ALETHIC MODAL LOGIC
Logics of necessity and possibility and their close relatives, interpreted over Kripke frames or neighborhood models. The operators read as metaphysical, logical, or physical necessity; the systems are individuated by the frame conditions they impose and the axioms those conditions validate.
Entries are organized along three lines. The system hierarchy runs from the minimal normal logic K through T, S4, S5, B, and their neighbors. The semantic apparatus covers relational, neighborhood, topological, hybrid, graded, and polyadic models, together with the correspondence theory (Sahlqvist, Goldblatt-Thomason) linking axioms to frames. Special-operator entries treat provability, justification, and the logic of proofs, and the intensional conditionals—strict, counterfactual, and their two-dimensional and counterpart refinements.