Hi YKY,
You asked:
How can you express "John kicks Mary" in term logic?
One obvious way is: By an Inheritance relation between the ordered
pair (John, Mary) and the term "kick"
If you want to explore term logic, besides Pei's dissertation and
papers, you should look up the book of Sommers and Englebretsen
http://www.bookkoob.co.uk/book/0754613666.htm
[also on Amazon.com, etc.]
IMO, asking basic questions on an email list is not the optimal way to
gain grounding in a moderately deep area of mathematical logic ;-)
-- Ben
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