Abstract

The goal of this work is to present a proof-theoretical justification for IT. In particular, we discuss the relationship between the intersection connective and the intuitionistic conjunction. For this purpose, we define a new logical system called Intersection Synchronous Logic (ISL), that proves properties of sets of deductions of the implicationconjunction fragment of NJ. The main idea behind ISL is the decomposition of the intuitionistic conjunction into two connectives, one with synchronous and the other with asynchronous behavior. Then we show how proofs of ISL can be decorated with terms in a way that it matches the standard IT assignment system when only the synchronous conjunction is taken into account, and the simple types assignment with pairs and projections when the asynchronous conjunction is considered. Finally, we prove that ISL enjoys both the strong normalization and subformula properties.

Citations