The Fortress Language Specification - CiteSeerX

24.2.19 possibly(self): Boolean
24.2.20 necessarily(self):Boolean
24.2.21 certainly(self): Boolean
The predicate possibly returns true if and only if true is a member of this boolean interval.
The predicate necessarily returns true if and only if false is not a member of this boolean interval (thus “necessarily”
is a concise way of saying “not possibly not”).
The predicate certainly returns true if and only if this boolean interval is True, that is, it contains true but not false
(thus “certainly” is a concise way of saying “both possibly and necessarily”).
The fourteen nontrivial functions from a value x of type BooleanInterval to type Boolean may thus be expressed as
follows:
necessarily(x) ∧ necessarily(¬x)
certainly(¬x)
necessarily(¬x)
certainly(x)
necessarily(x)
possibly(x) ≡ necessarily(x)
necessarily(x) ∨ necessarily(¬x)
possibly(x) ∧ possibly(¬x)
possibly(x) ∨ necessarily(x)
possibly(¬x)
¬certainly(x)
possibly(x)
¬certainly(¬x)
possibly(x) ∨ possibly(¬x))
There are other ways to express some of them; for example, necessarily(x) ∧ necessarily(¬x) is the same as
x = Impossible , and possibly(x) ∧ possibly(¬x) is the same as x = Uncertain .
24.2.22 getter empty():BooleanInterval
24.2.23 getter universe():BooleanInterval
The getter empty returns the value Impossible, and the getter universe returns the value Uncertain. These are defined
primarily for the benefit of the BooleanAlgebra trait that BooleanInterval extends.
24.2.24 opr =(self,other: BooleanInterval):Boolean
Two boolean intervals are strictly equivalent if and only if they are the same boolean interval.
24.2.25 getter hashCode(): Z64
24.2.26 toString():String
The toString method returns either “True” or “False” or “Uncertain” or “Impossible” as appropriate.
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