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By Abe J M (eds )

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PRICAF94, (1994) 180-186 [9] Nakamatsu,K. and Suzuki,A. : A Non-monotonic ATMS Based on Annotated Logic Programs with Strong Negation, in Agents and Multi-Agent Systems. M. and Suzuki,A. : A Defeasible Deontic Reasoning System Based on Annotated Logic Programming. Proc. 4th Int'l Conf. Computing Anticipatory Systems. AIP Conf. Proc. M. and Suzuki,A. : Annotated Semantics for Defeasible Deontic Reasoning. Rough Sets and Current Trends in Computing. K. : On the Relation Between Vector Annotated Logic Programs and Defeasible Theories.

Dk(k > 1) are constructed in this fashion. Then, MGPU Algorithm is defined to compute a MGPU substitution for \V. [Definition 8] (MGPU. MGPU Algorithm) MGPU Algorithm Let W be a set of expressions and each d3 is a difference set defined in [Definition 7](1) Set j' = 1, a — {}, where o is a substitution. (2) Find d3' for W as previously described, if it does not exist, terminate with a a MGPU of the set W. (3) If d? -th sort that does not contain v^ then let a = a U { t i / V i } and \V = \\'{ti/vt}.

4vP(s 1 ,... ,s m ), B\/ ~ P(tl,... tm) and a substitution a. the RUE resolvent of a (A V P(s\ . . , tm)) is oA V oB V D, where each s3 and t3(l < j < m) are terms that of the same sort, and D is the disjunction of the equalities specified by a disagreement set of the complimentary literals aP and a(~ P). a may be the null substitution, the MGPU of { P(sl,.... sm). P(tl t™) } or any substitution. The NRF Rule of Inference K. Nakamatsu and A. Suzuki / Automated Theorem Proving 27 Given a clause A V s ^ t and a substitution a, the NRF resolvent of a A V as / at is a A V Z), where D is the disjunction of the inequalities specified by the disagreement set of (as, at}.

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