Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: G\"{o}del-McKinsey-Tarski and Blok-Esakia for Heyting-Lewis Implication   Heyting-Lewis Logic is the extension of intuitionistic propositional logic
with a strict implication connective that satisfies the constructive
counterparts of axioms for strict implication provable in classical modal
logics. Variants of this logic are surprisingly widespread: they appear as
Curry-Howard correspondents of (simple type theory extended with) Haskell-style
arrows, in preservativity logic of Heyting arithmetic, in the proof theory of
guarded (co)recursion, and in the generalization of intuitionistic epistemic
logic.
  Heyting-Lewis Logic can be interpreted in intuitionistic Kripke frames
extended with a binary relation to account for strict implication. We use this
semantics to define descriptive frames (generalisations of Esakia spaces), and
establish a categorical duality between the algebraic interpretation and the
frame semantics. We then adapt a transformation by Wolter and Zakharyaschev to
translate Heyting-Lewis Logic to classical modal logic with two unary
operators. This allows us to prove a Blok-Esakia theorem that we then use to
obtain both known and new canonicity and correspondence theorems, and the
finite model property and decidability for a large family of Heyting-Lewis
logics.

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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc