Semantics for Fuzzy Disjunctive Programs with Weak Similarity

  • Dušan Guller
Conference paper
Part of the Advances in Soft Computing book series (AINSC, volume 14)


In the paper, we present declarative, model, and fixpoint semantics for fuzzy disjunctive programs with weak similarity — sets of graded strong literal disjunctions. We shall suppose that truth values (degrees) constitute a regular residuated lattice L = (L, ≤, *, ⇒, ∪, ∩, 0, 1). A graded strong literal disjunction will be viewed as a pair (d, c) where d is a formula of the form ¬(d 1 & … & d n ), i.e. a negation of a strong conjunction of literals d i ; and c is a truth value belonging to the lattice L. A graded literal disjunction can be understood as a means of representation of incomplete and imprecise information, where the incompleteness is formalised by its strong literal disjunction (a negation of a strong conjunction of literals), while the impreciseness by its truth degree. Such programs may contain the binary predicate symbol for weak similarity, denoted as ∼, which is the fuzzy counterpart of the ‘classical’ equality.


disjunctive logic programming fuzzy logics model theory knowledge representation and reasoning logic in artificial intelligence 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Dušan Guller
    • 1
  1. 1.Institute of InformaticsComenius UniversityBratislavaSlovakia

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