The aim of this paper is to give new kinds of modal logics suitable for reasoning about regions in discrete spaces. We call them dynamic logics of the region-based theory of discrete spaces. These modal logics are linguistic restrictions of propositional dynamic logic with the global diamond E. Their formulas are equivalent to Boolean combinations of modal formulas like E(A ∧ ⟨α⟩ B) where A and B are Boolean terms and α is a relational term. Examining what we can say (...) about dynamic models when we use formulas to describe them, we successively address the axiomatization/completeness issue and the decidability/complexity issue of our dynamic logics of the region-based theory of discrete spaces. (shrink)

We fine tune the distinction between the possible and what can be, mention some of the consequences and argue that the difference between material and logical implication is that of between what can be and what could have been.

Alex Blum ABSTRACT: We argue that the part of the future which is up to us is in principle unknowable. Download PDF.

We contend that a very seductive argument for theological fatalism fails. In the course of our discussion we point out that theological fatalism is incompatible with the existence of a being who is omnipotent, omniscient and infallible. We suggest that ‘possible’ formalized as ‘◊’ is to be understood as ‘can or could have been’ and not simply as ‘can’. The argument we discuss conflates the two. We end by rounding out, hope-fully, some left over corners of serious concern to the (...) theist. (shrink)