Package edu.cmu.tetrad.search

Class GraphoidAxioms

java.lang.Object

edu.cmu.tetrad.search.GraphoidAxioms

public class GraphoidAxioms
extends Object

Checks the graphoid axioms for a set of Independence Model statements.

Author:

josephramsey

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static class	GraphoidAxioms.GraphoidIndFact

Constructor Summary

Constructors

Constructor	Description
GraphoidAxioms(Set<GraphoidAxioms.GraphoidIndFact> facts, List<Node> nodes)	Constructor.
GraphoidAxioms(Set<GraphoidAxioms.GraphoidIndFact> facts, List<Node> nodes, Map<GraphoidAxioms.GraphoidIndFact,String> textSpecs)

Method Summary

Modifier and Type	Method	Description
boolean	composition()	(X ⊥⊥ Y | Z) ∧ (X ⊥⊥ W |Z) ==> X ⊥⊥ (Y ∪ W) |Z
boolean	compositionalGraphoid()
boolean	contraction()	(X ⊥⊥ Y |Z) ∧ (X ⊥⊥ W |Z ∪ Y) ==> X ⊥⊥ (Y ∪ W) |Z
boolean	decomposition()	X ⊥⊥ (Y ∪ W) |Z ==> (X ⊥⊥ Y |Z) ∧ (X ⊥⊥ W |Z)
IndependenceFacts	getIndependenceFacts()	Assumes decompositiona nd composition.
boolean	graphoid()
boolean	intersection()	(X ⊥⊥ Y | (Z ∪ W)) ∧ (X ⊥⊥ W | (Z ∪ Y)) ==> X ⊥⊥ (Y ∪ W) |Z
static void	main(String... args)
boolean	semigraphoid()
void	setSymmetryAssumed()	X ⊥⊥ Y | Z ==> Y ⊥⊥ X | Z
void	setTrivialtyAssumed()
boolean	symmetry()	X ⊥⊥ Y | Z ==> Y ⊥⊥ X | Z
boolean	weakUnion()	X _||_ Y U W | Z ==> X _||_ Y | Z U W

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

GraphoidAxioms

public GraphoidAxioms(Set<GraphoidAxioms.GraphoidIndFact> facts,
 List<Node> nodes)

Constructor.

Parameters:

facts - A set of GraphoidIdFacts.

GraphoidAxioms

public GraphoidAxioms(Set<GraphoidAxioms.GraphoidIndFact> facts,
 List<Node> nodes,
 Map<GraphoidAxioms.GraphoidIndFact,String> textSpecs)

Method Details

main

public static void main(String... args)

semigraphoid

public boolean semigraphoid()

graphoid

public boolean graphoid()

compositionalGraphoid

public boolean compositionalGraphoid()

getIndependenceFacts

public IndependenceFacts getIndependenceFacts()

Assumes decompositiona nd composition.

symmetry

public boolean symmetry()

X ⊥⊥ Y | Z ==> Y ⊥⊥ X | Z

decomposition

public boolean decomposition()

X ⊥⊥ (Y ∪ W) |Z ==> (X ⊥⊥ Y |Z) ∧ (X ⊥⊥ W |Z)

weakUnion

public boolean weakUnion()

X _||_ Y U W | Z ==> X _||_ Y | Z U W

contraction

public boolean contraction()

(X ⊥⊥ Y |Z) ∧ (X ⊥⊥ W |Z ∪ Y) ==> X ⊥⊥ (Y ∪ W) |Z

intersection

public boolean intersection()

(X ⊥⊥ Y | (Z ∪ W)) ∧ (X ⊥⊥ W | (Z ∪ Y)) ==> X ⊥⊥ (Y ∪ W) |Z

composition

public boolean composition()

(X ⊥⊥ Y | Z) ∧ (X ⊥⊥ W |Z) ==> X ⊥⊥ (Y ∪ W) |Z

setTrivialtyAssumed

public void setTrivialtyAssumed()

setSymmetryAssumed

public void setSymmetryAssumed()

X ⊥⊥ Y | Z ==> Y ⊥⊥ X | Z