Inference as doxastic agency. Part II: Ramifications and refinements

Justification stit logic is a logic for reasoning about proving as a certain kind of activity, namely seeing to it that a proof is publicly available. It merges the semantical analysis of deliberatively seeing-to-it-that from stit theory (Belnap, Perloff, Xu 2001) and the semantics of the epistemic logic with justification from (Artemov and Nogina 2005). In this paper, after recalling its language and basic semantical definitions, various ramifications and refinements of justification stit logic are presented and discussed: imposing natural restrictions upon the class of models under consideration, making use of modalities that assert the existence of a proof, introducing a variant of justification stit logic based on a semantics introduced by M. Fitting, and adding variable-binding operators and extending the set of proof polynomials.