trait Logic[A] extends BoundedDistributiveLattice[A]
Logic models a logic generally. It is a bounded distributive lattice with an extra negation operator.
The negation operator obeys the weak De Morgan laws:
- ¬(x∨y) = ¬x∧¬y
- ¬(x∧y) = ¬¬(¬x∨¬y)
For intuitionistic logic see Heyting For fuzzy logic see DeMorgan
- Self Type
- Logic[A]
- Source
- Logic.scala
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- BoundedDistributiveLattice
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- Lattice
- MeetSemilattice
- JoinSemilattice
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- abstract def and(a: A, b: A): A
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- abstract def join(lhs: A, rhs: A): A
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- JoinSemilattice
- abstract def meet(lhs: A, rhs: A): A
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- MeetSemilattice
- abstract def not(a: A): A
- abstract def one: A
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- BoundedMeetSemilattice
- abstract def or(a: A, b: A): A
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- BoundedJoinSemilattice
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- def dual: BoundedDistributiveLattice[A]
This is the lattice with meet and join swapped
This is the lattice with meet and join swapped
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- def joinPartialOrder(implicit ev: Eq[A]): PartialOrder[A]
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- def joinSemilattice: BoundedSemilattice[A]
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- BoundedJoinSemilattice → JoinSemilattice
- def meetPartialOrder(implicit ev: Eq[A]): PartialOrder[A]
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- MeetSemilattice
- def meetSemilattice: BoundedSemilattice[A]
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- BoundedMeetSemilattice → MeetSemilattice
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