Re nements for Restart Model Elimination

Restart Model Elimination (RME) has been introduced as a var iant of model elimination in [1] as a calculus which avoids contrapositives and which introd uces case analysis. In [4] a variant for computing answers to disjunctive logic programs was introd uce . RME is implemented as part of the PROTEIN system [2]. One result of this paper is a table of completeness results wi th respect to the combination of the refinementshead selection function , strictness, regularity, independance of the goal clause for RME (Figure 1 below). Another original result is completene ss of “early cancellation pruning” 1. In the following section we recall basic restart model elimi nat on calculus, and in Section 2.2 we introduce refinements. The main results of this paper are t hen presented in Section 3. 2 Restart Model Elimination (RME) A pair of literals (K;L) is aconnection with MGUσ iff σ is a most general unifier for K andL. A clauseis considered as a multiset of literals, usually written as a n implicationA1_ : : :_Am B1^ : : :^Bn where theAs andBs are atoms. Clauses with m 1 are calledprogram clauseswith head literals Ai andbody 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 f generality this can be achieved by introducing a new clause Goal whereGoal is a new predicate symbol, and by replacing every negative clause B1^ : : :^Bn by Goal B1^ ^Bn. We consider literal trees (aka t bleaux), 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 leafNn is usually written as[L1 : : : Ln] whereLi is the label ofNi. In general, we find it practical to confuse a node with its label. The letters p andq are branch-valued variables, and if p= [L1 : : : Ln 1] then[p Ln] is the branch[L1 : : : Ln 1 Ln]. The functionsFirst andLeaf return the firstlabeled, 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 bran ch [p] by jCj new nodes which are labelled with the literals from C.