LARA

Differences

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

Link to this comparison view

Both sides previous revision Previous revision
sav08:homework09 [2008/04/25 15:06]
vkuncak
sav08:homework09 [2008/04/25 15:10]
vkuncak
Line 9: Line 9:
 Prove that the quantifier-free theory of term algebras is convex (See [[Calculus of Computation Textbook]], Section 10.3.1). ​ That is, show that, if $C$ is a conjunction of literals of form $t=t'$ and $t\neq t'$ where $t,t'$ are terms in some language (containing variables), and if formula Prove that the quantifier-free theory of term algebras is convex (See [[Calculus of Computation Textbook]], Section 10.3.1). ​ That is, show that, if $C$ is a conjunction of literals of form $t=t'$ and $t\neq t'$ where $t,t'$ are terms in some language (containing variables), and if formula
 \[ \[
-    C \rightarrow \bigvee_{i=1} t_i=t'​_i+    C \rightarrow \bigvee_{i=1}^n t_i=t'​_i
 \] \]
 is valid (holds for all values of variables) in the Herbrand interpretation (where elements are ground terms and $\alpha(f)(t_1,​\ldots,​t_n)=f(t_1,​\ldots,​t_n)$),​ then for some $i$ is valid (holds for all values of variables) in the Herbrand interpretation (where elements are ground terms and $\alpha(f)(t_1,​\ldots,​t_n)=f(t_1,​\ldots,​t_n)$),​ then for some $i$