A Term Assignment for Polarized Bi-intuitionistic Logic and its Strong Normalization

Authors:
Corrado Biasi;Federico Aschieri
Affiliations:
(Correspd. Department of Computer Science, Queen Mary University of London, London E1 4NS, Great Britain) Department of Computer Science, Queen Mary University of London, London E1 4NS, Great Brit ...;Dipartimento di Informatica, SS.MM.FF.NN. Verona, Italy
Venue:
Fundamenta Informaticae - Logic for Pragmatics
Year:
2008

Citing 9
Cited 0

Proofs and types

Proofs and types
Lambda-calculus, types and models

Lambda-calculus, types and models
Basic proof theory

Basic proof theory
The duality of computation

ICFP '00 Proceedings of the fifth ACM SIGPLAN international conference on Functional programming
Subtractive logic

Theoretical Computer Science
Dual Intuitionistic Logic Revisited

TABLEAUX '00 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
A Lambda-Calculus Structure Isomorphic to Gentzen-Style Sequent Calculus Structure

CSL '94 Selected Papers from the 8th International Workshop on Computer Science Logic
Towards a Logic for Pragmatics. Assertions and Conjectures

Journal of Logic and Computation
A Formulae-as-Types Interpretation of Subtractive Logic

Journal of Logic and Computation

Quantified Score

Hi-index	0.00

Visualization

Abstract

We propose a term assignment (let calculus) for Intuitionistic Logic for Pragmatics ILP$_{AC}$, a polarized sequent calculus which includes ordinary positive intuitionistic logic LJ$^{⊃∩}$, its dual LJ$^{∖γ}$ and dual negations ()$^{⊥}$ which allow a formula to "communicate" with its dual fragment. We prove the strong normalization property for the term assignment which follows by soundly translating the let calculus into simply typed γ calculus with pairings and projections. A new and simple proof of strong normalization for the latter is also provided.