• Corpus ID: 244479222

Context, Judgement, Deduction

  title={Context, Judgement, Deduction},
  author={Greta Coraglia and Ivan Di Liberti},
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.



Intuitionistic Type Theory

The main idea is that mathematical concepts such as elements, sets and functions are explained in terms of concepts from programming such as data structures, data types and programs.

Modular correspondence between dependent type theories and categories including pretopoi and topoi

  • M. Maietti
  • Philosophy
    Mathematical Structures in Computer Science
  • 2005
A modular correspondence between various categorical structures and their internal languages in terms of extensional dependent type theories à la Martin-Löf is presented and formulas corresponding to subobjects can be regained as particular types that are equipped with proof-terms according to the isomorphism ‘propositions as mono types’.

An Introduction to Substructural Logics

This book introduces an important group of logics that have come to be known under the umbrella term 'susbstructural' and systematically survey the new results and the significant impact that this class oflogics has had on a wide range of fields.

Doctrines in Categorical Logic

Structural proof theory

From natural deduction to sequent calculus, diversity and unity in structural proof theory are explored and the quantifiers are explained.

The fibrational formulation of intuitionistic predicate logic I: completeness according to Gödel, Kripke, and Läuchli, Part 2

  • M. Makkai
  • Philosophy
    Notre Dame J. Formal Log.
  • 1993
This is the second, concluding part of a two-part paper that contains the treatment of the fibrational versions of the Kripke and the Lauchli completeness theorems.

A General Framework for the Semantics of Type Theory

We propose an abstract notion of a type theory to unify the semantics of various type theories including Martin-Lof type theory, two-level type theory and cubical type theory. We establish basic

Doctrines, modalities and comonads

Modal interior operators can be constructed from comonads in Dtn as well as from adjunctions in it, and it is shown the amount of information lost in the passage from a comonad, or from an adjunction, to the modal interior operator.

On the meanings of the logical constants and the justi cations of the logical laws

The following three lectures were given in the form of a short course at the meeting Teoria della Dimostrazione e Filosofia della Logica, organized in Siena, 6–9 April 1983, by the Scuola di

Natural models of homotopy type theory

  • S. Awodey
  • Mathematics
    Mathematical Structures in Computer Science
  • 2016
It is shown that a category admits a natural model of type theory if it has a class of maps that behave like the abstract fibrations in axiomatic homotopy theory: They should be stable under pullback, closed under composition and relative products, and there should be weakly orthogonal factorizations into the class.