Resolution in a new modal logic

• Authors: Masamichi Shimura
• Venue: IJCAI'79 Proceedings of the 6th international joint conference on Artificial intelligence - Volume 2
• Year: 1979

This paper proposes a new logic called manner logic(ML) and considers resolution techniques for mechanical theorem proving in the ML. The ML deals with statements which contain adverbs or verbs representing manner such as possibility, uncertainty and causality. Manner is expressed by a manner operator "*", which is a monadic operator. By using manner operators, a postulate can be four-valued; true(T), true in the sense of "*" (T*), false in the sense of "*" (F*), or false (F). In the ML, an atomic formula is assigned a value T or F, but a well-formed formula is assigned a value T, T*, F*, or F. Therefore, the ML can represent more complicated statements than the ordinal predicate logic. Its logical manipulation is quite simple, since it can be considered an extension of the oridinal binary logic. This paper also discusses resolution techniques in a refutation process. In our method, an additional valid clause is used in a refutation process to resolve clauses with manner operators which cannot be resolved directly.