Search results
Results from the WOW.Com Content Network
Up to a certain notion of isomorphism, the powerset operation is definable in second-order logic. Using this observation, Jaakko Hintikka established in 1955 that second-order logic can simulate higher-order logics in the sense that for every formula of a higher-order logic, one can find an equisatisfiable formula for it in second-order logic. [9]
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 ...
In mathematical logic, a sentence (or closed formula) [1] of a predicate logic is a Boolean-valued well-formed formula with no free variables. A sentence can be viewed as expressing a proposition , something that must be true or false.
The notion of a predicate in traditional grammar traces back to Aristotelian logic. [2] A predicate is seen as a property that a subject has or is characterized by. A predicate is therefore an expression that can be true of something. [3] Thus, the expression "is moving" is true of anything that is moving.
A predicate is a statement or mathematical assertion that contains variables, sometimes referred to as predicate variables, and may be true or false depending on those variables’ value or values. In propositional logic, atomic formulas are sometimes regarded as zero-place predicates. [1] In a sense, these are nullary (i.e. 0-arity) predicates.
A closed formula, also ground formula or sentence, is a formula in which there are no free occurrences of any variable. If A is a formula of a first-order language in which the variables v 1, …, v n have free occurrences, then A preceded by ∀v 1 ⋯ ∀v n is a universal closure of A.
predicate adverbials are not the same kind of thing as second-order predicates such as colour. Relative adjective Jumbo is a small elephant. Example cannot be analysed as Sj ∧ Ej; predicate adjectives are not the same kind of thing as second-order predicates such as colour. Predicate adverbial modifier John is walking very quickly. —
Propositional logic, as currently studied in universities, is a specification of a standard of logical consequence in which only the meanings of propositional connectives are considered in evaluating the conditions for the truth of a sentence, or whether a sentence logically follows from some other sentence or group of sentences.