The appeal to possible worlds in the semantics of modal logic and the philosophical defense of possible worlds as an essential element of ontology have led philosophers and logicians to introduce other kinds of `worlds' in order to study various philosophical and logical phenomena. The literature contains discussions of `non-normal worlds', `non-classical worlds', `non-standard worlds', and `impossible worlds'. These atypical worlds have been used in the following ways: (1) to interpret unusual modal logics, (2) to distinguish logically equivalent propositions, (3) (...) to solve the problems associated with propositional attitude contexts, intentional contexts, and counterfactuals with impossible antecedents, and (4) to interpret systems of relevant and paraconsistent logic. However, those who have attempted to develop a genuine metaphysical theory of such atypical worlds tend to move too quickly from philosophical characterizations to formal semantics. (shrink)

In this paper non-normal worlds semantics is presented as a basic, general, and unifying approach to epistemic logic. The semantical framework of non-normal worlds is compared to the model theories of several logics for knowledge and belief that were recently developed in Artificial Intelligence (AI). It is shown that every model for implicit and explicit belief (Levesque), for awareness, general awareness, and local reasoning (Fagin and Halpern), and for awareness and principles (van der Hoek and Meyer) induces a non-normal worlds (...) model validating precisely the same formulas (of the language in question). (shrink)

Mark Balaguer argues for full blooded platonism (FBP), and argues that FBP alone can solve Benacerraf's familiar epistemic challenge. I note that if FBP really can solve Benacerraf's epistemic challenge, then FBP is not alone in its capacity so to solve; RFBP—really full blooded platonism—can do the trick just as well, where RFBP differs from FBP by allowing entities from inconsistent mathematics. I also argue briefly that there is positive reason for endorsing RFBP.

Information is often modelled as a set of relevant possibilities, treated as logically possible worlds. However, this has the unintuitive consequence that the logical consequences of an agent's information cannot be informative for that agent. There are many scenarios in which such consequences are clearly informative for the agent in question. Attempts to weaken the logic underlying each possible world are misguided. Instead, I provide a genuinely psychological notion of epistemic possibility and show how it can be captured in a (...) formal model, which I call a fan. I then show how to use fans to build formal models of being informed, as well as knowledge, belief and information update. (shrink)