Intuitionistic fuzzy logic IF was introduced by Takeuti and Titani. This logic coincides with the first-order Gödel logic based on the real unit interval [0, 1] as set of truth-values. We present a natural deduction system NIF for IF . NIF is defined by suitably translating a first-order extension of Avron’s hypersequent calculus for Gödel logic. Soundness, completeness and normal form theorems...

In this paper, an Integrated C-Object Tool, namely ICOT, is proposed for knowledge-based programming. A major drawback of current rule-based expert system languages is that they have difficulty in handling composite objects as a unit of inference. An object-oriented model is a powerful alternative to complement the drawback. Each of these alone cannot capture all the semantics of knowledge, par...

When applying rules produced by induction from training examples to a test example, there are three possible cases that demand different actions: (i) no match; (ii) single match; and (iii) multiple match. Existing techniques for dealing with the "rst and third cases are exclusively based on probability estimation. However, when there are continuous attributes in the example space, and if these ...

We present a variant of the Datalog language (we call it Datalog ), which is able to deal with weights on ground facts. The weights are chosen from a semiring algebraic structure. Our goal is to use this language as a semantic foundation for trust-management languages, in order to express trust relationships associated with a preference (e.g., a cost, an uncertainty, a trust or a fuzzy value). ...

The Black–Scholes Option pricing model (OPM) developed in 1973 has always been taken as the cornerstone of option pricing model. The generic applications of such a model are always restricted by its nature of not being suitable for fuzzy environment since the decision-making problems occurring in the area of option pricing are always with a feature of uncertainty. When an investor faces an opti...

This paper provides a logical basis for manipulation with fuzzy IF-THEN rules. Our theory is wide enough and it encompasses not only finding a conclusion by means of the compositional rule of inference due to Lotfi A. Zadeh but also other kinds of approximate reasoning methods, e.g. perception-based deduction, provided that there exists a possibility to characterize them within a formal logical...

Existing search engines—with Google at the top—have many re­ markable capabilities; but what is not among them is deduction capability—the capability to synthesize an answer to a query from bodies of information which re­ side in various parts of the knowledge base. In recent years, impressive progress has been made in enhancing performance of search engines through the use of methods based on ...

Fuzzy set-based methods contribute to the formalization of different types of approximate reasoning, mainly in two ways. First, when modeling classes and properties, fuzzy sets naturally encode gradual properties, such as, e.g., 'large', whose satisfaction is a matter of degree and may be only partial for particular instances. Due to this ability, fuzzy sets are naturally entitled to capture in...

OWL EL is an extension of the tractable EL description logic. Despite their inference capabilities over TBoxes, DL reasoners have a high ABox reasoning complexity which may constitute a serious limitation in the Semantic Web where we rely mainly on query answering (i.e. instance checking). The subsomption algorithm used in fuzzy EL reduce instance checking into concept satisfiability. To allow ...