The ontological commitments we require to show the necessity of ultimately founded propositions are, on the one hand, the possibilist interpretation of the existential quantifier
or the assumption of a constant domain of the possible worlds W*; and, on the other hand, the modal logic S5.
Queries that have twisted universal and existential quantifiers
can be stunning for students, practitioners, or even instructors.
We need at most m extra variable for existential quantifiers
, where m is the maximum arity of a schema relation.
The issue is whether (Two) is deducible on the basis of the introduction and elimination rules for negation, identity, and the first-order existential quantifier
Hintikka adds a proviso that 'moves connected with existential quantifiers
are always independent of earlier moves with existential quantifiers
Therefore, the existential quantifier
on z only depends on x and can be moved before [inverted] Ay.
Predicate-vagueness is characterised by "there being border cases", yet the existential quantifier
is precise(3) so the notion of a border case must be vague.
The naive view of existence is as a first order predicate and not as derivative from the so-called existential quantifier
For "predicate-vagueness is characterised by 'there being border cases', yet the existential quantifier
Thus, my suggestion that the constructibility quantifier has virtually the same semantics as the ordinary, existential quantifier
These formulas extend propositional formulas by allowing both universal and existential quantifiers
over propositional variables, and are useful for modeling problems in artificial intelligence and computer science.
For example, for the universal and existential quantifiers
, we can see the boolean circuits creation that they will be replaced by a binary tree balanced (by means of the use of the algorithms and-tree and or-tree).