Modal logics with propositional constants

This dissertation aims at providing a unified treatment of propositional constants in modal logic. Languages enriched with constants have been used at least from the Fifties, but a systematic study of them is still not available.The main contribution consists in the development of a semantic approach based on structures with sets of possible interpretations for propositional constants, called specific restrictions; such structures are compared with those in which every constant has a fixed interpretation, usually adopted in the literature. We show that the presence of specific restrictions allows one to define the notion of strict range of a formula, that turns out to be important for model-theoretic purposes. Furthermore, we use the semantic approach here introduced to develop systems of temporal logic whose language includes primitive operators of contingency, showing that propositional constants are useful to obtain characterization results with reference to different classes of temporal frames. Finally, we move from languages with propositional constants to languages with propositional quantifiers (the latter being intended as a generalization of the former) and analyse their proof theory in natural deduction calculi.