Procedural Semantics for Fuzzy Disjunctive Programs on Residuated Lattices
In the paper, we present a procedural semantics for fuzzy disjunctive programs – sets of graded implications of the form:
\((h_1 \vee ... \vee h_n \longleftarrow b_1 \& ... \& b_m, c)~~~~~~~(n > 0, m \geq 0)\)
where hi, bj are atoms and c a truth degree from a complete residuated lattice
\(L = (L, \leq, \vee, \wedge, *, \Longrightarrow, 0, 1).\)
A graded implication can be understood as a means of the representation of incomplete and uncertain information; the incompleteness is formalised by the consequent disjunction of the implication, while the uncertainty by its truth degree. We generalise the results for Boolean lattices in  to the case of residuated ones. We take into consideration the non-idempotent triangular norm ⋆, instead of the idempotent ∧, as a truth function for the strong conjunction &. In the end, the coincidence of the proposed procedural semantics and the generalised declarative, fixpoint semantics from  will be reached.
KeywordsDisjunctive logic programming multivalued logic programming fuzzy logic knowledge representation and reasoning
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- 2.Brewka, G., Dix, J.: Knowledge Representation with Logic Programs. In: Handbook of Phil. Logic, ch. 6, 2nd edn., vol. 6. Oxford University Press, Oxford (2001)Google Scholar
- 4.Guller, D.: Model and fixpoint semantics for fuzzy disjunctive programs with weak similarity. In: Abraham, A., Jain, L.C., Zwaag, B.J. v.d. (eds.) Innovations in Intelligent Systems. Studies in Fuzziness and Soft Computing, vol. 140. Springer, Heidelberg (to appear, 2004)Google Scholar
- 8.Lukasiewicz, T.: Fixpoint characterizations for many-valued disjunctive logic programs with probabilistic semantics. In: Eiter, T., Faber, W., Truszczyński, M. (eds.) LPNMR 2001. LNCS (LNAI), vol. 2173, pp. 336–350. Springer, Heidelberg (2001)Google Scholar
- 12.Subrahmanian, V.S.: On the semantics of quantitative logic programs. In: Proc. of the 4th IEEE Symposium on Logic Programming, Washington DC, pp. 173–182. Computer Society Press (1987)Google Scholar