12 Negation

Everyday negation

In everyday language, we operate with negation all the time; for example, we often say things like "I don't feel like coming", "I can't do that", "He isn't my enemy", "She isn't stupid". In all of these sentences, negation plays a part.

Negation in logic

In logic, there is also a symbol for negation. The convention is to use this symbol: "" and place it in front of whatever is negated.

   (!!x:Sun)(Shining(x))
   "The sun is not shining."

Negation in conceptual graphs

In conceptual graphs, the convetion is to place the symbol "" in front of a context. If you want to negate a conceptual graph, place a context around it (with a type such as "Situation" or "Proposition"), and place the "" symbol to the right of the context.

Examples

For example:

    [Situation: [Sun: #]<-(Agnt)<-[Shine] ]
   "The sun is not shining."

Another example:

    [Proposition: [Man]<-(Expr)<-[Understand]-
                         ->(Thme)->[Woman: {*}] ]
   "It is not the case that there exists 
    a man who understands women"
   "All men do not understand any women"
   "No man understands women" 

Conclusion

We see, then, that in order to negate a conceptual graph, the method is to place a context around it (with the type "Situation" or "Proposition" or the like), and then to place the symbol "" in front of the context.


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