# Cut-free Calculi and Relational Semantics for Temporal STIT Logics

## TL;DR

This paper develops cut-free labelled sequent calculi for temporal STIT logics, providing soundness, completeness, and relational semantics for these formal systems of agency and time.

## Contribution

It introduces new cut-free calculi for Ldm, Tstit, and Xstit logics, with structural properties and relational semantics, advancing proof theory in temporal agency logics.

## Key findings

- Calculi G3Ldm and G3TSTIT are sound and complete for their semantics.
- XSTIT logic is characterized through relational frames without BT+AC frames.
- All presented calculi have contraction- and cut-admissibility.

## Abstract

We present cut-free labelled sequent calculi for a central formalism in logics of agency: STIT logics with temporal operators. These include sequent systems for Ldm, Tstit and Xstit. All calculi presented possess essential structural properties such as contraction- and cut-admissibility. The labelled calculi G3Ldm and G3TSTIT are shown sound and complete relative to irreflexive temporal frames. Additionally, we extend current results by showing that also XSTIT can be characterized through relational frames, omitting the use of BT+AC frames.