Abstract not found

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,

It is well known that many two-dimensional products of modal logics with at least one `transitive' (but not `symmetric') component lack the product finite model property. Here we show that products of two `transitive' logics (such as, e.g., K4 K4, S4 S4, GrzGrz and GLGL) do not have the (abstract) finite model property either. These are the first known examples of 2D modal product logics without the finite model property where both components are natural unimodal logics having the finite model property.

Abstract not found