Hallden's Logic of Nonsense and Its Expansions in View of Logics of Formal Inconsistency

Abstract

The paper explores the connection between Soren Hallden's logic of nonsense (and its expansions) and Logics of Formal Inconsistency (LFIs), one of the main traditions in paraconsistency. Although not much attention has been payed by paraconsistentists, Hallden's logic can be nicely connected to LFIs. The main result of the paper is a reformulation of an expansion of logic of nonsense studied by Lennart Aqvist and Krister Segerberg in the light of LFIs. More specifically, we present a three-valued semantics and a Hilbert-style system, and prove soundness and completeness results. We also observe some definability results related to the consistency and just-true operators, and briefly discuss an 'interpretation' of truth values of the three-valued semantics in view of the recent work of Graham Priest on plurivalent semantics.