Re nements for Restart Model Elimination

Restart Model Elimination (RME) has been introduced as a variant of model elimination in [1] as a calculus which avoids contrapositives and which introduces case analysis. In [4] a variant for computing answers to disjunctive logic programs was introduced. RME is implemented as part of the PROTEIN system [2]. One result of this paper is a table of completeness results with respect to the combination of the refinements head selection function, strictness, regularity, independance of the goal clause for RME (Figure 1 below). Another original result is completeness of “early cancellation pruning”1 . In the following section we recall basic restart model elimination calculus, and in Section 2.2 we introduce refinements. The main results of this paper are then presented in Section 3. 2 Restart Model Elimination (RME) A pair of literals (K;L) is a connection with MGU σ iff σ is a most general unifier for K and L. A clause is considered as a multiset of literals, usually written as an implication A1_ : : :_Am B1^ : : :^Bn where the As and Bs are atoms. Clauses with m 1 are called program clauses with head literals Ai and body literals Bi, if present. Negative clauses are written as B1^ : : :^Bn. We assume our clause sets to be in Goal normal form, i.e. there exists only one negative clause which furthermore does not contain variables. Without loss of generality this can be achieved by introducing a new clause Goal where Goal is a new predicate symbol, and by replacing every negative clause B1^ : : :^Bn by Goal B1^ ^Bn. We consider literal trees (aka tableaux), i.e. finite, ordered trees, all nodes of which, except the root, are labeled with a literal. A branch of length n consisting of the nodes N0;N1; : : : ;Nn with root N0 and leaf Nn is usually written as [L1 : : : Ln] where Li is the label of Ni. In general, we find it practical to confuse a node with its label. The letters p and q are branch-valued variables, and if p = [L1 : : : Ln 1] then [p Ln] is the branch [L1 : : : Ln 1 Ln]. The functions First and Leaf return the first labeled, resp. last node of a branch. The extension of [p] with clause C, written as [p] C, is the branch set f[p L] j L 2 Cg. Equivalently, in tree view this operation extends the branch [p] by jCj new nodes which are labelled with the literals from C.