# First order Logic

• Jan 15th 2011, 08:46 PM
nick1978
First order Logic
For the above set:
a)Find an interpretation A of T ,with Domain the set |A|={a,b,c} ,which is model of T.In the interpretation at the constant a is assigned a, at the constant b is assigned b, at the constant c is assigned c.

b)Find an interpretation A of T ,with Domain the set |A|={a,b,c} ,which is NOT model of T.In the interpretation at the constant a is assigned a, at the constant b is assigned b,
at the constant c is assigned c.
Moreover it must be $\displaystyle \prec$a,b$\displaystyle \succ$http://s3.amazonaws.com/answer-board...4312734879.gif$\displaystyle P^A$ and$\displaystyle \prec$b,c$\displaystyle \succ$http://s3.amazonaws.com/answer-board...4312734879.gif$\displaystyle P^A$.

c)Find an interpretation$\displaystyle A_1$ of T ,with Domain the set |$\displaystyle A_1$|={0} ,which is model of T.Find also an interpretation $\displaystyle A_2$of T ,with Domain the set |$\displaystyle A_2$|={0} ,which is NOT model of T. For $\displaystyle A_2$ it must be$\displaystyle \prec$0$\displaystyle \succ$http://s3.amazonaws.com/answer-board...4312734879.gif$\displaystyle P^_A_2$.
Thank you..

• Jan 16th 2011, 12:46 AM
DrSteve
I'll start you off.

For (a), I believe you can let $\displaystyle P$ be $\displaystyle <$ and let $\displaystyle R$ be $\displaystyle \leq$.
• Jan 16th 2011, 04:41 AM
emakarov
In c) it should probably say, "For $\displaystyle A_2$, it must be $\displaystyle \langle 0,0\rangle\in P^{A_2}$" since P is a binary predicate.