Abstract
In this chapter we introduce the proof-theory of propositional hybrid logic. The chapter is structured as follows. In the first section of the chapter we sketch the basics of natural deduction systems and in the second section we introduce a natural deduction system for hybrid logic. In the third section we sketch the basics of Gentzen systems and in the fourth section we introduce a Gentzen system corresponding to the natural deduction system for hybrid logic. In the fifth section we give an axiom system for hybrid logic. The natural deduction system and the Gentzen system are taken from Brauner (2004a) whereas the axiom system is taken from Brauner (2006).
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