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Disjunction in natural languages does not precisely match the interpretation of in classical logic. Notably, classical disjunction is inclusive while natural language disjunction is often understood exclusively, as the following English example typically would be. [1] Mary is eating an apple or a pear.
propositional logic, Boolean algebra, Heyting algebra: is false when A is true and B is false but true otherwise. may mean the same as (the symbol may also indicate the domain and codomain of a function; see table of mathematical symbols).
Wherever logic is applied, especially in mathematical discussions, it has the same meaning as above: it is an abbreviation for if and only if, indicating that one statement is both necessary and sufficient for the other. This is an example of mathematical jargon (although, as noted above, if is more often used than iff in statements of definition).
Disjunction is often understood exclusively in natural languages. In English, the disjunctive word "or" is often understood exclusively, particularly when used with the particle "either". The English example below would normally be understood in conversation as implying that Mary is not both a singer and a poet. [4] [5] 1. Mary is a singer or a ...
The name "disjunctive syllogism" derives from its being a syllogism, a three-step argument, and the use of a logical disjunction (any "or" statement.) For example, "P or Q" is a disjunction, where P and Q are called the statement's disjuncts. The rule makes it possible to eliminate a disjunction from a logical proof. It is the rule that
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 meanings of natural language connectives are not precisely identical to their nearest equivalents in classical logic. In particular, disjunction can receive an exclusive interpretation in many languages. Some researchers have taken this fact as evidence that natural language semantics is nonclassical.
A symbol or word used in logic to connect propositions or sentences, forming more complex expressions that convey relationships such as conjunction, disjunction, and negation. logical consequence A relationship between statements where the truth of one or more premises necessitates the truth of a conclusion, based on the logical structure of ...