Schubert’s proposal ([Sch00]) that sentences not only describe but also characterize situations is worked out in the context of Linear Temporal Logic (LTL), a well-known propositional logic with linear future operators (e.g. [HR04]). The resulting formalism LTL∗∗ illustrates an approach that diverges from Schubert’s FOL∗∗ in technical details but shares many (if not all) its motivations.
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Marcelo Finger & Dov M. Gabbay (1992). Adding a Temporal Dimension to a Logic System. Journal of Logic, Language and Information 1 (3):203-233.
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