It is a set of truth degrees such as [0,1] equipped with truth functions of logical connectives. For instance, for the connective of implication, one can use (Lukasiewicz implication), or for and for a > b (Goguen implication). There are many choices of truth functions of logical connectives. However, the chosen collection of connectives should obey reasonable properties such as the adjointness property, which is required to be satisfied by the truth functions of conjunction and implication.
Published in Chapter:
Data Dependencies in Codd's Relational Model with Similarities
Radim Belohlavek (Binghamton University–SUNY, USA) and Vilem Vychodil (Palacky University, Czech Republic)
Copyright: © 2008
|Pages: 24
DOI: 10.4018/978-1-59904-853-6.ch025
Abstract
This chapter deals with data dependencies in Codd’s relational model of data. In particular, we deal with fuzzy logic extensions of the relational model that consist of adding similarity relations to domains and consider functional dependencies in these extensions. We present a particular extension and functional dependencies in this extension that follow the principles of fuzzy logic in a narrow sense. We present selected features and results regarding this extension. Then, we use this extension as a reference model and compare it to several other extensions proposed in the literature. We argue that following the principles of fuzzy logic in a narrow sense, the same way we can follow the principles of classical logic in the case of the ordinary Codd relational model, helps achieve transparency, versatility, conceptual clarity, and theoretical and computational tractability of the extension. We outline several topics for future research.