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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.
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.
For predicate logic, the atoms are predicate symbols together with their arguments, each argument being a term. According to some terminology, an open formula is formed by combining atomic formulas using only logical connectives, to the exclusion of quantifiers. [15] This is not to be confused with a formula which is not closed.
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.
The predicate calculus goes a step further than the propositional calculus to an "analysis of the inner structure of propositions" [4] It breaks a simple sentence down into two parts (i) its subject (the object (singular or plural) of discourse) and (ii) a predicate (a verb or possibly verb-clause that asserts a quality or attribute of the object(s)).
The predicate is a verb phrase that consists of more than one word. In the backyard, the dog barked and howled at the cat. This simple sentence has one independent clause which contains one subject, dog, and one predicate, barked and howled at the cat. This predicate has two verbs, known as a compound predicate: barked and howled. (This should ...
In logic, a truth function [1] is a function that accepts truth values as input and produces a unique truth value as output. In other words: the input and output of a truth function are all truth values; a truth function will always output exactly one truth value, and inputting the same truth value(s) will always output the same truth value.
In linguistics, a compound verb or complex predicate is a multi-word compound that functions as a single verb. One component of the compound is a light verb or vector , which carries any inflections , indicating tense , mood , or aspect , but provides only fine shades of meaning.