Lab for Automated Reasoning and Analysis LARA

Differences

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

Link to this comparison view

Both sides previous revision Previous revision
Next revision
Previous revision
sav08:exists-forall_class_definition [2010/05/03 11:15]
vkuncak
sav08:exists-forall_class_definition [2015/04/21 17:30] (current)
Line 1: Line 1:
-====== Exists-Forall Class Definition ======+====== Exists-Forall Class (EPR, BSR) Definition ======
  
 Also called [[wp>​Paul Bernays|Berneys]]-[[wp>​Schoenfinkel]] class and Effectively Propositional Logic (EPR). Also called [[wp>​Paul Bernays|Berneys]]-[[wp>​Schoenfinkel]] class and Effectively Propositional Logic (EPR).
Line 14: Line 14:
  
 For binary relations $r,s,t$ to express $r \circ s \subseteq t$, we can introduce binary relation symbols $R$, $S$, $T$ and write formula For binary relations $r,s,t$ to express $r \circ s \subseteq t$, we can introduce binary relation symbols $R$, $S$, $T$ and write formula
-\[+\begin{equation*}
     \forall x, y, z. R(x,y) \land S(y,z) \rightarrow T(x,z)     \forall x, y, z. R(x,y) \land S(y,z) \rightarrow T(x,z)
-\]+\end{equation*}
  
 To express $r^{-1} = r$ we would write To express $r^{-1} = r$ we would write
-\[+\begin{equation*}
     \forall x, y. R(x,y) \leftrightarrow R(y,x)     \forall x, y. R(x,y) \leftrightarrow R(y,x)
-\]+\end{equation*}
  
 List contains no duplicates: List contains no duplicates:
-\[+\begin{equation*}
    ​\forall x,y,z. ListNode(x) \land ListNode(y) \land data(x,z) \land data(y,z) \rightarrow x=y    ​\forall x,y,z. ListNode(x) \land ListNode(y) \land data(x,z) \land data(y,z) \rightarrow x=y
-\]+\end{equation*}
  
 Relation $r$ is a partial function Relation $r$ is a partial function
-\[+\begin{equation*}
     \forall x, y_1, y_1. R(x,y_1) \land R(x,y_2) \rightarrow y_1=y_2     \forall x, y_1, y_1. R(x,y_1) \land R(x,y_2) \rightarrow y_1=y_2
-\]+\end{equation*}
  
 We **cannot** express in this class that $R$ is a total function, or property like $\forall x. \exists y. R(x,y)$ because we need an existential quantifier after a universal one. We **cannot** express in this class that $R$ is a total function, or property like $\forall x. \exists y. R(x,y)$ because we need an existential quantifier after a universal one.
  
 
sav08/exists-forall_class_definition.txt · Last modified: 2015/04/21 17:30 (external edit)
 
© EPFL 2018 - Legal notice