Differences

This shows you the differences between two versions of the page.

--- sav08:first-order_logic_syntax [2008/03/18 11:44]
vkuncak
+++ sav08:first-order_logic_syntax [2008/03/18 12:17]
vkuncak
@@ Line 30: / Line 30: @@
 When in doubt, use parentheses.
-Example: Consider language ${\cal L} = \{ P, Q, R, f \}$ with
+Example: Consider language ${\cal L} = \{ P, Q, R, f \}$ with $ar(P) = 1$, $ar(Q) = 1$, $ar(R) = 2$, $ar(f) = 2$. Then
-\[\begin{array}{l}
-   ar(P) = 1 \\
-   ar(Q) = 1 \\
-   ar(R) = 2 \\
-   ar(f) = 2
-\end{array}
-\]
-Then
 \[
     \lnot \forall x.\, \forall y. R(x,y) \land Q(x) \rightarrow Q(f(y,x)) \lor P(x)
@@ Line 77: / Line 69: @@
 $FV$ denotes the set of free variables in the given propositional formula and can be defined recursively as follows:
-\[\begin{array}{l}
+\[\begin{array}{rcl}
-  FV(x) = \{ x \}, \mbox{ for } x \in V \\
+  FV(x) &=& \{ x \}, \mbox{ for } x \in V \\
+  FV(f(t_1,\ldots,t_n) &=& F(t_1) \cup \ldots \cup F(t_n) \\
+  FV(R(t_1,\ldots,t_n) &=& F(t_1) \cup \ldots \cup F(t_n) \\
+  FV(t_1 = t_2) &=& F(t_1) \cup F(t_2) \\
   FV(\lnot F) = FV(F) \\
   FV(F_1 \land F_2) = FV(F_1) \cup FV(F_2) \\