View-Based Explicit Knowledge

In the information based deenition of knowledge, an agent is said to know at a state s if is true in all states that look the same as s to that agent. However, in systems where an agent's view of the system is partial, even if a state s 0 may be logically indistinguishable from a state s, s 0 may not be visible from s. For instance, in a distributed system, all global states in which the agent's local state does not change look the same to that agent, but this set of global states may not be accessible because the agent may not even be aware of the existence of many agents in the network. We propose a logic of explicit knowledge built on agents' views and show it to be decidable. 1 A distinction 1.1 Basic logic of knowledge During the last decade, there has been extensive research into the notion of ascribing knowledge to reasoning agents, particularly in the contexts of distributed systems, artiicial intelligence and mathematical economics. The book FHMV95] provides an excellent summary of dominant themes in this line of research. Following Hintikka's logical treatment ((Hi62]), knowledge is studied as a modality in (typically) a propositional modal logic, with the semantics of formulas given in Kripke frames where the accessibility relation is an equivalence. Formally, we have a countable set of propositions P = fp 0 ; p 1 1 This paper is a revised and expanded version of R96b], prepared in honour of Rohit Parikh, on his 60th birthday.