Solving the Steamroller, and Other Puzzles, with Extended Disjunctive Logic Programming

We show how to solve the classical ATP benchmark test problem Schu-bert's Steamroller, and other puzzles, in the nonclassical framework of extended disjunctive logic programming (EDLP) where neither Contrapo-sition nor Reasoning by Cases are valid principles of inference. While thèSteamroller' can be solved using only Detachment and Disjunctive Syl-logism, another puzzle, `Who killed aunt Agatha ?', needs in addition a local form of Contraposition, resp. Reasoning by Cases, which is achieved by declaring certain predicates as exact in the sense of KK or66]. Besides being able to solve certain classical ATP problems in a monotonic reasoning mode, EDLP can as well treat commonsense reasoning problems by employing its intrinsic nonmonotonic inference capabilities. This is illustrated by means of a nonmonotonic variant of thèSteamroller' problem. EDLP thus proves itself as a powerful general-purpose AI reasoning system.