Fixed-parameter complexity in AI and nonmonotonic reasoning

We study the fixed-parameter complexity of various problems in AI and nonmonotonic reasoning. We show that a number of relevant parameterized problems in these areas are fixed-parameter tractable. Among these problems are constraint satisfaction problems with bounded treewidth and fixed domain, restricted satisfiability problems, propositional logic programming under the stable model semantics where the parameter is the dimension of a feedback vertex set of the program’s dependency graph, and circumscriptive inference from a positive k-CNF restricted to models of bounded size. We also show that circumscriptive inference from a general propositional theory, when the attention is restricted to models of bounded size, is fixed-parameter intractable and is actually complete for a novel fixed-parameter complexity class.