In this paper we consider logical inference as an activity that results in proofs and hence produces knowledge. We suggest to merge the semantical analysis of deliberatively seeing-to-it-that from stit theory and the semantics of the epistemic logic with justification from. The general idea is to understand proving that A as seeing to it that a proof of A is available. We introduce a semantics of various notions of proving as an activity and present a number of valid principles that (...) relate the various notions of proving to each other and to notions of justified knowledge, implicit knowledge, and possibility. We also point out and comment upon certain principles our semantics fails to validate. (shrink)

In Part I of this paper we presented a Hilbert-style system $\Sigma _D$ axiomatizing stit logic of justification announcements interpreted over models with discrete time structure. In this part, we prove three frame definability results for $\Sigma _D$ using three different definitions of a frame plus another version of completeness result.

We consider the propositional logic equipped withChellas stitoperators for a finite set of individual agents plus the historical necessity modality. We settle the question of whether such a logic enjoys restricted interpolation property, which requires the existence of an interpolant only in cases where the consequence contains no Chellas stit operators occurring in the premise. We show that if action operators count as logical symbols, then such a logic has restricted interpolation property iff the number of agents does not exceed (...) three. On the other hand, if action operators are considered to be nonlogical symbols, then the restricted interpolation fails for any number of agents exceeding one. It follows that unrestricted Craig interpolation also fails for almost all versions of stit logic. (shrink)