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In linguistic semantics, a downward entailing (DE) propositional operator is one that denotes a monotone decreasing function. A downward entailing operator reverses the relation of ''semantic strength'' among expressions. An expression like “run fast” is semantically ''stronger'' than the expression “run” since “run fast” is ''true of'' fewer things than the latter. Thus the proposition “John ran fast” entails the proposition “John ran”. Examples of DE contexts include “not”, “nobody”, “few people”, “at most two boys”. They reverse the entailment relation of sentences formed with the predicates “run fast” and “run”, for example. The proposition “Nobody ran” entails that “Nobody ran fast”. The proposition “At most two boys ran” entails that “At most two boys ran fast”. Conversely, an upward entailing operator is one that ''preserves'' the relation of semantic strength among a set of expressions (for example, “more”). A context that is neither downward nor upward entailing is ''non-monotone'', such as “exactly”. Ladusaw (1980) proposed that downward entailment is the property that licenses polarity items. Indeed, “Nobody saw ''anything''“ is downward entailing and admits the negative polarity item ''anything'', while * “I saw ''anything''” is ungrammatical (the upward entailing context does not license such a polarity item). This approach explains many but not all typical cases of polarity item sensitivity. Subsequent attempts to describe the behavior of polarity items rely on a broader notion of nonveridicality. ==Strawson-DE== Downward entailment does not explain the licensing of ''any'' in certain contexts such as with ''only'': : Only John ate any vegetables for breakfast. This is not a downward entailing context because the above proposition does not entail “Only John ate kale for breakfast” (John may have eaten spinach, for example). Von Fintel (1999) claims that although ''only'' does not exhibit the classical DE pattern, it can be shown to be DE in a special way. He defines a notion of Strawson-DE for expressions that come with presuppositions. The reasoning scheme is as follows: # P → Q # # # Therefore, Here, (2) is the intended presupposition. For example: # Kale is a vegetable. # Somebody ate kale for breakfast. # Only John ate any vegetables for breakfast. # Therefore, only John ate kale for breakfast. Hence ''only'' is a Strawson-DE and therefore licenses ''any''. Giannakidou (2002) argues that Strawson-DE allows not just the presupposition of the evaluated sentence but just any arbitrary proposition to count as relevant. This results in over-generalization that validates the use if ''any' in contexts where it is, in fact, ungrammatical, such as clefts, preposed exhaustive focus, and ''each''/''both'': : * It was John who talked to ''anybody''. : * JOHN talked to ''anybody''. : * Each student who saw anything reported to the Dean. : * Both students who saw anything reported to the Dean. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Downward entailing」の詳細全文を読む スポンサード リンク
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