Abstract
In accordance with Hilbert’s approach, in this chapter we will show that it is possible to define the deduction operator of a fuzzy logic by a suitable extension of the notions of inference rule and proof. To justify such an extension we start from the famous paradox, the “Heap Paradox”, involving the vague predicate “is small”. A similar paradox is the “Bald Man Paradox”. An interesting treatment of such paradoxes by means of fuzzy logic can be found in Goguen [1968/69]. The paradox runs as follows:
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(a)
If you add one stone to a small heap, it remains small.
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(b)
A heap containing just one stone is small, therefore:
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(c)
every heap is small.
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© 2001 Springer Science+Business Media Dordrecht
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Gerla, G. (2001). Approximate Reasoning. In: Fuzzy Logic. Trends in Logic, vol 11. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9660-2_4
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DOI: https://doi.org/10.1007/978-94-015-9660-2_4
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5694-8
Online ISBN: 978-94-015-9660-2
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