• Corpus ID: 244479222

Context, Judgement, Deduction

@article{Coraglia2021ContextJD,
  title={Context, Judgement, Deduction},
  author={Greta Coraglia and Ivan Di Liberti},
  journal={ArXiv},
  year={2021},
  volume={abs/2111.09438}
}
We introduce judgemental theories and their calculi as a general framework to present and study deductive systems. As an exemplification of their expressivity, we approach dependent type theory and natural deduction as special kinds of judgemental theories. Our analysis sheds light on both the topics, providing a new point of view. In the case of type theory, we provide an abstract definition of type constructor featuring the usual formation, introduction, elimination and computation rules. For… 

A unified treatment of structural definitions on syntax for capture-avoiding substitution, context application, named substitution, partial differentiation, and so on

A category-theoretic abstraction of a syntax with auxiliary functions, called an admissible monad morphism, is introduced, based on an abstract form of structural recursion, and generic tools to construct admissible Monad morphisms from basic data are designed.

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