Class/Object

at.logic.gapt.expr.hol

SkolemFunctions

Related Docs: object SkolemFunctions | package hol

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case class SkolemFunctions(skolemDefs: Map[Const, LambdaExpression]) extends Product with Serializable

List of definitions of Skolem symbols.

A Skolem definition is similar but slightly different from the epsilon operator:

Syntactically it is a map s_i → λx_1 .. λx_n Qy φ(x_1, .., x_n, y), where Q is a quantifier. Then s_i(x_1, .., x_n) is the Skolem term used for the formula Qy φ(x_1, .., x_n, y), where Qy is strong.

This Skolem term corresponds to the epsilon term εy φ(x_1, .., x_n, y) or εy ¬φ(x_1, .., x_n), depending on whether Q is ∃ or ∀. The reason we don't use epsilon terms directly is that this makes it impossible to deskolemize a formula based on just the Skolem definitions: for example both ∃x ∀y φ and ∃x ¬∃y¬ φ would define their Skolem functions using the same epsilon terms.

Source
SkolemFunctions.scala
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  1. SkolemFunctions
  2. Serializable
  3. Serializable
  4. Product
  5. Equals
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  7. Any
Implicitly
  1. by any2stringadd
  2. by StringFormat
  3. by Ensuring
  4. by ArrowAssoc
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Instance Constructors

  1. new SkolemFunctions(skolemDefs: Map[Const, LambdaExpression])

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Value Members

  1. final def !=(arg0: Any): Boolean

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    Definition Classes
    AnyRef → Any
  2. final def ##(): Int

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    Definition Classes
    AnyRef → Any
  3. def +(other: String): String

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    Implicit information
    This member is added by an implicit conversion from SkolemFunctions to any2stringadd[SkolemFunctions] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  4. def ->[B](y: B): (SkolemFunctions, B)

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    Implicit information
    This member is added by an implicit conversion from SkolemFunctions to ArrowAssoc[SkolemFunctions] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @inline()
  5. final def ==(arg0: Any): Boolean

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    Definition Classes
    AnyRef → Any
  6. final def asInstanceOf[T0]: T0

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    Any
  7. def clone(): AnyRef

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    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  8. val dependencyOrder: Seq[Const]

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  9. def ensuring(cond: (SkolemFunctions) ⇒ Boolean, msg: ⇒ Any): SkolemFunctions

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    Implicit information
    This member is added by an implicit conversion from SkolemFunctions to Ensuring[SkolemFunctions] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  10. def ensuring(cond: (SkolemFunctions) ⇒ Boolean): SkolemFunctions

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    Implicit information
    This member is added by an implicit conversion from SkolemFunctions to Ensuring[SkolemFunctions] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  11. def ensuring(cond: Boolean, msg: ⇒ Any): SkolemFunctions

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    Implicit information
    This member is added by an implicit conversion from SkolemFunctions to Ensuring[SkolemFunctions] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  12. def ensuring(cond: Boolean): SkolemFunctions

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    Implicit information
    This member is added by an implicit conversion from SkolemFunctions to Ensuring[SkolemFunctions] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  13. final def eq(arg0: AnyRef): Boolean

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    Definition Classes
    AnyRef
  14. def finalize(): Unit

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    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  15. def formatted(fmtstr: String): String

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    Implicit information
    This member is added by an implicit conversion from SkolemFunctions to StringFormat[SkolemFunctions] performed by method StringFormat in scala.Predef.
    Definition Classes
    StringFormat
    Annotations
    @inline()
  16. final def getClass(): Class[_]

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    Definition Classes
    AnyRef → Any
  17. final def isInstanceOf[T0]: Boolean

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    Definition Classes
    Any
  18. final def ne(arg0: AnyRef): Boolean

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    Definition Classes
    AnyRef
  19. final def notify(): Unit

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    Definition Classes
    AnyRef
  20. final def notifyAll(): Unit

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    Definition Classes
    AnyRef
  21. val skolemDefs: Map[Const, LambdaExpression]

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  22. final def synchronized[T0](arg0: ⇒ T0): T0

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    Definition Classes
    AnyRef
  23. def toString(): String

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    Definition Classes
    SkolemFunctions → AnyRef → Any
  24. final def wait(): Unit

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    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  25. final def wait(arg0: Long, arg1: Int): Unit

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    Definition Classes
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    Annotations
    @throws( ... )
  26. final def wait(arg0: Long): Unit

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    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  27. def [B](y: B): (SkolemFunctions, B)

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    Implicit information
    This member is added by an implicit conversion from SkolemFunctions to ArrowAssoc[SkolemFunctions] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc

Inherited from Serializable

Inherited from Serializable

Inherited from Product

Inherited from Equals

Inherited from AnyRef

Inherited from Any

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

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

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

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

Ungrouped