In lexical semantics, opposites are words lying in an inherently incompatible binary relationship. 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.
Opposition is a semantic relation in which one word has a sense or meaning that negates or is, in the sense of scale, distant from a related word. Other words are capable of being opposed, but the language in question has an accidental gap in its 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:
- binarity, the occurrence of opposites as a lexical pair
- inherentness, whether the relationship may be presumed implicitly
- patency, the quality of how obvious a pair is
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").
Some classes of opposites include:
- antipodals, pairs of words which describe opposite ends of some axis, either literal (such as "left" and "right," "up" and "down," "east" and "west") or figurative or abstract (such as "first" and "last," "beginning" and "end," "entry" and "exit")
- disjoint opposites (or "incompatibles"), members of a set which are mutually exclusive but which leave a lexical gap unfilled, such as "red" and "blue," "one" and "ten," or "monday" and "friday."
- reversives, pairs of verbs which denote opposing processes, in which one is the reverse of the other. They are (or may be) performed by the same or similar subject(s) without requiring an object of the verbs, such as "rise" and "fall," "accelerate" and "decelerate," or "shrink" and "grow."
- converses (or relational opposites or relational antonyms), 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.
- overlapping antonyms, a pair of comparatives in which one, but not the other, implies the positive:
- An example is "better" and "worse." The sentence "x is better than y" does not imply that x is good, but "x is worse than y" implies that x is bad. Other examples are "faster" and "slower" ("fast" is implied but not "slow") and "dirtier" and "cleaner" ("dirty" is implied but not "clean"). The relationship between overlapping antonyms is often not inherent, but arises from the way they are interpreted most generally in a language. There is no inherent reason that an item be presumed to be bad when it is compared to another as being worse (it could be "less good"), but English speakers have combined the meaning semantically to it over the development of the language.
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, sometimes called a binary or contradictory antonym (Aarts, Chalker & Weiner 2014), 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 odd and even but they are opposite in meaning and are therefore complementary antonyms. Other examples include: mortal : immortal, exit : entrance, exhale : inhale, occupied : vacant.
A relational antonym is one of a pair of words that refer to a relationship from opposite points of view. 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: doctor : patient, predator : prey, teach : learn, servant : master, come : go, parent : child.
An auto-antonym is a word that can have opposite meanings in different contexts or under separate definitions:
- 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'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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