Lab for Automated Reasoning and Analysis LARA

Differences

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

Link to this comparison view

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