Neighbourhood semantics and axioms for strategic fragment of classical stit logic

TL;DR

This paper explores a strategic fragment of classical STIT logic using neighborhood semantics, establishing soundness, strong completeness, and discussing potential epistemic extensions to enhance understanding of agency and strategic abilities.

Contribution

It introduces a neighborhood semantics framework for a strategic fragment of classical STIT logic, providing soundness, canonicity, and strong completeness results, and discusses epistemic extensions.

Findings

Neighborhood semantics for the fragment is sound and strongly complete.

The logic's properties are characterized through canonicity.

Initial considerations on epistemic extensions are presented.

Abstract

STIT (sees to it that) semantics is one of the most prominent tools in modal logic of agency, widely used among both philosophers and responsible AI scholars. STIT logic surveys the properties of agents seeing to it that some state of affairs holds without specifying concrete actions by which that state of affairs is guaranteed. In comparison with other multi-agent modal logics, the main advantage of STIT theories is expressive power. STIT logic allows to study not only statements about agents abilities to perform certain actions (as it is in variations of Coalition Logic or Propositional Dynamic Logic), but about what choices they make and what they de-facto achieve as well. Nevertheless, in some occasions such expressivity may be redundant. This paper surveys a specific fragment of classical STIT logic, which has only strategic modal operator, standing for the fact that agent has an ability to see to it that some state of affairs holds. The neighbourhood semantics for the fragment is presented, accompanied with the soundness, canoniciy hence strong completeness results. Furthermore, the paper presents basic considerations on epistemic extension of the presented fragment.