[FOM] Fuzziness

[Patrik Eklund]

You should note that Hajek and his followers treat many-valuedness in 
logic only from the viewpoint of algebras of truth values. Signatures 
and terms are traditionally bivalent. This is basically the Czech school 
of fuzzy logic.

Ever since the 1980's, fuzzy logic has had a branch drawing heavily upon 
category theory. This is still in continuation. Later on there are 
several contributions also in direction of considering multivalence in 
signatures and terms (fuzzy terms). In this approach, term constructions 
are monadic, and clearly separates terms from sentences, the latter 
being constructed by functors not extendable to monads (otherwise 
sentences are terms as well).

As far as foundations and multivalence is concerned, type theory and 
category theory should not be neglected. Type constructors are usually 
not seen as 'operators', but if we do see them as operators, we arrive 
at extended views of signatures, where the semantics of such type 
constructors as operators are closer to functors than to functions. 
Clearly, if syntax is treated categorically, semantics cannot be just 
about sets and functions.

Best,

Patrik



On 2016-06-23 09:58, aa at tau.ac.il wrote:
> Available are  now three volumes of the Handbook of Mathematical Fuzzy 
> Logic
> (edited by Petr Cintula, Petr Hájek and Carles Noguea). Especially
> the first two chapters of Vol. 1 provide a very good, up to date,
> introduction to mathematical fuzzy logic.
> 
>   An older (but still very good) introduction to this field
> is the monograph "Metamathematics of Fuzzy Logic" by Petr Hájk.
> 
> Arnon Avron
>