Conference Paper

Computed answer based on fuzzy knowledgebase - a model for handling uncertain information.

Conference: Proceedings of the Joint 4th Conference of the European Society for Fuzzy Logic and Technology and the 11th Rencontres Francophones sur la Logique Floue et ses Applications, Barcelona, Spain, September 7-9, 2005
Source: DBLP

ABSTRACT The basic question of our study is how we can give a possible model for handling uncertain information. This model is worked out in the framework of DATALOG. The concept of fuzzy knowledge-base will be defined as a quadruple of any background knowledge; a deduction mechanism; a connecting algorithm, and a decoding set of the program, which help us to determine the uncertainty level of the results. A possible evaluation strategy is given also.

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    ABSTRACT: In deductive databases, knowledge is usually represented in terms of Datalog programs, i.e., crudely speaking, logic programs. The simplest Datalog programs, which contain neither function symbols nor negation, consist of rules of the type q←q 1 ,...,q n in which q and q i are atoms (atomic statements). In logic programming, there exist different semantics that, given a program, determine which atoms are true and which are not. For function-free and negation-free programs, all these semantics produce the same answer that can be described as follows: We start with the empty set T 0 . Then, if the set T α is already defined, we define the next set T α+1 by adding, to T α , all the atoms that follow from the already deduced ones, i.e., all the atoms q for which there is a rule q←q 1 ,...,q n in which all conditions q i are already known to be true (q i ∈T α ). (In particular, T 1 consists of all the atoms for which the unconditional rule q← appears in the knowledge base.) This procedure T is repeated again and again; if necessary, we use T α for infinite ordinals α. As a result, we get a (non-strictly) increasing sequence of sets T 0 ⊆T 1 ...⊆T α ⊆... which inevitable converges. Its limit L is a fixed point of the mapping T, and it is known that if we consider the rules of the logic program as statements in standard logic, then L is the smallest model of the corresponding theory (i.e., the smallest model for which all thus interpreted statements are true). The paper under review considers fuzzy datalog, in which to each rule q←q 1 ,...,q n , we attach a “degree of confidence” in this rule (a number from the interval [0,1]), and a function that describes to what extent confidence in the conditions q i enables us to believe in the conclusion q. Since we are not 100% confident in the rules, we cannot be 100% confident in our conclusions either. So, as a result, for each atomic query q, we expect, in general, not a “crisp” answer like “q is true” or “q is false”, but a “fuzzy” answer: “q is true with a degree of confidence d”. The authors generalize the above fixpoint semantics to such fuzzy programs, prove that the corresponding fixpoint always exists, and show that (similarly to the non-fuzzy case) the resulting fixpoint is the smallest model of the corresponding logical theory.
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    ABSTRACT: In this paper we define the fuzzy Datalog programs as sets of Horn-formulae with uncertainty degrees, and we define the deterministic and nondeterministic semantics. The meaning of programs are the fixpoints of deterministic consecutive transformations. In the second part of the paper we deal with evaluation strategies of fuzzy Datalog programs. We determine the bottom-up and top-down strategies and we show the equivalence of them. At last we deal with the top-down evalution in the case of special implication operator.
    Acta Cybern. 01/1995; 12:153-166.
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    ABSTRACT: The paper falls into the field of logic programming used in fuzzy relational databases. For this purpose, the author extends a Datalog-like language into a fuzzified version. A fuzzy Datalog program is then a set of rules of the form (Q←Q 0 ,...,Q n ,I,β) where Q is an atom, Q 0 ,...,Q n are literals, I is an implication operator interpreted by one of the Gödel, Łukasiewicz, Goguen, Kleene-Dienes, Reichenbach or Gainess-Rescher type, and β∈[0,1] is a truth evaluation. Let us note that the author interprets it incorrectly as a degree of uncertainty. In the article, the evaluation strategies, namely bottom-up and top-down (goal evaluation), and the corresponding algorithms are described.
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