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Abstract:
In previous work we gave an approach, based on labelled natural
deduction, for formalizing proof systems for a large class of
propositional modal logics, including K, D, T, B, S4, S4.2, KD45,
and S5. Here we extend this approach to quantified modal logics,
providing formalizations for logics with varying, increasing,
decreasing, or constant domains. The result is modular both with
respect to properties of the accessibility relation in the Kripke
frame and the way domains of individuals change between worlds.
Our approach has a modular metatheory too; soundness, completeness,
and normalization are proved uniformly for every logic in our class.
Finally, our work leads to a simple implementation of a modal logic
theorem prover in standard logical frameworks.
