A geometrical view of I/O logic

TL;DR

This paper presents a geometric interpretation of I/O logic, illustrating how generators act as jumps within a lattice structure, and discusses soundness and completeness results for simple-minded I/O operations.

Contribution

It introduces a novel geometric framework for understanding I/O logic, extending previous results to a lattice-based perspective.

Findings

Soundness and completeness for simple-minded I/O logic

Generators act as jumps within a lattice structure

Finite case analysis of the geometric account

Abstract

We describe a geometrical account of the I/O logic put forth by Makinson and van der Torre. A soundness and completeness results was reported for the simplest I/O operation called simple-minded, and in the finite case only. On this account a generator acts as a "jump" within a lattice.