We present initial limit Datalog, a new extensible class of constrained Horn clauses for which the satisfiability problem is decidable. The class may be viewed as a generalisation to higher-order logic (with a simple restriction on types) of the first-order language limit Datalog Z (a fragment of Datalog modulo linear integer arithmetic), but can be instantiated with any suitable background theory. For example, the fragment is decidable over any countable well-quasi-order with a decidable first-order theory, such as natural number vectors under componentwise linear arithmetic, and words of a bounded, context-free language ordered by the subword relation. Formulas of initial limit Datalog have the property that, under some assumptions on the background theory, their satisfiability can be witnessed by a new kind of term model which we call entwined structures. Whilst the set of all models is typically uncountable, the set of all entwined structures is recursively enumerable, and model checking is decidable.
|Title of host publication||Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS 2021)|
|Publisher||Institute of Electrical and Electronics Engineers (IEEE)|
|Number of pages||1|
|Publication status||Published - 7 Jul 2021|
|Event||2021 36th Annual Symposium on Logic in Computer Science - Online|
Duration: 29 Jun 2021 → 2 Jul 2021
|Name||Proceedings - Symposium on Logic in Computer Science|
|Conference||2021 36th Annual Symposium on Logic in Computer Science|
|Abbreviated title||ACM/IEEE LICS 2021|
|Period||29/06/21 → 2/07/21|
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