Equative cases and clauses are used in some languages to mark that the noun it is marking is like or identical to the subject. English equivalents of this include "to be" and conjugations thereof, as well as "as", "like", and "in the capacity of".
An example is the Draseléq sentence "qüt sar dim," meaning "I was green".
I have never met a real example of the equative case: note that the 'Draseléq' mentioned above is a made-up language. But it is basically the same as the essive case, which does occur in Finnish.

Though the existence of the equative case in real languages is doubtful, we can certainly talk of equative clauses, where the equation is marked by syntax rather than a case affix. But when we examine what an equative clause would be we find several overlapping possibilities.

Consulting several linguistics guides, I find that the putative difference between the equative and the essive is that the former is said to be permanent ('He is my father') while the latter is transient 'My father is at home'. In Spanish this distinction is marked by two different verbs, ser and estar, as it is in Portuguese. You can make a finer distinction with this pair: 'my father is a cook' (= works as a chef) versus 'my father is (the) cook' (is acting as one at today's barbecue). As you see, in English this difference is marked here by the choice of article. So linguists might want to talk about equative versus essive sentences, making such a distinction for the purpose of explaining the slightly different syntax.

Another possible distinction is between identity and membership. This is obvious in mathematical terms, but is disguised when we use the same verb 'to be' in English. Compare 'my father is a serial killer' (membership of the class of serial killers) with 'my father is the Yorkshire Ripper' (A = B). Offhand I can't think of any language that makes any clearer distinction between these than we do in English: 'is an X' versus 'is the Y'. It would be logical to use the term equative (or perhaps equational) for the A = B sense.

Not all uses of 'to be' are equative or essive. In Japanese, there is one verb desu meaning 'to be a thing', and two others imasu and arimasu meaning 'to be in a place' (imasu for animate subjects).

A genuine use of the term equative is in Welsh grammar. It can apply to any language, but Welsh is the only one I know that has a special morphological marker (an affix) for it. In English, and in many European languages, we have a gradation of adjectives: big, bigger, biggest, called respectively the positive, the comparative, and the superlative. Welsh has a fourth form, the equative, meaning as big as.

The ending is -ed, so oer 'cold' forms oered 'as cold as' (and oerach 'colder', oeraf 'coldest'), but this being Welsh there is mutation to complicate it, soft mutation in this case. The full form is cyn oered â, but cryf 'strong' becomes cyn gryfed â 'as strong as', and so on. It may also be indicated by mor before, with the same mutation, and no ending on the adjective: so mor gryf â 'as strong as'.

Just as we have a few irregular adjective comparisons like good, better, best in English, similar ones exist in Welsh, in some of which the cyn has fused with the following adjective: da 'good', cystal â 'as good as'; mawr 'big', cymaint â 'as big as'; and many more.

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