Logic of prototypes and counterexamples: possibilities and limits

DOI

10.2991/ifsa-eusflat-15.2015.99How to use a DOI?

Keywords

Vague property, prototypical examples, counterexamples, logic of vagueness, Kleene logic.

Abstract

Fuzzy sets are a popular tool to model vague properties. It is, however, well-known that this model usually involves a good degree of arbitrariness. In this contribution we consider the possibility of standardising the construction of fuzzy sets at least withregard to the borderline cases. To this end, we identify a vague property with the sets of clearly positive cases and clearly negative cases and under the assumption that the universe of discourse is a metric space, we determine the fuzzy set by what can be described as a linear interpolation. Following this idea, we discuss a number of logic-based approaches to reasoning under vagueness.

Copyright

© 2015, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Thomas Vetterlein
PY  - 2015/06
DA  - 2015/06
TI  - Logic of prototypes and counterexamples: possibilities and limits
BT  - Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology
PB  - Atlantis Press
SP  - 697
EP  - 704
SN  - 1951-6851
UR  - https://doi.org/10.2991/ifsa-eusflat-15.2015.99
DO  - 10.2991/ifsa-eusflat-15.2015.99
ID  - Vetterlein2015/06
ER  -