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In lexical semantics, opposites are words that lie in an inherently incompatible binary relationship as in the opposite pairs big : small, long : short, and precede : follow. The notion of incompatibility here refers to the fact that one word in an opposite pair entails that it is not the other pair member. For example, something that is long entails that it is not short. 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. A member of a pair of opposites can generally be determined by the question What is the opposite of X ?
The term antonym (and the related antonymy) is commonly taken to be synonymous with opposite, but antonym also has other more restricted meanings. Graded (or gradable) antonyms are word pairs whose meanings are opposite and which lie on a continuous spectrum (hot, cold). Complementary antonyms are word pairs whose meanings are opposite but whose meanings do not lie on a continuous spectrum (push, pull). Relational antonyms are word pairs where opposite makes sense only in the context of the relationship between the two meanings (teacher, pupil). These more restricted meanings may not apply in all scholarly contexts, with Lyons (1968, 1977) defining antonym to mean gradable antonyms, and Crystal (2003) warns that antonymy and antonym should be regarded with care.
Opposites are simultaneously different and similar in meaning. Typically, they differ in only one dimension of meaning, but are similar in most other respects, including similarity in grammar and positions of semantic abnormality. Additionally, not all words have an opposite. Some words are non-opposable. For example, animal or plant species have no binary opposites (other than possible gender opposites such as lion/lioness, etc.); the word platypus therefore has no word that stands in opposition to it (hence the unanswerability of What is the opposite of platypus?).
Other words are opposable but have an accidental gap in a given language's lexicon. For example, the word devout lacks a lexical opposite, but it is fairly easy to conceptualize a parameter of devoutness where devout lies at the positive pole with a missing member at the negative pole. Opposites of such words can nevertheless sometimes be formed with the prefixes un- or non-, with varying degrees of naturalness. For example, the word undevout appears in Webster's dictionary of 1828, while the pattern of non-person could conceivably be extended to non-platypus. Conversely, some words appear to be a prefixed form of an opposite, but the opposite term does not exist, such as inept, which appears to be in- + *ept; such a word is known as an unpaired word.
Opposites may be viewed as a special type of incompatibility. Words that are incompatible create the following type of entailment (where X is a given word and Y is a different word incompatible with word X):
- sentence A is X entails sentence A is not Y 
An example of an incompatible pair of words is cat : dog:
- It's a cat entails It's not a dog 
This incompatibility is also found in the opposite pairs fast : slow and stationary : moving, as can be seen below:
- It's fast entails It's not slow 
- It's stationary entails It's not moving
Cruse (2004) identifies some basic characteristics of opposites:
An antonym is one of a pair of words with opposite meanings. Each word in the pair is the antithesis of the other. A word may have more than one antonym. There are three categories of antonyms identified by the nature of the relationship between the opposed meanings. Where the two words have definitions that lie on a continuous spectrum of meaning, they are gradable antonyms. Where the meanings do not lie on a continuous spectrum and the words have no other lexical relationship, they are complementary antonyms. Where the two meanings are opposite only within the context of their relationship, they are relational antonyms.
A gradable antonym is one of a pair of words with opposite meanings where the two meanings lie on a continuous spectrum. Temperature is such a continuous spectrum so hot and cold, two meanings on opposite ends of the spectrum, are gradable antonyms. Other examples include: heavy : light, fat : skinny, dark : light, young : old, early : late, empty : full, dull : interesting.
A complementary antonym is one of a pair of words with opposite meanings, where the two meanings do not lie on a continuous spectrum. There is no continuous spectrum between push and pull but they are opposite in meaning and are therefore complementary antonyms. Other examples include: dead : alive, off : on, day : night, exit : entrance, exhale : inhale, occupied : vacant, identical : different.
A relational antonym is one of a pair of words with opposite meanings, where opposite makes sense only in the context of the relationship between the two meanings. There is no lexical opposite of teacher, but teacher and pupil are opposite within the context of their relationship. This makes them relational antonyms. Other examples include: husband : wife, doctor : patient, predator : prey, teach : learn, servant : master, come : go, parent : child.
Some planned languages abundantly use such devices to reduce vocabulary multiplication. Esperanto has mal- (compare bona = "good" and malbona = "bad"), Damin has kuri- (tjitjuu "small", kuritjitjuu "large") and Newspeak has un- (as in ungood, "bad").
- converses (or relational opposites)
- Relational antonyms (Converses) are pairs in which one describes a relationship between two objects and the other describes the same relationship when the two objects are reversed, such as parent and child, teacher and student, or buy and sell.
An auto-antonym is a word that can have opposite meanings in different contexts or under separate definitions:
- enjoin (to prohibit, issue injunction; to order, command)
- fast (moving quickly; fixed firmly in place)
- cleave (to split; to adhere)
- sanction (punishment, prohibition ; permission)
- stay (remain in a specific place, postpone; guide direction, movement)
- Incompatibility can be compared to exclusive disjunction in logic.
- There are four types of entailment useful to lexical semantics:
- unilateral entailment: It's a fish unilaterally entails It's an animal. (It is unilateral, i.e. one-directional, because It's an animal does not entail It's a fish since it could be a dog or a cat or some other animal.)
- logical equivalence (or multilateral entailment): The party commenced at midnight entails The party began at midnight AND The party began at midnight also entails The party commenced at midnight.
- contrariety: The sentences 'X is blue all over' and 'X is red all over' are contraries since both cannot be simultaneously true. On the Aristotelian square of opposition, the A and E type propositions ('All As are Bs' and 'No As are Bs', respectively) are contraries of each other. Propositions that cannot be simultaneously false (e.g. 'Something is red' and 'Something is not red') are said to be subcontraries.
- contradiction: It's dead entails It's not alive AND It's not alive entails It's dead AND It's alive entails It's not dead AND It's not dead entails It's alive. It's dead and It's alive are said to be in a contradictory relation.
- Stated differently, if the proposition expressed by the sentence A is X is TRUE, then the proposition expressed by the sentence A is not Y is also TRUE.
- It is assumed here that it has the same referent.
- It is also assumed here the reference point of comparison for these adjectives remains the same in both sentences. For example, a rabbit might be fast compared to turtle but slow compared to a sport car. It is essential when determining the relationships between the lexical meaning of words to keep the situational context identical.
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