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Contraposition. In logic and mathematics, contraposition, or transposition, refers to the inference of going from a conditional statement into its logically equivalent contrapositive, and an associated proof method known as § Proof by contrapositive. The contrapositive of a statement has its antecedent and consequent inverted and flipped.
Logical grammar. Logical grammar or rational grammar is a term used in the history and philosophy of linguistics to refer to certain linguistic and grammatical theories that were prominent until the early 19th century and later influenced 20th-century linguistic thought. These theories were developed by scholars and philosophers who sought to ...
For example, with the predicate P as "x is mortal" and the domain of x as the collection of all humans, () means "a person x in all humans is mortal" or "all humans are mortal". The negation of it is ¬ ∀ x P ( x ) ≡ ∃ x ¬ P ( x ) {\displaystyle \neg \forall xP(x)\equiv \exists x\neg P(x)} , meaning "there exists a person x in all humans ...
Opposite (semantics) In lexical semantics, opposites are words lying in an inherently incompatible binary relationship. For example, something that is male entails that it is not female. It is referred to as a 'binary' relationship because there are two members in a set of opposites. The relationship between opposites is known as opposition.
Inverse (logic) In logic, an inverse is a type of conditional sentence which is an immediate inference made from another conditional sentence. More specifically, given a conditional sentence of the form , the inverse refers to the sentence . Since an inverse is the contrapositive of the converse, inverse and converse are logically equivalent to ...
Lexical semantics. Lexical semantics (also known as lexicosemantics), as a subfield of linguistic semantics, is the study of word meanings. [ 1 ][ 2 ] It includes the study of how words structure their meaning, how they act in grammar and compositionality, [ 1 ] and the relationships between the distinct senses and uses of a word.