Package org.tweetyproject.logics.fol.syntax

Class Implication

java.lang.Object

org.tweetyproject.logics.commons.syntax.RelationalFormula

org.tweetyproject.logics.fol.syntax.FolFormula

org.tweetyproject.logics.fol.syntax.Implication

All Implemented Interfaces:

Formula, ClassicalFormula, ComplexLogicalFormula, Conjunctable, Disjunctable, Invertable, LogicStructure, ProbabilityAware, QuantifiedFormula, SimpleLogicalFormula

public class Implication
extends FolFormula

The implication of first-order logic.

Author:

Anna Gessler

Constructor Summary

Constructors

Constructor	Description
Implication(Pair<RelationalFormula,RelationalFormula> formulas)	Creates a new implication with the given pair of formulas
Implication(RelationalFormula a, RelationalFormula b)	Creates a new implication a=>b with the two given formulas

Method Summary

Modifier and Type	Method	Description
Implication	clone()	Creates a deep copy of this formula
RelationalFormula	collapseAssociativeFormulas()	This method collapses all associative operations appearing in this term, e.g.
boolean	containsQuantifier()	Checks whether this formula contains any quantification.
boolean	equals(Object obj)
Set<? extends Atom>	getAtoms()	Processes the set of all atoms which appear in this formula
RelationalFormula	getFirstFormula()	Get the left side formula of the implication left => right.
Pair<RelationalFormula,RelationalFormula>	getFormulas()	Returns the formulas of the implication.
Set<Functor>	getFunctors()
Set<? extends Predicate>	getPredicates()	Processes the set of all predicates which appear in this formula
RelationalFormula	getSecondFormula()	Get the right side formula of the implication left => right
Set<Term<?>>	getTerms()
<C extends Term<?>> Set<C>	getTerms(Class<C> cls)	Processes the set containing all terms of type C.
Set<Variable>	getUnboundVariables()
int	hashCode()
boolean	isClosed()	Checks whether this formula is closed, i.e.
boolean	isClosed(Set<Variable> boundVariables)	Checks whether this formula is closed, i.e.
boolean	isDnf()	Checks whether this formula is in disjunctive normal form.
boolean	isLiteral()
boolean	isWellBound()	Checks whether this formula is well-bound, i.e.
boolean	isWellBound(Set<Variable> boundVariables)	Checks whether this formula is well-bound, i.e.
void	setFirstFormula(RelationalFormula left)	Sets the left side formula of the implication left => right
void	setFormulas(Pair<RelationalFormula,RelationalFormula> formulas)	Sets the formulas of the implication.
void	setFormulas(RelationalFormula left, RelationalFormula right)	Sets the formulas of the implication.
void	setSecondFormula(RelationalFormula right)	Sets the right side formula of the implication left => right
FolFormula	substitute(Term<?> v, Term<?> t)	Substitutes all occurrences of term "v" in this formula by term "t" and returns the new formula.
FolFormula	toNnf()	Makes the negation normal form of this formula.
String	toString()

Methods inherited from class org.tweetyproject.logics.fol.syntax.FolFormula

combineWithAnd, combineWithOr, complement, getQuantifierVariables, getSignature, getUniformProbability, toDnf

Methods inherited from class org.tweetyproject.logics.commons.syntax.RelationalFormula

allGroundInstances, allSubstitutions, containsTermsOfType, exchange, getFormula, getPredicateCls, getSatisfactionRatio, isGround, isWellFormed, substitute

Methods inherited from class java.lang.Object

getClass, notify, notifyAll, wait, wait, wait

Constructor Details

Implication

public Implication(RelationalFormula a,
 RelationalFormula b)

Creates a new implication a=>b with the two given formulas

Parameters:

a - a relational formula.

b - a relational formula.

Implication

public Implication(Pair<RelationalFormula,RelationalFormula> formulas)

Creates a new implication with the given pair of formulas

Parameters:

formulas - a pair of formulas

Method Details

getFormulas

public Pair<RelationalFormula,RelationalFormula> getFormulas()

Returns the formulas of the implication.

Returns:

the formulas that are part of the implication

setFormulas

public void setFormulas(Pair<RelationalFormula,RelationalFormula> formulas)

Sets the formulas of the implication.

Parameters:

formulas - the formulas

setFormulas

public void setFormulas(RelationalFormula left,
 RelationalFormula right)

Sets the formulas of the implication.

Parameters:

left - left formula

right - right formula

setFirstFormula

public void setFirstFormula(RelationalFormula left)

Sets the left side formula of the implication left => right

Parameters:

left - formula.

setSecondFormula

public void setSecondFormula(RelationalFormula right)

Sets the right side formula of the implication left => right

Parameters:

right - formula.

getFirstFormula

public RelationalFormula getFirstFormula()

Get the left side formula of the implication left => right.

Returns:

the 1st relational formula

getSecondFormula

public RelationalFormula getSecondFormula()

Get the right side formula of the implication left => right

Returns:

the second relational formula

getPredicates

public Set<? extends Predicate> getPredicates()

Description copied from interface: SimpleLogicalFormula

Processes the set of all predicates which appear in this formula

Returns:

all predicates that appear in this formula

isLiteral

public boolean isLiteral()

Returns:

true if the formula represents a literal in the language or false otherwise

getUnboundVariables

public Set<Variable> getUnboundVariables()

Returns:

a set of of unbound variables

containsQuantifier

public boolean containsQuantifier()

Description copied from interface: QuantifiedFormula

Checks whether this formula contains any quantification.

Returns:

"true" if this formula contains a quantification.

isWellBound

public boolean isWellBound()

Description copied from interface: QuantifiedFormula

Checks whether this formula is well-bound, i.e. whether no variable bound by a quantifier is again bound by another quantifier within the first quantifier's range.

Returns:

"true" if this formula is well-bound, "false" otherwise.

isWellBound

public boolean isWellBound(Set<Variable> boundVariables)

Description copied from interface: QuantifiedFormula

Checks whether this formula is well-bound, i.e. whether no variable bound by a quantifier is again bound by another quantifier within the first quantifier range. Every variable in "boundVariables" is assumed to be bound already.

Parameters:

boundVariables - the variables assumed to be bound.

Returns:

"true" if this formula is well-bound, "false" otherwise.

isClosed

public boolean isClosed()

Description copied from interface: QuantifiedFormula

Checks whether this formula is closed, i.e. whether every variables occurring in the formula is bound by a quantifier.

Returns:

"true" if this formula is closed, "false" otherwise.

isClosed

public boolean isClosed(Set<Variable> boundVariables)

Description copied from interface: QuantifiedFormula

Checks whether this formula is closed, i.e. whether every variables occurring in the formula is bound by a quantifier. Every variable in "boundVariables" is already assumed to be bound.

Parameters:

boundVariables - the variables assumed to be bound.

Returns:

"true" if this formula is closed wrt. "boundVariables", "false" otherwise.

getTerms

public Set<Term<?>> getTerms()

Returns:

a set containing all terms of this logical structure

getTerms

public <C extends Term<?>> Set<C> getTerms(Class<C> cls)

Description copied from interface: LogicStructure

Processes the set containing all terms of type C. This method uses the equals method of the given Class and therefore does not add terms which are sub classes of type C to the set.

Type Parameters:

C - the type of terms

Parameters:

cls - The Class structure containing type information about the searched term

Returns:

A set containing all terms of type C of this logical structure

toNnf

public FolFormula toNnf()

Description copied from class: FolFormula

Makes the negation normal form of this formula.

Specified by:

toNnf in class FolFormula

Returns:

the NNF of this formula

collapseAssociativeFormulas

public RelationalFormula collapseAssociativeFormulas()

Description copied from class: FolFormula

This method collapses all associative operations appearing in this term, e.g. every a||(b||c) becomes a||b||c.

Specified by:

collapseAssociativeFormulas in class FolFormula

Returns:

the collapsed formula.

isDnf

public boolean isDnf()

Description copied from class: FolFormula

Checks whether this formula is in disjunctive normal form.

Specified by:

isDnf in class FolFormula

Returns:

"true" iff this formula is in disjunctive normal form.

substitute

public FolFormula substitute(Term<?> v,
 Term<?> t)
                      throws IllegalArgumentException

Description copied from class: RelationalFormula

Substitutes all occurrences of term "v" in this formula by term "t" and returns the new formula. NOTE: if "v" is a variable and bound to a quantifier then "v" is not substituted in that quantifiers inner formula.

Specified by:

substitute in interface ComplexLogicalFormula

Specified by:

substitute in class FolFormula

Parameters:

v - the term to be substituted.

t - the term to substitute.

Returns:

a formula where every occurrence of "v" is replaced by "t".

Throws:

IllegalArgumentException - if "v" and "t" are of different sorts (NOTE: this exception is only thrown when "v" actually appears in this formula).

clone

public Implication clone()

Description copied from interface: SimpleLogicalFormula

Creates a deep copy of this formula

Specified by:

clone in interface ComplexLogicalFormula

Specified by:

clone in interface SimpleLogicalFormula

Specified by:

clone in class FolFormula

Returns:

the cloned formula

getAtoms

public Set<? extends Atom> getAtoms()

Description copied from interface: SimpleLogicalFormula

Processes the set of all atoms which appear in this formula

Specified by:

getAtoms in interface SimpleLogicalFormula

Specified by:

getAtoms in class RelationalFormula

Returns:

all atoms that appear in this formula.

getFunctors

public Set<Functor> getFunctors()

Specified by:

getFunctors in class RelationalFormula

Returns:

all functors that appear in this formula.

toString

public String toString()

Specified by:

toString in class RelationalFormula

hashCode

public int hashCode()

Specified by:

hashCode in interface SimpleLogicalFormula

Overrides:

hashCode in class Object

equals

public boolean equals(Object obj)

Specified by:

equals in interface SimpleLogicalFormula

Overrides:

equals in class Object