×

Inference as doxastic agency. II: Ramifications and refinements. (English) Zbl 1422.03026

Summary: 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 [N. D. Belnap, M. Perloff, M. Xu, Facing the future: agents and choices in our indeterminist world. New York: Oxford Univ. Press (2001)] and the semantics of the epistemic logic with justification from [S. Artemov and E. Nogina, J. Log. Comput. 15, No. 6, 1059–1073 (2005; Zbl 1088.03015)]. 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 [Ann. Pure Appl. Logic 152, No. 1–3, 67–83 (2008; Zbl 1133.03008)], and adding variable-binding operators and extending the set of proof polynomials.
For Part I see [the authors, Stud. Log. 107, No. 1, 167–194 (2019; Zbl 07055416)].

MSC:

03B42 Logics of knowledge and belief (including belief change)
03B40 Combinatory logic and lambda calculus
PDFBibTeX XMLCite
Full Text: Link