Abstract
The classification of the fragments of Halpern and Shoham’s logic with respect to decidability/undecidability of the satisfiability problem is now very close to the end. We settle one of the few remaining questions concerning the fragment \(\mathsf{A\bar{A}B\bar{B}}\), which comprises Allen’s interval relations “meets” and “begins” and their symmetric versions. We already proved that \(\mathsf{A\bar{A}B\bar{B}}\) is decidable over the class of all finite linear orders and undecidable over ordered domains isomorphic to ℕ. In this paper, we first show that \(\mathsf{A\bar{A}B\bar{B}}\) is undecidable over ℝ and over the class of all Dedekind-complete linear orders. We then prove that the logic is decidable over ℚ and over the class of all linear orders.
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Montanari, A., Puppis, G., Sala, P. (2014). Decidability of the Interval Temporal Logic \(\mathsf{A\bar{A}B\bar{B}}\) over the Rationals. In: Csuhaj-Varjú, E., Dietzfelbinger, M., Ésik, Z. (eds) Mathematical Foundations of Computer Science 2014. MFCS 2014. Lecture Notes in Computer Science, vol 8634. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44522-8_38
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DOI: https://doi.org/10.1007/978-3-662-44522-8_38
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