A Simple Sequent Calculus for Angell's Logic of Analytic Containment

1 July 2016

Australasian Association for Logic Conference, Melbourne

In a number of publications dating from 1977, R.B. Angell put forward a novel relevant logic whose arrow formulas are most naturally read as recording that the content of the consequent is analytically contained in the content of the antecedent. More recently, Kit Fine has suggested that the first-degree fragment of this logic is a natural formulation of the notion of partial content, presenting an intuitive semantics for it in terms of truth-maker semantics.

In the present paper I put forward a simple sequent calculus for Angell’s logic, and show why this is the correct logic of partial content for a range of logics including classical logic as well as illustrating some vistas that this approach opens up for treating the notion of logical subtraction.