Expressive Logical Combinators for Free

Pierre Genevès (1) , Alan Schmitt (2)

1 TYREX - Types and Reasoning for the Web
2 CELTIQUE - Software certification with semantic analysis

A popular technique for the analysis of web query languages relies on the translation of queries into logical formulas. These formulas are then solved for satisfiability using an off-the-shelf satisfiabil-ity solver. A critical aspect in this approach is the size of the obtained logical formula, since it constitutes a factor that affects the combined complexity of the global approach. We present logical combi-nators whose benefit is to provide an exponential gain in succinctness in terms of the size of the logical representation. This opens the way for solving a wide range of problems such as satisfiability and containment for expressive query languages in exponential-time, even though their direct formulation into the underlying logic results in an exponential blowup of the formula size, yielding an incorrectly presumed two-exponential time complexity. We illustrate this from a practical point of view on a few examples such as numerical occurrence constraints and tree frontier properties which are concrete problems found with semi-structured data.

Domaines: Intelligence artificielle [cs.AI]; Complexité [cs.CC]; Logique en informatique [cs.LO]; Théorie et langage formel [cs.FL]

Pierre Genevès, Alan Schmitt. Expressive Logical Combinators for Free. International Joint Conference on Artificial Intelligence (IJCAI 2015), Jul 2015, Buenos Aires, Argentina. ⟨hal-00868724v4⟩