Contextual Entailment and Containment: A Ternary Approach to Information and Topic Inclusion

The paper introduces a relevant containment logic according to which the analytic implication φ↠ψ is analyzed as the conjunction of two theses: φ contextually entails ψ and φ contextually contains ψ. By doing so, we are able to extend the ternary semantics of relevant logic to the analysis of topic containment, thus lifting some limitations of Richard Sylvan’s relevant containment logic. We offer a ternary account of topic containment, in that led by the consideration that topic inclusions are evaluated in situ, i.e. with respect to the discursive context fixed by an information state. The main technical result of the paper is a sound and complete axiomatisation of relevant containment logic. Finally, Sylvan’s logic turns out as a special case of our relevant containment logic.