13 Conjunction (and)

Everyday usage of "and"

In everyday language, we use "and" all the time. For example, "I am both happy and satisfied", "She is both beautiful and wise", "He is both competent and a nice guy."

The usage of "and" in these examples closely mirrors the usage of "and" in logic. For "and" to be true in logic, both of the predicates connected by "and" have to be true. In the above examples, both of the predicates in each example are true simultaneously.

In everyday language, "and" also has other meanings. One of them is to indicate temporal succession. For example, "He was sick and died". In this example, "and" indicates that first, he was sick and then he died.

Usage of "and" in logic

This usage is not the one we use in logic. In logic, only the usage where both predicates are true simultaneously is used.

In logic, the convention is to place the symbol "" between the two predicates which must be connected. For example:

   (x:Woman)(beautiful(x)  dangerous(x))
   There exists a woman who is both beautiful and dangerous"

"And" in conceptual graphs

As already noted, when conceptual graphs stand beside each other (or underneath each other) in the same context, without any connecting arcs, the interpretation is that both are true at the same time. For example:

  [Proposition:
    [Woman: *x]->(Attr)->[Beautiful]

    [Woman: ?x]->(Attr)->[Dangerous]
  ]
  "There exists a woman x who is beautiful.
   And this woman x is also dangerous."
  "There exists a woman who is both beautiful and dangerous"

In this example, the two subgraphs are juxtaposed in the same context, but without any connecting relation and arcs between them. Therefore, the interpretation is that both are true at the same time.

Conclusion

Thus we see that in order to say that two conceptual graphs are both true, we just need to place them together in the same context without any connecting relation and arcs between them.


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