Enumerating Teams in FirstOrder Team Logics
Abstract
We start the study of the enumeration complexity of different satisfiability problems in firstorder team logics. Since many of our problems go beyond DelP, we use a framework for hard enumeration analogous to the polynomial hierarchy, which was recently introduced by Creignou et al. (Discret. Appl. Math. 2019). We show that the problem to enumerate all satisfying teams of a fixed formula in a given firstorder structure is DelNPcomplete for certain formulas of dependence logic and independence logic. For inclusion logic formulas, this problem is even in DelP. Furthermore, we study the variants of this problems where only maximal, minimal, maximum and minimum solutions, respectively, are considered. For the most part these share the same complexity as the original problem. An exception is the minimumvariant for inclusion logic, which is DelNPcomplete.
 Publication:

arXiv eprints
 Pub Date:
 June 2020
 arXiv:
 arXiv:2006.06953
 Bibcode:
 2020arXiv200606953H
 Keywords:

 Computer Science  Logic in Computer Science