@article{Kamide_2009, title={Temporal non-commutative logic: Expressing time, resource, order and hierarchy}, volume={18}, url={https://apcz.umk.pl/LLP/article/view/LLP.2009.007}, DOI={10.12775/LLP.2009.007}, abstractNote={A first-order temporal non-commutative logic TN[l], which has no structural rules and has some l-bounded linear-time temporal operators, is introduced as a Gentzen-type sequent calculus. The logic TN[l] allows us to provide not only time-dependent, resource-sensitive, ordered, but also hierarchical reasoning. Decidability, cut-elimination and completeness (w.r.t. phase semantics) theorems are shown for TN[l]. An advantage of TN[l] is its decidability, because the standard first-order linear-time temporal logic is undecidable. A correspondence theorem between TN[l] and a resource indexed non-commutative logic RN[l] is also shown. This theorem is intended to state that “time” is regarded as a “resource”.}, number={2}, journal={Logic and Logical Philosophy}, author={Kamide, Norihiro}, year={2009}, month={Nov.}, pages={97–126} }