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Anupam Das

Brouwer meets Kripke: constructivising modal logic

Posted on August 19, 2022August 30, 2022 by Anupam Das

Intuitionistic logic and modal logic each admit meaningful projections of classical theories. While intuitionistic logic can interpret classical logic by a host of translations, thus yielding computational interpretations, modal logic can be employed to understand notions of provability and truth. However, the enrichment of intuitionistic logic by modalities is far less canonical than its classical…

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Deterministic – nondeterministic pairs in proof theory

Posted on December 30, 2020December 31, 2020 by Anupam Das

This is meant to be a light post, posing a perhaps naive question. One of the hallmarks of computational proof theory is the association between arithmetic theories and complexity classes, in terms of their provably recursive functions. But is there a general rule for identifying the provably recursive functions of a class of induction invariants?

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‘Simple’ proofs of cut-elimination II: intuitionistic logic

Posted on September 7, 2020September 10, 2020 by Anupam Das

Cut-elimination for intuitionistic logic has particular significance to proof theorists due to the constructive nature of the logic. Cut-free proofs give rise to significant computational information, including interpolants of implications and, in the case of predicate logic, witnesses of existentials. Moreover, the process of cut-elimination can itself be viewed as a computational process thanks to…

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A new linear inference of size 8

Posted on June 25, 2020June 26, 2020 by Anupam Das

Linear inferences are propositional tautologies of the form , where and are formulas with at most one occurrence of each propositional variable. These form a -complete set, but surprisingly little is known about their structure, despite their importance in structural proof theory (and beyond). In this post I will cover some of the background on…

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