Inference as Doxastic Agency. Part I: The Basics of Justification Stit Logic

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 (Belnap et al. in Facing the future: agents and choices in our indeterminist world, Oxford University Press, New York, 2001) and the semantics of the epistemic logic with justification from (Artemov and Nogina in Journal of Logic and Computation 15:1059-1073, 2005). The general idea is to understand proving that A as seeing to it that a proof of A is (publicly) 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.