KED: A Deontic Theorem Prover

Deontic logic (DL) is increasingly recognized as an indispensable tool in such application areas as formal representation of legal knowledge and reasoning, formal specification of computer systems and formal analysis of database integrity constraints. Despite this acknowledgement, there have been few attempts to provide computationally tractable inference mechanisms for DL (most notably [Bel87], [McC83], [McC86], [Sus87]). In this paper we shall be concerned with providing a computationally oriented proof method for standard DL (SDL), i.e., normal systems of modal logic with the usual possible-worlds semantics ([Aq87], [Ch80], [Han65]). Because of the natural and easily implementable style of proof construction it uses, this method seems particularly well-suited for applications in the AI and Law field, and though in the present version it works for SDL only, it forms an appropriate basis for developing efficient proof methods for more expressive and sophisticated extensions of SDL. The content of the paper is as follows. In Section 2, we briefly introduce SDL together with the logical notation being used. In Section 3, we describe the theorem proving system KED. In Sections 4 and 5, we present KED method of proof search. In the last section, we provide a sample of the KED Prolog implementation and give an example output of the program.