2016/04/30 by Davide Bresolin, Agi Kurucz, Emilio Muñoz-Velasco +3
Computer Science · #Boolean satisfiability problem #Constraint Satisfaction and Optimization #Decidability #Formal Methods in Verification #French horn #Horn clause #Interval (graph theory) #Logic, Reasoning, and Knowledge #Modal logic #Satisfiability #Undecidable problem #cs.CC #cs.LO
paper · pdf · doi:10.1145/3105909
published as ACM Trans. Comput. Logic 18, 3, Article 22 (August 2017), 39 pages
openalex created_date 2016/06/24 · openalex publication_date 2017/07/31 · arxiv created 2017/08/28 · arxiv updated 2017/08/29 · openalex updated_date 2026/08/05
We investigate the satisfiability problem for Horn fragments of the Halpern-Shoham interval temporal logic depending on the type (box or diamond) of the interval modal operators, the type of the underlying linear order (discrete or dense), and the type of semantics for the interval relations (reflexive or irreflexive). For example, we show that satisfiability of Horn formulas with diamonds is undecidable for any type of linear orders and semantics. On the contrary, satisfiability of Horn formulas with boxes is tractable over both discrete and dense orders under the reflexive semantics and over dense orders under the irreflexive semantics but becomes undecidable over discrete orders under the irreflexive semantics. Satisfiability of binary Horn formulas with both boxes and diamonds is always undecidable under the irreflexive semantics.