A Process Theory of Non-monotonic Inference

Artificial Intelligence needs a formal theory of the process of non-monotonic reasoning. Ideally, such a theory would decide, for every proposition and state of the process, whether the program should believe the proposition in that state, or remain agnostic. Without non-monotonic inference rules, non-monotonic inferences cannot be explained in the same relational, rule-based fashion as other inferences. But with such rules, theoremhood is often formally undecidable and thus a useless criterion for our purpose. So how could any system be a "non-monotonic logic programming language"? Our method uses the language, inference rules and proofs of non-monotonic logics, but ignores theoremhood. Instead, it defines states of the reasoning process, and focuses on current proof as the criterion for belief. It defines "admissible beliefs" and "valid proof" for given states, and we prove in [5] that a belief is currently admissible iff it is currently proven. The primitive non-monotonic condition is "currently unproven". The theory, Logical Process Theory, can accept a range of non-monotonic logics. It was inspired by Doyle's RMS [3] and is similar to his more recent theory in [4|. A model implementation, WATSON, exists and has been used to write a small diagnostic reasoner, which reasons non-monotonic ally using violation of expectations and an abstraction hierarchy. 1. DEFINITION OF LOGICAL PROCESSES Briefly, Logical Process Theory (LPT) accepts a triple where L and I are the object language and inference rule of some suitable logic, and £, the enumeration, is a control parameter. The theory then specifies the admissible statet of an inference process which obeys that logic and makes inferences in the order indicated by £ A state consists simply of the set of inferences made so far, and the set of formulas taken to be believed by the machine executing the process. At no point is theoremhood in the given logic defined or used by LPT itself; LPT deals always with finite, computable states. LPT requires of L only that it be a denumerable set of formulas; their grammatical structure and semantics is opaque to LPT and hence unrestricted. The inference rule I may be any set of inference ttept. An inference step is a triple , where the monotonic antecedents M are a set of formulas of L; the non-monotonic antecedents N are a set of formulas of L; and the consequent c is a formula of L. We also require some finite bound on the site …