Biological process

positive regulation of cytotoxic T lymphocyte differentiation, positive regulation of cytotoxic T-cell differentiation, positive regulation of cytotoxic T-lymphocyte differentiation, up regulation of cytotoxic T cell differentiation, up-regulation of cytotoxic T cell differentiation, upregulation of cytotoxic T cell differentiation

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

positive regulation of cytotoxic 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'.