modal logic

Wiktionary

1. n. logic Any formal system that attempts to deal with modalities, such as possibility and necessity, but also obligation and permission.

GNU Webster's 1913

1. n. A system of logic which studies how to combine propositions which include the concepts of necessity, possibility, and obligation.

WordNet 3.0

1. n. the logical study of necessity and possibility
2. n. a system of logic whose formal properties resemble certain moral and epistemological concepts