Jie Bao's Notes of Knowledge Representation
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Jie Bao's notes on the book "Handbook of Knowledge Representation", Elsevier, 2008
Contents |
Chapter 1: Knowledge Representation and Classical Logic
March 29, 2008
Question on FOL:
- Q: why FOL has sound and complete proof [Natural deduction, p14], but is not decidable?
- A: Gödel's completeness theorem only says that the natural deduction process is sound and complete, but [I guess] may not always terminating.
- Q: Why trans. closure (tc) is not expressible in FOL [p15]. For example, to say that Q is a tc of P can we have Failed to parse (Missing texvc executable;
please see math/README to configure.): \forall x,y P(x,y)->Q(x,y) and Failed to parse (Missing texvc executable; please see math/README to configure.): \forall
x,y,z Q(x,y)^Q(y,z)->Q(x,z).
- A: It only says P's tc is a subset of Q. There is no way in FOL to say that Q is a subset of P's tc.
Further reading
