Modelling Communicating Agents in Timed Reasoning Logics Natasha Alechina, Brian Logan, and Mark Whitsey School of Computer Science and IT, University of Nottingham, UK. (nza,mtw,bsl)@cs.nott.ac.uk Abstract. Practical reasoners are resource-bounded—in particular they require time to derive consequences of their knowledge. Building on the Timed Reason- ing Logics (TRL) framework introduced in [1], we show how to represent the time required by an agent to reach a given conclusion. TRL allows us to model the kinds of rule application and conflict resolution strategies commonly found in rule-based agents, and we show how the choice of strategy can influence the information an agent can take into account when making decisions at a particular point in time. We prove general completeness and decidability results for TRL, and analyse the impact of communication in an example system consisting of two agents which use different conflict resolution strategies. 1 Introduction Most research in logics for belief, knowledge and action (see, for example, [2–11]) makes the strong assumption that whatever reasoning abilities an agent may have, the results of applying those abilities to a given problem are available immediately. For example, if an agent is capable of reasoning from its observations and some restricted set of logical rules, it derives all the consequences of its rules instantaneously. While this is a reasonable assumption in some situations, there are many cases where the time taken to do deliberation is of critical importance. Practical agents take time to derive the consequences of their beliefs, and, in a dynamic environment, the time required by an agent to derive the consequences of its observations will determine whether such derivations can play an effective role in action selection. Another example involves more standard analytical reasoning and a classical domain for the application of epistemic logics: verifying cryptographic protocols. An agent intercepting a coded message usually has all the necessary “inference rules” to break the code. The only problem is that if the encoding is decent, it would take the intercepting agent millen- nia to actually derive the answer. On the other hand, if the encryption scheme is badly designed or the key length is short, the answer can be derived in an undesirably short period of time. The kind of logical results we want to be able to prove are therefore of the form agent i is capable of reaching conclusion φ within time bound t. In this paper we show how to model the execution of communicating rule-based agents using Timed Reasoning Logics (TRL). TRL is a context-logic style formalism for describing rule-based resource bounded reasoners who take time to derive the conse- quences of their knowledge. This paper builds on the work in [1], where we introduced