(untitled) (EPISTEMEUS, 2026)
Modal logic studies modalities such as possibility and necessity within a formal framework. This paper explores the fundamental principles governing possibility operators in various modal logic systems, ranging from the basic K system to the stronger S5 system, as well as alternative modal logics such as epistemic, deontic, and temporal logic. We examine the axioms that define the behavior of possibility operators, possible worlds semantics, and accessibility relations between worlds. A comparative analysis of the principles within each system demonstrates that differences in accessibility relations produce fundamentally different calculi of possibility. The implications for philosophy, computer science, and linguistics are also discussed.