Diversity of Agents

Diversity of agents is investigated in the context of standard epistemic logic, dynamic information update, and belief revision. We provide a systematic discussion of different sources of diversities, such as introspection ability, powers of observation, memory capacity, and revision policies. In each case, we show how this diversity can be encoded in a logical system allowing for individual variation among rational agents. We conclude by raising some general issues concerning this view of a logic as a system for encoding a society of diverse agents and their interaction. 1 Diversity Inside Logical Systems Logical systems seem to prescribe one norm for an “idealized agent”. Any discrepancies with actual human behavior are then irrelevant, since the logic is meant to be normative, not descriptive. But logical systems would not be of much appeal if they did not have a plausible link with reality. And this is not just a matter of confronting one ideal norm with one kind of practical behavior. The striking fact is that human and virtual agents are not all the same: actual reasoning takes place in societies of diverse agents. This diversity shows itself particularly clearly in epistemic logic. There have been long debates about the appropriateness of various basic axioms, and they have to do with agents’ different powers. In particular, the modal Distribution Axiom has the following epistemic flavor: Example 1.1 Logical omniscience: K(φ → ψ) → (Kφ → Kψ). Do rational agents always know the consequences of what they know? Most philosophers deny this. There have been many attempts at bringing the resulting diversity into the logic as a legitimate feature of agents. Some authors have used “awareness” as a sort of restriction on short-term memory ([FH85]), others have concentrated on the stepwise dynamics of making inferences ([Kon88], [Dun95]). A well-informed up-to-date philosophical summary is found in [Egr04]. The next case for diversity lies in a different power of agents: Example 1.2 Introspection axioms: Kφ → KKφ, ¬Kφ → K¬Kφ. Do agents know when they know (or do not know)? Many philosophers doubt this, too. This time, there is a well-established way of incorporating different powers into the logic, using different accessibility relations between possible worlds in Kripke models. Accordingly, we get different modal logics: K , T , S4, or S5. Each of these modal logics can be thought of as describing one sort of agents. The interesting setting is then one of combinations. E.g., a combined language with two modalities K1, K2 describes a two-person society of introspectively different agents! This gives an interestingly different take on current logic combinations ([GS98], [KZ03]): the various ways of forming combined logics, by “fusions” S5+S4 or “products” S5 × S4, correspond to different assumptions about how the agents interact. Effects may be surprising here. E.g., later on, in our discussion of memory-free agents, we see that knowledge of memory-free agents behaves much like “universal modalities”. But in certain modal logic combinations, I would like to thank Johan van Benthem and three anonymous reviewers for their constructive comments that greatly improved this paper.