 The most influential work on conversational implicature conventions describes “Horn scales”.[77]  Horn (1972, 1989) observed that the quantifiers all, most, many, some form a scale with the following properties. Instances of “___ S are P” with one term entail instances with any term to the right, but not to the left; the terms are thus ordered by logical strength. Moreover, the result of substituting one term implicates the denial of the result of substituting any term to the left, but not to the right. In the negative context “It is not the case that ___ S are P”, the logical and pragmatic relations are reversed. Other Horn scales are ⟨necessarily, actually, possibly⟩, ⟨certainly, probably, possibly⟩, and ⟨must, should, may⟩. Horn (1989: §4.5) correlates the existence of scales with the absence of certain lexical items, such as a quantifier meaning “not  all”.[78]  Levinson (2000: 156) looked for a generalization that would cover these cases but not scales like ⟨Over 90%, over 10%, some⟩ which have the same logical relations as Horn scales but not the pragmatic relations. One generalization is that the items on a Horn scale are widely and frequently used monolexemes. A companion problem is to explain why some common monolexemes with similar logical relations lack the pragmatic relations, as several illustrates. Given the conventional nature of generalized conversational implicatures, there may be no systematic (“synchronic”) explanation. All languages are “irregular” to some extent. For example, the regular pattern for adjectives in English is that of tall, taller, tallest. But there are exceptions, such as good, better, best. No one expects that anything other than a historical (“diachronic”) explanation exists for these facts.