A generalized Wittgensteinian semantics for propositional languages is presented, based on a lattice of elementary situations. Of these, maximal ones are possible worlds, constituting a logical space; minimal ones are logical atoms, partitioned into its dimensions. A verifier of a proposition is an elementary situation such that if real it makes true. The reference (or objective) of a proposition is a situation, which is the set of all its minimal verifiers. (Maximal ones constitute its locus.) Situations are shown to form (...) a Boolean algebra, and the Boolean set algebra of loci is its representation. Wittgenstein's is a special case, admitting binary dimensions only. (shrink)