Complexity and expressive power of logic programming

Abstract

This paper surveys various complexity results on different forms of logic programming. The main focus is on decidable forms of logic programming, in particular, propositional logic programming and datalog, but we also mention general logic programming with function symbols. Next to classical results on plain logic programming (pure Hom clause programs), more recent results on various important extensions of logic programming are surveyed. These include logic programming with different forms of negation, disjunctive logic programming, logic programming with equality, and constraint logic programming. The complexity of the unification problem is also addressed.

Modular Nonmonotonic Logic Programming Revisited

“…As MLPs (Proposition 1) subsume ordinary logic programs, we thus obtain by known results (cf. [12]) the same complexity. With slight abuse of notation, for a ground atom α and an interpretation M of P, we write α ∈ M if α ∈ M i /S for a given P i [S] ∈ VC (P).…”

“…by encodings of Turing machines, which adapt constructions in [12]. Superficially, one uses modules P [c, t], where c amounts to a tape cell index and t to a time stamp during a computation; with |c| = |t| = n, 2 n cells and 2 n time stamps can be modeled.…”

Conceptual Graphs and First Order Logic

“…We reduce the question-answering problem to the derivation of a conjunction of propositional literals corresponding to the graph g (propositional datalog). Hence the complexity is polynomial [17,18,19,20].…”

“…The hypothesis is to keep both graphs g and h variables. In the previous section, the projection problem was NPcomplete (the algorithm shows that it is in NP; the hard part can be shown by considering the three colours problem in a graph) even when the graphs h and g were kept fixed ('constant' according to the terminology in [17]). Suppose for the moment that we have just a single relation and a single concept for defining both graphs, and that we want to show that h ¢ g and consider the full projection algorithm.…”

Efficient Inclusion Checking for Deterministic Tree Automata and DTDs

“…We first characterize inclusion into deterministic tree automata, second, express the characterization in Datalog [6] and third, turn it into an efficient algorithm. While the two first steps are easy, the last step is nontrivial.…”