Approximation Spaces of Temporal Processes and Effectiveness of Interval Semantics

A series of positive results related to the generalized problem of Yu.L. Ershov on the structure of \(\varSigma \)-degrees of dense linear orders is obtained. In particular, we prove that interval models of temporal logic, as well as finite fragments of approximation spaces generated by interval Boolean algebras, are \(\varSigma \)-definable (effectively interpretable) in hereditarily finite superstructures over dense linear orders. These results are used in the analysis of semantics of verbs in natural languages within the approach in formal semantics proposed by R. Montague.

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