the
main idea is combining an existent temporal framework, M ETATE M, and a recently specified probabilistic language, PF KD45. Together those systems describe the framework we refer as P ROT EM.
In the M ETATE M framework a representation of simple dynamic agents was considered [Fisher 95].
Later extensions include a representation of deliberation within agents, and agents that have beliefs
[Fisher and Ghidini 99]. However, there was no consideration of handling uncertainty. Our main aim
is extending the M ETATE M language, both in terms of its logical specification and its implementation,
using an appropriate logical formalism to incorporate uncertainty (associated to an agent’s beliefs).
The language we use for this purpose is PF KD45.
PF KD45 [de Carvalho Ferreira et al. 04] is a complete, compact and conceptually simple logical
approach to probabilistic reasoning that is useful for representing and reasoning about uncertainty
within computational agents. Its basic modal operator is Px> , where the meaning of Px> ϕ is: “ϕ
is believed to have a probability strictly greater than x”. A peculiar characteristic of PF KD45 is
that, although its syntax allows for an operator Px> for every rational number x, in the semantics it is
∗
Author gratefully acknowledges support by the Brazilian Government under CAPES-scholarship.
1
assumed that probabilities are only taken from a finite base F = {r0 , r1 , ..., rn } ⊆ [0, 1] ∩ Q. When
building models for the agent specification we only need to consider finitely many ones. It may be
important to highlight that this is not a real restriction, once an agent does not need an infinite set of
probability values in order to reason about uncertainty.
The basic idea underlying M ETATE M is building a model for an agent’s formulae. When including
beliefs, instead of generating a set of choices based only upon temporal rules, both temporal and belief
rules must be considered. This leads to the construction of belief contexts and (simulated) temporal
sequences. With the development of the decision procedure for the PF KD45 language, we have a
computational module whose output is the set of probability values that satisfy the set of probabilistic
beliefs given as input. That is, a number of possible values that can be explored when having the
belief contexts built.
An independent combination of those approaches creates what we have called P ROT EM. In other
words, P ROT EM is a fusion of M ETATE M and PF KD45 approaches, allowing us to maintain important properties of both logics. And, finally, the combined execution procedure builds the belief
contexts taking into consideration the temporal and probabilistic belief rules.
At this point of our research, we have the description of P ROT EM Logic, where its properties
include soundness, completeness and the finite model property. Correctness of its decision procedure
is another important result. Implementation of a PF KD45 decision procedure was produced as part
of this project, and combining it with the existing M ETATE M execution implementation is our next
step. We can then use this framework for describing an application that combines both temporal and
probabilistic beliefs follows. Although this PhD project is an ongoing research activity, consistent
description of the involved systems, as well as their algorithm implementations, lead us to state that
we will probably succeed in the attempt of providing a logical framework, P ROT EM, that allows the
representation and implementation of uncertain agents.
References
[Bradshaw et al. 99] J. Bradshaw, M. Greaves, H. Holmback, T. Karygiannis, B. Silverman, N. Suri,
and A. Wong. Agents for the Masses: Is it possible to make development of sophisticated agents
simple enough to be practical? IEEE Intelligent Systems, 14(2): 53–63, 1999.
[de Carvalho Ferreira et al. 04] N. de Carvalho Ferreira, M. Fisher, and W. van der Hoek. Practical
Reasoning for Uncertain Agents. In Proc. Ninth European Conf. on Logics in Artificial Intelligence
(JELIA), pages 82–94, 2004.
[Fisher and Ghidini 99] M. Fisher and C. Ghidini. Programming Resource-Bounded Deliberative
Agents. In Proc. International Joint Conf. on Artificial Intelligence (IJCAI), pages 200–206. Morgan Kaufmann, 1999.
[Fisher 95] M. Fisher. Representing and Executing Agent-Based Systems. In M. Wooldridge and
N. R. Jennings, editors, Intelligent Agents, pages 307–323. Springer-Verlag, 1995.
[Halpern 03] J. Y. Halpern. Reasoning About Uncertainty. MIT Press, 2003.
[Meyer and van der Hoek 95] J.-J. Ch. Meyer and W. van der Hoek. Epistemic Logic for AI and
Computer Science. Cambridge University Press: Cambridge, England, 1995.
[Rao and Georgeff 95] A. S. Rao and M. Georgeff. BDI Agents: from Theory to Practice. In Proc.
ICMAS, pages 312–319, 1995.
2