What is a linguistic paradigm?
In linguistics, a paradigm is a set of semantic relations between morphemes (micro sense units) or words of the same language. They may be etymological or taxonomical relations, oppositions or differences. These relations may be the inflectional forms of a word, like « (one) apple » and « (several) apples ». Languages may comprise paradigms to indicate verb tenses (past, present, future) or mode (active, passive). For example, the paradigm for « go » is « go, went, gone. » The notion of paradigm also indicates a set of morphemes which cover a particular functional or thematic area. For instance, most languages include paradigms for economic actions (buy, sell, lend, repay…), or colours (red, blue, yellow…). A speaker may transform a sentence by replacing one morpheme from a paradigm by another from the same paradigm and get a sentence that still makes sense. In the sentence « I bought a car », you could easily replace « bought » by « sold » because « buy » and « sell » are part of the same paradigm: they have some meaning in common. But in that sentence, you can’t replace « bought » by « yellow » for instance. Two morphemes from the same paradigm may have inverse meanings (if you are buying, you are not selling) but they are always connected by some semantic invariant.
What is a paradigm in IEML?
Except for conjugations and grammatical cases, natural languages dictionaries don’t organize their morphemes or words by paradigms, but by alphabetical order (with the exception of Chinese dictionaries that are organized by ideographic « radicals », number of strokes, etc.). For instance, in an English dictionary, there is no paradigm for colors. But such a paradigm of colors exists in the IEML dictionary. Indeed, each element (or morpheme) belongs explicitly and exclusively to a unique root-paradigm, generated by one single paradigmatic function. In IEML, the elements of the same paradigm have a common phonetic or signifier part. The semantic invariant is represented by a syntactic invariant. Paradigms are represented by one or more tables – or matrices –, whose cells are elements. A paradigmatic table works as a keyboard in edition mode and as a data dashboard in exploration mode.
Phrase paradigms work according to the same principles. As a consequence, it is easy to select a semantic unit or to explore its semantic relationships when editing a text. When looking at paradigmatic tables, IEML semantic units quickly reveal themselves as nodes in matrixes of relationships. As a first approximation, a paradigm can be defined as the set of internal differences within a semantic field. A paradigm thus represents a range of variations on a common theme and its morphemes are designed as the moments of a cycle. Furthermore, a paradigm may be recursively broken down into sub-paradigms. Not only do all cells in a table have the same theme (colours, size adjectives, verb tenses, etc.) but cells in the same column or row have common sub-themes (red variations among colours, lengths or widths among sizes, different modes among the same tense, etc.). Semantic constants in columns or rows correspond to « algebraic » constants in the semantic unit structure: element in the same row have a common substance and elements in the same column have a common attribute.
A distinct IEML element belongs to one single paradigm. Formally, a paradigm is a set of morpheme at the same layer which is generated by a semantic function. For example, the table of performative acts above shows the paradigm resulting from the function O:M:.O:M:.-
- The input variables, in substance and in attribute (O:M:. = y. + o. + e. + u. + a. + i.) are all vowels from layer 1.
- The resulting elements are all made up of a multiplication of two letters (one in substance and one in attribute).
- The rows contains the elements with an identical substance, the columns shows elements with the same attribute and all the elements of the paradigm have the same mode (E) that is not represented.
The respective positions of the elements on the tables display as much as possible their semantic relations. At a glance, the paradigmatic tables show the elements most related to each other, like those on the same row, on the same column or those that appear linked by various symmetric patterns, like an exchange of substance and attribute on the diagonal. An example of the way formal symmetries between elements of the same paradigm correspond to semantic symmetries is the relation between y.u.- « to question » and u.y.- « to respond » in the above table of « performative acts ».