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

Stit logic of justification announcements: a completeness result

“…As an obvious corollary of Theorem 2 we get the compactness property. Thus, building up on an earlier work on justification stit formalisms, we have defined the explicit fragment of basic jstit logic introduced in [9]. For this logic we have presented a strongly complete axiomatization which is stable relative to extensions with constant specifications.…”

“…Basic justification stit (or jstit, for short) logic was introduced in [9] as an environment for analysis of doxastic actions related to proving activity within a somewhat idealized community of agents. This logic combines expressive means of stit logic by N. Belnap et al [4] with those of justification logic by S. Artemov et al [2].…”

“…In order to represent the proving activity of agents under the above-described set of assumptions, basic jstit logic features a set of four new modalities which were called in [9] proving modalities. Proving modalities capture four different modes in which one can speak about proving activity of an agent.…”

Justification announcements in discrete time. Part II: Frame definability results

“…Due to space limitations, we skip the explanation of the intuitions behind jstit models. The interested reader may find such an explanation either in Section 2 of Part I of this paper, or in [7,Section 3].…”

Restricted Interpolation and Lack Thereof in Stit Logic

“…More recently emerged the attempts to enrich stit logic with other types of operators, e.g. the ones borrowed from temporal logic (see, e.g., [9]) or justification logic (see, e.g., [10] and [11]). Sometimes these attempts were intertwined with attempts to recast the stit semantics itself so as to make it more suitable for the enrichment in question.…”