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# Exercise 58 - Chapter 2

edited June 2018

Recall the monoidal preorder $$\textbf{NMY} := (P, \le, yes, min)$$ from Exercise 2.31. Interpret what a category enriched in $$\textbf{NMY}$$ would be.

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1.

I think it would look like a preorder, except that some edges (necessarily between different objects) would be labelled as "maybe" and all paths that include a "maybe" edge should be counted as "maybe", too. For example, if we are dealing with a set of propositions and we interpret edges (or lack thereof) as "there is no proof/there may be a proof/there is a proof", then there would be a proof between two propositions linked by a path of "yes" edges, there may be a proof between two propositions linked only by a path of "yes" and (at least one) "maybe" edges, and there is no proof otherwise (i.e., "no" means "no edges").

Comment Source:I think it would look like a preorder, except that some edges (necessarily between different objects) would be labelled as "maybe" and all paths that include a "maybe" edge should be counted as "maybe", too. For example, if we are dealing with a set of propositions and we interpret edges (or lack thereof) as "there is no proof/there may be a proof/there is a proof", then there would be a proof between two propositions linked by a path of "yes" edges, there may be a proof between two propositions linked only by a path of "yes" and (at least one) "maybe" edges, and there is no proof otherwise (i.e., "no" means "no edges").
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2.

It provides a sort of fuzzy logic, answers to "is it possible?" where "maybe" is an allowed answer.

Comment Source:It provides a sort of fuzzy logic, answers to "is it possible?" where "maybe" is an allowed answer.