- April 2015
A unified treatment of propositional constants in modal logic
The history of propositional constants in modal logic dates back at least to the Fifties. Such constants have been used for several purposes, including: the definition of deontic modalities in terms of alethic ones, the definition of notions of actuality such as “the current world” or “the present instant”, the representation of the states of a relational frame within a modal language, the development of normal systems of contingency logic in which necessity is definable and some results of Post-completeness. My work consists in providing a unified semantic framework for modal languages enriched with constants. The basic idea is to use a special sort of general frames where any propositional constant has its own set of possible interpretations. Within this approach I will discuss some model-theoretic issues and analyze some differences between languages with constants and standard languages of modal logic.