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Procedural Semantics for Fuzzy Disjunctive Programs on Residuated Lattices

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LATIN 2004: Theoretical Informatics (LATIN 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2976))

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Abstract

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 h i , b j 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 [3] 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 [4] will be reached.

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Author information

Authors and Affiliations

  1. Institute of Informatics, Comenius University, Mlynská dolina, 842 15, Bratislava, Slovakia

    Dušan Guller

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  1. Dušan Guller
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Rutgers University, NJ 08854, Piscataway

    Martín Farach-Colton

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Guller, D. (2004). Procedural Semantics for Fuzzy Disjunctive Programs on Residuated Lattices. In: Farach-Colton, M. (eds) LATIN 2004: Theoretical Informatics. LATIN 2004. Lecture Notes in Computer Science, vol 2976. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24698-5_55

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  • DOI: https://doi.org/10.1007/978-3-540-24698-5_55

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-21258-4

  • Online ISBN: 978-3-540-24698-5

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