Modeling Simultaneous Events with Default Reasoning and Tight Derivations

D This report describes how an arbitrator for the game of Diplomacy was implemented in PROLOG, and discusses the advantages of logic programming for this type of problem. The design of the program is greatly simplified by using a default reasoning style to express many of the game rules. The technique of default reasoning is to specify a predicate (or property or situation) by stating sufficient conditions for a general rule, and then stating exceptions to it. Logic programming supports the expression of default reasoning quite directly with negation as failure. Tight derivations were employed to analyze cycles correctly. A tight derivation is one in which no goal has an identical ancestor. Speaking informally, any provable goal is provable by a tight derivation, so restricting the proof searches to tight derivations does not lose any proofs. Only the parts of the program that are susceptible to infinite recursions check for tightness. It is known that the use of tight derivations corresponds to a certain “preferred”, or “canonical”, minimal model for many programs that contain negation as failure; in such programs, there is normally no minimum model. Care must be taken in the way defaults are expressed to achieve proper correspondence between the model and the game rules. a