c

at.logic.gapt.proofs.expansion

ETSkolemQuantifier

case class ETSkolemQuantifier(shallow: Formula, skolemTerm: Expr, skolemDef: Expr, child: ExpansionTree) extends ETQuantifier with UnaryExpansionTree with Product with Serializable

A tree representing a formula beginning with a strong quantifier, i.e., a positive universal or a negative existential.

As an example let us consider an expansion proof of ∀z P(c,z) :- ∃x ∀y P(x,y). For Skolemization we introduce the Skolem function s_1 (for the single strong quantifier), this function has the Skolem definition λx ∀y P(x,y) (see at.logic.gapt.expr.hol.SkolemFunctions for details). The natural expansion proof has the deep formula P(c,s_1(c)) :- P(c,s_1(c)), so we need a Skolem node with the shallow formula ∀y P(c,y), and deep formula P(c,s_1(c)). This Skolem node is constructed as ETSkolemQuantifier(∀y P(c,y), s_1(c), λx ∀y P(x,y), ETAtom(P(c,s_1(c)), InSuc)).

shallow

Shallow formula of the expansion tree.

skolemTerm

Skolem term that instantiates the strong quantifier, e.g. s_3(c)

skolemDef

Skolem definition for the Skolem symbol, see at.logic.gapt.expr.hol.SkolemFunctions

child

Expansion tree of the instantiated formula.

Source
expansionTrees.scala
Ordering
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  2. By Inheritance
Inherited
  1. ETSkolemQuantifier
  2. Serializable
  3. Serializable
  4. UnaryExpansionTree
  5. ETQuantifier
  6. ExpansionTree
  7. DagProof
  8. Product
  9. Equals
  10. AnyRef
  11. Any
Implicitly
  1. by any2stringadd
  2. by StringFormat
  3. by Ensuring
  4. by ArrowAssoc
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Visibility
  1. Public
  2. All

Instance Constructors

  1. new ETSkolemQuantifier(shallow: Formula, skolemTerm: Expr, skolemDef: Expr, child: ExpansionTree)

    shallow

    Shallow formula of the expansion tree.

    skolemTerm

    Skolem term that instantiates the strong quantifier, e.g. s_3(c)

    skolemDef

    Skolem definition for the Skolem symbol, see at.logic.gapt.expr.hol.SkolemFunctions

    child

    Expansion tree of the instantiated formula.

Value Members

  1. final def !=(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  2. final def ##(): Int
    Definition Classes
    AnyRef → Any
  3. def +(other: String): String
    Implicit
    This member is added by an implicit conversion from ETSkolemQuantifier to any2stringadd[ETSkolemQuantifier] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  4. def ->[B](y: B): (ETSkolemQuantifier, B)
    Implicit
    This member is added by an implicit conversion from ETSkolemQuantifier to ArrowAssoc[ETSkolemQuantifier] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @inline()
  5. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  6. def apply(pos: HOLPosition): Set[ExpansionTree]
    Definition Classes
    ExpansionTree
  7. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  8. val boundVar: Var
  9. val child: ExpansionTree
    Definition Classes
    ETSkolemQuantifierUnaryExpansionTree
  10. def clone(): AnyRef
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @native() @throws( ... )
  11. def dagLike: DagLikeOps[ExpansionTree]

    Operations that view the sub-proofs as a DAG, which ignore duplicate sub-proofs, see DagProof.DagLikeOps for a list.

    Operations that view the sub-proofs as a DAG, which ignore duplicate sub-proofs, see DagProof.DagLikeOps for a list.

    Definition Classes
    DagProof
  12. def deep: Formula

    The formula represented by this tree, fully instantiated.

    The formula represented by this tree, fully instantiated.

    Definition Classes
    ETSkolemQuantifierExpansionTree
  13. def depth: Int

    Depth of the proof, which is the maximum length of a path you can take via immediateSubProofs.

    Depth of the proof, which is the maximum length of a path you can take via immediateSubProofs.

    Definition Classes
    DagProof
  14. def ensuring(cond: (ETSkolemQuantifier) ⇒ Boolean, msg: ⇒ Any): ETSkolemQuantifier
    Implicit
    This member is added by an implicit conversion from ETSkolemQuantifier to Ensuring[ETSkolemQuantifier] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  15. def ensuring(cond: (ETSkolemQuantifier) ⇒ Boolean): ETSkolemQuantifier
    Implicit
    This member is added by an implicit conversion from ETSkolemQuantifier to Ensuring[ETSkolemQuantifier] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  16. def ensuring(cond: Boolean, msg: ⇒ Any): ETSkolemQuantifier
    Implicit
    This member is added by an implicit conversion from ETSkolemQuantifier to Ensuring[ETSkolemQuantifier] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  17. def ensuring(cond: Boolean): ETSkolemQuantifier
    Implicit
    This member is added by an implicit conversion from ETSkolemQuantifier to Ensuring[ETSkolemQuantifier] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  18. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  19. def equals(that: Any): Boolean
    Definition Classes
    DagProof → Equals → AnyRef → Any
  20. def finalize(): Unit
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  21. def formatted(fmtstr: String): String
    Implicit
    This member is added by an implicit conversion from ETSkolemQuantifier to StringFormat[ETSkolemQuantifier] performed by method StringFormat in scala.Predef.
    Definition Classes
    StringFormat
    Annotations
    @inline()
  22. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  23. val hashCode: Int
    Definition Classes
    DagProof
  24. def immediateSubProofs: Seq[ExpansionTree]

    The immediate subproofs of this rule.

    The immediate subproofs of this rule.

    Definition Classes
    UnaryExpansionTreeDagProof
  25. def instances: Iterable[(Expr, ExpansionTree)]
    Definition Classes
    ETSkolemQuantifierETQuantifier
  26. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  27. def longName: String

    The name of this rule (in words).

    The name of this rule (in words).

    Definition Classes
    DagProof
  28. def name: String

    The name of this rule (in symbols).

    The name of this rule (in symbols).

    Definition Classes
    DagProof
  29. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  30. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  31. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  32. val polarity: Product with Serializable with Polarity { def unary_!: Product with Serializable with at.logic.gapt.expr.Polarity }
    Definition Classes
    ETSkolemQuantifierExpansionTree
  33. val qfFormula: Formula
  34. val shallow: Formula
    Definition Classes
    ETSkolemQuantifierExpansionTree
  35. val skolemArgs: List[Expr]
  36. val skolemConst: Const
  37. val skolemDef: Expr
  38. val skolemTerm: Expr
  39. def stepString(subProofLabels: Map[Any, String]): String
    Attributes
    protected
    Definition Classes
    DagProof
  40. def subProofAt(pos: List[Int]): ExpansionTree

    Returns the subproof at the given position: p.subProofAt(Nil) is p itself; p.subProofAt(i :: is) is the ith subproof of p.subProofAt(is).

    Returns the subproof at the given position: p.subProofAt(Nil) is p itself; p.subProofAt(i :: is) is the ith subproof of p.subProofAt(is).

    Definition Classes
    DagProof
  41. def subProofs: Set[ExpansionTree]

    Set of all (transitive) sub-proofs including this.

    Set of all (transitive) sub-proofs including this.

    Definition Classes
    DagProof
  42. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  43. def toSigRelativeString(implicit sig: BabelSignature): String
    Definition Classes
    ExpansionTree
  44. def toString(): String
    Definition Classes
    ExpansionTreeDagProof → AnyRef → Any
  45. def treeLike: TreeLikeOps[ExpansionTree]

    Operations that view the sub-proofs as a tree, see DagProof.TreeLikeOps for a list.

    Operations that view the sub-proofs as a tree, see DagProof.TreeLikeOps for a list.

    Definition Classes
    DagProof
  46. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  47. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  48. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @throws( ... )
  49. def [B](y: B): (ETSkolemQuantifier, B)
    Implicit
    This member is added by an implicit conversion from ETSkolemQuantifier to ArrowAssoc[ETSkolemQuantifier] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc

Inherited from Serializable

Inherited from Serializable

Inherited from UnaryExpansionTree

Inherited from ETQuantifier

Inherited from ExpansionTree

Inherited from DagProof[ExpansionTree]

Inherited from Product

Inherited from Equals

Inherited from AnyRef

Inherited from Any

Inherited by implicit conversion any2stringadd from ETSkolemQuantifier to any2stringadd[ETSkolemQuantifier]

Inherited by implicit conversion StringFormat from ETSkolemQuantifier to StringFormat[ETSkolemQuantifier]

Inherited by implicit conversion Ensuring from ETSkolemQuantifier to Ensuring[ETSkolemQuantifier]

Inherited by implicit conversion ArrowAssoc from ETSkolemQuantifier to ArrowAssoc[ETSkolemQuantifier]

Ungrouped