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Qualitative predicates, like green, can be assessed without knowing the spatial or temporal relation of x to a particular time, place or event. Locational predicates, like grue, cannot be assessed without knowing the spatial or temporal relation of x to a particular time, place or event, in this case whether x is being observed before or after ...
The same is true when horse B is removed. However, the statement "the first horse that was excluded is of the same color as the non-excluded horses, who in turn are of the same color as the other excluded horse" is meaningless, because there are no "non-excluded horses" (common elements (horses) in the two sets, since each horse is excluded once).
A sentence can be viewed as expressing a proposition, something that must be true or false. The restriction of having no free variables is needed to make sure that sentences can have concrete, fixed truth values : as the free variables of a (general) formula can range over several values, the truth value of such a formula may vary.
First-order logic—also called predicate logic, predicate calculus, quantificational logic—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables.
In propositional calculus, a propositional function or a predicate is a sentence expressed in a way that would assume the value of true or false, except that within the sentence there is a variable (x) that is not defined or specified (thus being a free variable), which leaves the statement undetermined.
There are at least two types of raising predicates/verbs: raising-to-subject verbs and raising-to-object predicates. Raising-to-object predicates overlap to a large extent with so-called ECM-verbs (= exceptional case-marking). These types of raising predicates/verbs are illustrated with the following sentences: a. They seem to be trying.
Resultatives appear as predicates of sentences, and are generally composed of a verb (denoting the event), a post-verbal noun phrase (denoting the entity that has undergone a change) and a so-called resultative phrase (denoting the state achieved as the result of the action named by the verb [1]) which may be represented by an adjective, a ...
However, we cannot do the same with the predicate. That is, the following expression: ∃P P(b) is not a sentence of first-order logic, but this is a legitimate sentence of second-order logic. Here, P is a predicate variable and is semantically a set of individuals. [1] As a result, second-order logic has greater expressive power than first ...
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