Biological process

positive regulation of NK T lymphocyte differentiation, positive regulation of NK T-cell differentiation, positive regulation of NK T-lymphocyte differentiation, positive regulation of NKT cell differentiation, positive regulation of NT cell differentiation, positive regulation of natural T cell differentiation, positive regulation of natural killer T cell differentiation, up regulation of NK T cell differentiation, up-regulation of NK T cell differentiation, upregulation of NK T cell differentiation

Any process that activates or increases the frequency, rate or extent of natural killer T cell differentiation.

positive regulation of NK T cell development

Note that immunologists typically use the word 'development' to refer to cells of B or T cell lineages undergoing the process that GO describes as 'cell differentiation'.