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The aim of this paper is to establish a new notion of equivalence between temporal models, so-called S-similarity, as the appropriate notion of bisimilarity for temporal logic with Since and U ntil. The main technical results of the paper provide semantical characterizations of the first-order formulas that are equivalent to a temporal formula: Theorem 3.7 concerns the equivalence of temporal and first-order formulas with respect to pointed temporal models, whereas Theorem 4.4 takes the leveldoi:10.12775/llp.2002.010 fatcat:qavib7i72vbe5dmlootzyunlcy