This chapter introduces a more general approach to logical semantics called *possibility semantics*, which replaces possible worlds with possibly *partial* "possibilities." In classical possibility semantics, propositions are interpreted as regular open sets of a poset or compact regular open sets of an upper Vietoris space. The elements of these sets, viewed as possibilities, may be partial, meaning they can make a disjunction true without settling which disjunct is true. The chapter explains how possibilities can be used in semantics for classical logic, modal logics, and intuitionistic logics. It highlights the benefits of this approach, including overcoming incompleteness results for traditional semantics, avoiding nonconstructivity, and providing richer structures for interpreting new languages. The chapter also discusses the philosophical motivation for possibility semantics, the representation of Boolean algebras using posets and topological spaces, and the construction of possibility frames from Boolean algebras.This chapter introduces a more general approach to logical semantics called *possibility semantics*, which replaces possible worlds with possibly *partial* "possibilities." In classical possibility semantics, propositions are interpreted as regular open sets of a poset or compact regular open sets of an upper Vietoris space. The elements of these sets, viewed as possibilities, may be partial, meaning they can make a disjunction true without settling which disjunct is true. The chapter explains how possibilities can be used in semantics for classical logic, modal logics, and intuitionistic logics. It highlights the benefits of this approach, including overcoming incompleteness results for traditional semantics, avoiding nonconstructivity, and providing richer structures for interpreting new languages. The chapter also discusses the philosophical motivation for possibility semantics, the representation of Boolean algebras using posets and topological spaces, and the construction of possibility frames from Boolean algebras.