Cut-free Calculi and Relational Semantics for Temporal STIT Logics
This work provides formal proof systems for logics of agency, which is incremental in extending existing results for specific temporal operators.
The authors developed cut-free labelled sequent calculi for temporal STIT logics, including Ldm, Tstit, and Xstit, with essential structural properties like contraction- and cut-admissibility, and demonstrated soundness and completeness for some relative to irreflexive temporal frames, while extending relational frame characterizations for XSTIT.
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.