feat(Logic): General Modal Logic - #863
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Sep 4, 2026
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It seems the unary poly functor stuff is useful even beyond modal logic and could be factored into a separate PR. This would shorten this PR.
| public import Cslib.Init | ||
| public import Mathlib.Data.PFunctor.Univariate.Basic | ||
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| /-! # Additional basic theory on polynomial functors -/ |
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This PR seems a bit large. Maybe this API for PFunctors could be a separate PR. It seems fairly straightforward merge.
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This PR adds general modal logic (
Modal/Basic.lean), formalising the approach in the reference textbook 'Modal Logic' by Blackburn et al. based on similarity types (operator signatures). The formalisation is actually a bit more general: operator signatures are formalised using polynomial functors (PFunctor), so the argument positions of different operators can be of different types, and there are no assumptions on finiteness of operator arities.Basic modal logic, unary modal logics, dynamic modal logics, and HML are all recovered as special cases that impose assumptions on the operator signature. This allows for reusing proof infrastructure across all modal logics. All tests have been accordingly refactored to check that reuse works as intended and that abstractions do not leak too aggressively across specialisations of general modal logic.