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(LaTeX) 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 that includes 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 with respect
to both 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 a standard logical framework. |
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