Abstract
Dependencies in data describing objects and their attributes represent a key topic in understanding relational data. In this paper, we examine certain dependencies of data described by fuzzy attributes such as green or high performance, i.e. attributes which apply to objects to certain degrees. Such attributes subsume Boolean attributes as a particular case. We utilize the framework of residuated structures of truth degrees as developed in modern fuzzy logic and examine several fundamental problems for our dependencies. These include connections to existing dependencies for fuzzy as well as Boolean attributes, connections to interior- and closure-like structures, definition and properties of semantic entailment including an efficient check of entailment, various model-theoretical properties, a logical calculus of the dependencies inspired by the well-known Armstrong rules with its ordinary-style as well as graded-style syntactico-semantical completeness, fully informative sets of all dependencies that are valid in given data including a constructive description of minimal such sets, as well as various other problems.
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