Some Remarks on the Logic of Probabilistic Relevance

Davide Fazio; Raffaele Mascella

doi:10.12775/LLP.2023.020

Authors

Davide Fazio Dipartimento di Scienze della Comunicazione, Università degli Studi di Teramo
Raffaele Mascella Dipartimento di Scienze della Comunicazione, Università degli Studi di Teramo

DOI:

https://doi.org/10.12775/LLP.2023.020

Keywords

relevance, statistical relevance, relevant implication, history of relating logic, connexive logic

Abstract

In this paper we deepen some aspects of the statistical approach to relevance by providing logics for the syntactical treatment of probabilistic relevance relations. Specifically, we define conservative expansions of Classical Logic endowed with a ternary connective ⇝ - indeed, a constrained material implication - whose intuitive reading is “x materially implies y and it is relevant to y under the evidence z”. In turn, this ensures the definability of a formula in three-variables R(x, z, y) which is the representative of relevance in the object language. We outline the algebraic semantics of such logics, and we apply the acquired machinery to investigate some termdefined weakly connexive implications with some intuitive appeal. As a consequence, a further motivation of (weakly) connexive principles in terms of relevance and background assumptions obtains.

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