Stit Semantics for Epistemic Notions Based on Information Disclosure in Interactive Settings

TL;DR

This paper develops a new stit logic framework to formalize four types of agentive knowledge related to information disclosure and responsibility in interactive settings, with soundness and completeness proofs.

Contribution

It introduces an extended stit logic with knowledge operators for formalizing various epistemic notions and clarifies their interpretation in responsibility attribution.

Findings

Defines four types of agentive knowledge in stit semantics.

Provides an axiomatic system with proven soundness and completeness.

Offers alternative interpretations aligned with responsibility studies.

Abstract

We characterize four types of agentive knowledge using a stit semantics over branching discrete-time structures. These are \emph{ex ante} knowledge, \emph{ex interim} knowledge, \emph{ex post} knowledge, and know-how. The first three are notions that arose from game-theoretical analyses on the stages of information disclosure across the decision making process, and the fourth has gained prominence both in logics of action and in deontic logic as a means to formalize ability. In recent years, logicians in AI have argued that any comprehensive study of responsibility attribution and blameworthiness should include proper treatment of these kinds of knowledge. This paper intends to clarify previous attempts to formalize them in stit logic and to propose alternative interpretations that in our opinion are more akin to the study of responsibility in the stit tradition. The logic we present uses an extension with knowledge operators of the Xstit language, and formulas are evaluated with respect to branching discrete-time models. We also present an axiomatic system for this logic, and address its soundness and completeness.