We define sequent-style calculi for nominal tense logics characterized by classes of modal frames that are first-order definable by certain (Formula Presented)-formulae and (Formula Presented)-formulae. The calculi are based on d'Agostino and Mondadori's calculus KE and therefore they admit a restricted cutrule that is not eliminable. A nice computational property of the restriction is, for instance, that at any stage of the proof, only a finite number of potential cut-formulae needs to be taken under consideration. Although restrictions on the proof search (preserving completeness) are given in the paper and most of them are theoretically appealing, the use of those calculi for mechanization is however doubtful. Indeed, we present sequent calculi for fragments of classical logic that are syntactic variants of the sequent calculi for the nominal tense logics.
Demri, S. (1999). Sequent calculi for nominal tense logics: A step towards mechanization? In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1617, pp. 140–155). Springer Verlag. https://doi.org/10.1007/3-540-48754-9_15