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We develop a Hilbert style calculus for modal propositional logic which allows for the deduction theorem. Labels are used to keep track of both modalities that have been entered and assumptions that have been made. The main technical result of this paper is the equivalence of the labelled deductive calculus to the normal calculus for modal propositional logic.
In this paper we investigate the semantic properties of contexts. We describe the syntax and semantics of the propositional logic of context. This logic extends classical propositional logic in two ways. Firstly, a new modality, ist (κ, Φ), is introduced. It is used to express that the sentence, Φ, holds in the context κ. Secondly, each context has its own vocabulary, i.e. a set of propositional atoms...
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