In physics, Feynman diagrams are used to reason about quantum processes. In the 1980s, it
became clear that underlying these diagrams is a powerful analogy between quantum …

Intuitionistic linear logic regains the expressive power of intuitionistic logic through the!('of
course') modality. Benton, Bierman, Hyland and de Paiva have given a term assignment …

This chapter provides an introduction to the interaction between category theory and
mathematical logic. Category theory describes properties of mathematical structures via their …

We present a new intuitionistic linear logic, Dual Intuitionistic Linear Logic, designed to
reflect the motivation of exponentials as translations of intuitionistic types, and provide it with …

This is a monograph about logic. Specifically, it presents the mathe matical theory of the
logic of bunched implications, BI: I consider Bl's proof theory, model theory and computation …

We present the linear type theory λΠ⊸ &⊤ as the formal basis for LLF, a conservative
extension of the logical framework LF. LLF combines the expressive power of dependent …

Inductive datatypes provide mechanisms to define finite data such as finite lists and trees via
constructors and allow programmers to analyze and manipulate finite data via pattern …

This dissertation presents a theory of resumption based on semantic composition. The
theory achieves a unified explanation of resumptive pronouns and copy raising. The basis is …

This is the first book-length treatment of hybrid logic and its proof-theory. Hybrid logic is an
extension of ordinary modal logic which allows explicit reference to individual points in a …

This paper re-addresses the old problem of providing a categorical model for Intuitionistic
Linear Logic (ILL). In particular we compare the now standard model proposed by Seely to …