Sentence examples for disjunction property from inspiring English sources
The disjunction property (2) holds in a Boolean topos if and only if, for every closed formula p, either p is true or ¬p is true.
Also, the disjunction property, essential in constructivism, is easily established for the additive disjunction.
Moreover, C satisfies the disjunction property and the constructible falsity property.
The intermediate logic obtained by adding the schema ((¬ ¬ D → D) → (D ∨ ¬ D)) → (¬ ¬ D ∨ ¬ D), corresponding to Rose's counterexample, to IPC also has the disjunction property.
The system CK is shown to be faithfully embeddable into QC, to be decidable, and to enjoy the disjunction property and the constructible falsity property.
However, if HA proved ∃yG y) ∨ ∀x¬G x) then by the disjunction property, HA must prove either ∃yG y) or ∀x¬G x).
As realisability techniques have proved crucial in investigations on the existence and disjunction properties for constructive and intuitionistic set theories, we discuss the outcomes of these studies in the next section.
For intermediate values of the inputs, this neuron produces a fuzzy logic disjunction if property 3 of Table 1 is also generalized to say the neuron's output is an increasing function of each of the input variables.
Strong global supervenience entails strong individual supervenience as long as the base set B is taken to be closed under complementation, infinitary conjunction, infinitary disjunction, and property-forming operations involving quantification and identity.
But neither i) nor ii) follows from the possible world versions of either weak or strong supervenience unless B is assumed to be closed under the Boolean operations of complementation, infinitary conjunction, infinitary disjunction, and property-forming operations involving quantification (McLaughlin 1995).
Here we recall the disjunction and existence property, formulated for a set theory T. The informal motivation for the disjunction and the existence property is based on our understanding of the constructive proofs of disjunctive and existential statements.
