17 Example of usage (Ad)
Most of us would argue that if it is true that "No cat is sleeping in the kitchen", then it is also true that "No black cat is sleeping in the kitchen". Adding the extra qualifier "black" does not change the truth-value of the statement. But how do we prove this?
Using one of Peirce's rules
With Peirce's rules, we can. Consider the following graph:
Recall that one of the rules is:
Since we have a graph (the Cat graph) that is oddly enclosed (in the negative Proposition context), we are entitled to add any graph. The new graph could look like this:
[Proposition: [Kitchen: #]<-(Loc)<-[Cat]<-(Expr)<-[Sleep] [Cat: #]->(Attr)->[Black] ] "No cat is sleeping in the kitchen. The cat that is not in the kitchen is black.". "No black cat is sleeping in the kitchen."
Next, we give another example.
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