Word of the Day

Monday, September 9, 2013

Fun Math to Deal with Inflections Using Matrices

For understanding the Basque diskidazue, we begin by sorting five parameters expressed in the conjugated form.  They are tense, number of arguments (see note 1 below), the person and the number of the accusative noun, those for the dative noun, those for the nominative noun (may have to check if the subject is nominative as well as ergative or absolutive).

These five parameters are expressed in four apparent morphemes.  We are looking into the product of a 5-dimensinal vector times a 5×4 matrix.

$$\begin{pmatrix}tense & arg. & acc. & dat. & nom \end{pmatrix} multiplied by \begin{pmatrix} f() & 1 & 0 & g() \\ 1 & 1 & 0 & g() \\ 1 & 1 & 0 & g() \\ 1 & 1 & 0 & g() \\ 1 & 0 & 1 & 0 \\ \end{pmatrix}$$
Using the above formula to analyze diskidazue, we get:

$$\begin{pmatrix}pres. & \underline{11}^1 & 3pl & 1sg & 2pl \end{pmatrix} \begin{pmatrix} 1 & 0 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ person() & number() & 0 & 0 \\ 0 & 0 & person() & 0 \\ 0 & 0 & 0 & 1 \\ \end{pmatrix} = \begin{pmatrix}di & ski & da & zue \end{pmatrix}$$

for which

1. binary expressions for arguments structures
\left\{\begin{aligned} \underline{0}&=\text{none other than nominative}\\ \underline{1}&=\text{+ accusative}\\ \underline{10}&=\text{+ dative}\\ \underline{11}&=\text{+ dative + accusative}\\ \end{aligned} \right.