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• W1589736618 abstract "We present a sound and complete model of lambda-calculus reductions based on structures inspired by modal logic (closely related to Kripke structures). Accordingly we can construct a logic which is sound and complete for the same models, and we identify lambda-terms with certain simple sentences (predicates) in this logic, by direct compositional translation. Reduction then becomes identified with logical entailment. Thus, the models suggest a new way to identify logic and computation. Both have elementary and concrete representations in our models; where these representations overlap, they coincide. In a concluding speculation, we note a certain subclass of the models which seems to play a role analogous to that played by the cumulative hierarchy models in axiomatic set theory and the natural numbers in formal arithmetic — there are many models of the respective theories, but only some, characterised by a fully second order interpretation, are the ‘intended’ ones." @default.
• W1589736618 created "2016-06-24" @default.
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• W1589736618 date "2010-01-01" @default.
• W1589736618 modified "2023-10-07" @default.
• W1589736618 title "A Simple Class of Kripke-Style Models in Which Logic and Computation Have Equal Standing" @default.
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• W1589736618 doi "https://doi.org/10.1007/978-3-642-17511-4_14" @default.
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