Depth-bounded bottom-up evaluation of logic programs

AbstractWe present here a depth-bounded bottom-up evaluation algorithm for logic programs. We show that it is sound, complete, and terminating for finite-answer queries if the programs are syntactically restricted to DatalognS, a class of logic programs with limited function symbols. DatalognS is an extension of Datalog capable of representing infinite phenomena. Predicates in DatalognS can have arbitrary unary and limited n-ary function symbols in one distinguished argument. We precisely characterize the computational complexity of depth-bounded evaluation for DatalognS and compare depth-bounded evaluation with other evaluation methods, top-down and Magic Sets among others. We also show that universal safety (finiteness of query answers for any database) is decidable for DatalognS

Playing with Trees and Logic

This document proposes an overview of my research sinc

Strategies for improving the efficiency of automatic theorem-proving

In an attempt to overcome the great inefficiency of theorem proving methods, several existing methods are studied, and several now ones are proposed. A concentrated attempt is made to devise a unified proof procedure whose inference rules are designed for the efficient use by a search strategy. For unsatisfiable sets of Horn clauses, it is shown that p1-resolution and selective linear negative (SLN) resolution can be alternated heuristically to conduct a bi-directional search. This bi-directional search is shown to be more efficient than either of P.-resolution and SLN-resolution. The extreme sparseness of the SLN-search spaces lead to the extension of SLN-resolution to a more general and more powerful resolution rule, selective linear (SL) resolution, which resembles Loveland's model elimination strategy. With SL-resolution, all immediate descendants of a clause are obtained by resolving upon a single selected literal of that clause. Linear resolution, s-linear resolution and t-linear resolution are shown to be as powerful as the most powerful resolution systems. By slightly decreasing the power, considerable increase in the sparseness of search spaces is obtained by using SL-resolution. The amenability of SL-resolution to applications of heuristic methods suggest that, on these grounds alone, it is at least competitive with theorem-proving procedures designed solely from heuristic considerations. Considerable attention is devoted to various anticipation procedures which allow an estimate of the sparseness of search trees before their generation. Unlimited anticipation takes the form of pseudo-search trees which construct outlines of possible proofs. Anticipation procedures together with a number of heuristic measures are suggested for the implementation of an exhaustive search strategy for SL-resolution