Parameterised Complexity of Propositional Inclusion and Independence Logic

Abstract

In this work we analyse the parameterised complexity of propositional inclusion (PIN C) and independence logic (PIN D). The problems of interest are model checking (MC) and satisfiability (SAT). The complexity of these problems is well understood in the classical (non-parameterised) setting. Mahmood and Meier (FoIKS 2020) recently studied the parameterised complexity of propositional dependence logic (PDL). As a continuation of their work, we classify inclusion and independence logic and thereby come closer to completing the picture with respect to the parametrised complexity for the three most studied logics in the propositional team semantics setting. We present results for each problem with respect to 8 different parameterisations. It turns out that for a team based logic L such that L-atoms can be evaluated in polynomial time, the MC parameterised by teamsize is FPT. As a corollary, we get an FPT-membership under the following parameterisations: formula-size, formula-depth, treewidth, and number of variables. The parameter teamsize shows interesting behavior for SAT. For PIN C the parameter teamsize is not meaningful, whereas for PDL and PIN D the satisfiability is paraNP-complete. Finally, we prove that when parameterised by arity, both MC and SAT are paraNP-complete for each of the considered logics.