Logics of variable inclusion and the lattice of consequence relations

TL;DR

This paper explores the structure of sublogics within variable inclusion for finitary logics with partition functions, analyzing their placement in the broader lattice of consequence relations.

Contribution

It determines the number of sublogics of variable inclusion and studies their position within the lattice of consequence relations for such logics.

Findings

Number of sublogics of variable inclusion is established.

Positions of these sublogics in the lattice are characterized.

Insights into the structure of consequence relations are provided.

Abstract

In this paper, firstly, we determine the number of sublogics of variable inclusion of an arbitrary finitary logic L with partition function. Then, we investigate their position into the lattice of consequence relations over the language of L.