By Brazil) Congress of Logic Applied to Technology 2002 (Sao Paulo, Joao Inacio Da Silva Filho, Jair Minoro Abe
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Extra resources for Advances in Logic, Artificial Intelligence and Robotics: Laptec 2002
M. : Modal Provability Foundations for Negation by Failure. Proc. Int'l Workshop Extension of Logic Programming, LNAI 475, (1989) 179-222  Kunen,K. : Negation in Logic Programming. J. W. : Foundations of Logic Programming (2nd edition). Springer-Verlag (1987)  Nakamatsu,K. and Suzuki,A. : Automatic Theorem Proving for Modal Predicate Logic. Trans. IECE Japan, E67 (1984) 203-210  Nakamatsu,K. and Suzuki,A. : Annotated Semantics for Default Reasoning. Proc. PRICAI'94, (1994) 180-186  Nakamatsu,K.
Thus, we try to uniformly represent the declarative semantics for such nonmonotonic reasonings and inconsistency based on annotated logic. We have already characterized some nonmonotonic reasonings with inconsistency by annotated logic programs [8, 9, 10, 11, 12, 13]. In this paper, we characterize the Negation as Failure by annotated semantics called annotated completion and prove its completeness and soundness. Annotated logics are a family of paraconsistent logics that were proposed initially by Subrahmanian  and da Costa .
S m ) and ~ P(tl,... tm) is the union : D = (J™=1Dj, where Dj is a disagreement set of (s3. t3}. MGU(most general unifier) is used in standard resolution, on the other hand, MGPU(most general partial unifier) is used in the RUE-NRF. MGPU is the substitution used when two terms s, t are not completely unifiable. [Definition 7] (difference set) Let W be a non-empty set of expressions. The first difference set is obtained by locating the first position (counting from the left) at which not all the expressions in W have exactly the same symbol and then extracting from each expression the subexpression that begins with the symbol occupying that position.