Into paradigms

We define a paradigm $\mathrm{\Pi }$ over $(\mathrm{\Sigma },L)$ as a triple $(C,S,\psi )$ where:

• $C$ is a set of categories that $\mathrm{\Pi }$ inflects for,
• $S=(S_0,S_1,\dots ,S_{p-1})$ is a sequence of subsets of ${\mathrm{\Sigma }}^{*}$, such that $S_i$ defines the set of values that the $i$th variable part can take, and
• $\psi :S_0\times S_1\times \cdots \times S_{p-1}\times C\to L$ determines the form of an inflected word.

In most cases, we constrain $\psi$ such that $\psi (s_0,\dots ,s_{p-1},c)$ is the result of concatenating elements of $\{s_0,\dots s_{p-1}\}$ in a manner that depends only on the value of $c$. (The particular semantics of concatenation depends on the language being modeled, but we require truncation to be available.)