Results

**1 - 5**of**5**### On the Parameterized Complexity of Default Logic and Autoepistemic Logic∗

"... Abstract. We investigate the application of Courcelle’s Theorem and the logspace version of Elberfeld et al. in the context of the implica-tion problem for propositional sets of formulae, the extension existence problem for default logic, as well as the expansion existence problem for autoepistemic ..."

Abstract
- Add to MetaCart

(Show Context)
Abstract. We investigate the application of Courcelle’s Theorem and the logspace version of Elberfeld et al. in the context of the implica-tion problem for propositional sets of formulae, the extension existence problem for default logic, as well as the expansion existence problem for autoepistemic logic and obtain fixed-parameter time and space efficient algorithms for these problems. On the other hand, we exhibit, for each of the above problems, families of instances of a very simple structure that, for a wide range of different parameterizations, do not have efficient fixed-parameter algorithms (even in the sense of the large class XPnu), unless P = NP. 1

### Generalized Complexity of ALC Subsumption

"... The subsumption problem with respect to terminologies in the description logic ALC is EXP-complete. We investigate the computational complexity of fragments of this problem by means of allowed Boolean operators. Hereto we make use of the notion of clones in the context of Post’s lattice. Furthermore ..."

Abstract
- Add to MetaCart

(Show Context)
The subsumption problem with respect to terminologies in the description logic ALC is EXP-complete. We investigate the computational complexity of fragments of this problem by means of allowed Boolean operators. Hereto we make use of the notion of clones in the context of Post’s lattice. Furthermore we consider all four possible quantifier combinations for each fragment parameterized by a clone. We will see that depending on what quantifiers are available the classification will be either tripartite or a quartering. 1

### Parameterized Complexity of Weighted Satisfiability Problems

"... Abstract. We consider the weighted satisfiability problem for Boolean circuits and propositional formulæ, where the weight of an assignment is the number of variables set to true. We study the parameterized complexity of these problems and initiate a systematic study of the complexity of its fragmen ..."

Abstract
- Add to MetaCart

(Show Context)
Abstract. We consider the weighted satisfiability problem for Boolean circuits and propositional formulæ, where the weight of an assignment is the number of variables set to true. We study the parameterized complexity of these problems and initiate a systematic study of the complexity of its fragments. Only the monotone fragment has been considered so far and proven to be of same complexity as the unrestricted problems. Here, we consider all fragments obtained by semantically restricting circuits or formulæ to contain only gates (connectives) from a fixed set B of Boolean functions. We obtain a dichotomy result by showing that for each such B, the weighted satisfiability problems are either W[P]-complete (for circuits) or W[SAT]-complete (for formulæ) or efficiently solvable. We also consider the related counting problems. 1