Upside-down meta-interpretation of the model elimination theorem-proving procedure for deduction and abduction

Abstract

Typical bottom-up, forward-chaining reasoning systems such as hyperresolution lack goaldirectedness while typical top-down, backward-chaining reasoning systems like Prolog or model elimination repeatedly solve the same goals. Reasoning systems that are goal-directed and avoid repeatedly solving the same goals can be constructed by formulating the topdown methods metatheoretically for execution by a bottom-up reasoning system (hence, "upside-down meta-interpretation" is being used). This also facilitates the use of flexible search strategies, such as merit-ordered search, that are common to bottom-up interpreters. The model elimination theorem proving procedure, its extension by an assumption rule for abduction and its restriction to Horn clauses, are adapted here for such upside-down metainterpretation. This work can be regarded as an extension of the magic set method for query evaluation in deductive databases to both non-Horn clauses and abductive reasoning.

Blocking and Other Enhancements for Bottom-Up Model Generation Methods

“…An in-depth comparison and analysis of BUMG approaches with our techniques and MACE-style or SEM-style model generation would also be of interest. Another source for future work is to combine the presented transformations with other BUMG techniques, such as magic sets transformations [Hasegawa et al, 1997, Stickel, 1994, a typed version of range-restriction [Baumgartner et al, 1997], and minimal model computation [Bry and Yahya, 2000, Bry and Torge, 1998, Papacchini and Schmidt, 2011. Having been designed to be generic, we believe that our transformations carry over to formalisms with default negation, which could provide a possible basis for enhancements to answer-set programming systems.…”