Denial Logic

Abstract

Denial Logic is the logic of an agent whose justified beliefs are false, who cannot avow his own propositional attitudes or believe tautologies, but who can believe contradictions. Denial Logic DL is defined as justification logic JL together with the Denial axiom t : E → ¬E and the Evidence Pairing axiom s :Using Artemov's natural JL semantics, in which justifications are interpreted as sets of formulas, we provide an inductive construction of models of DL, and show that DL is sound and complete. Some notions developed for JL, such as constant specifications and internalization, are inconsistent with DL. In contrast, we define negative constant specifications, which can be used to model agents in DL with justified false beliefs. Denial logic can therefore be relevant to philosophical skepticism. We define coherent negative constant specifications for DL to model a Putnamian brain in a vat with the justified false belief that it is not a brain in a vat, and prove a "Blue Pill" theorem, which produces a model of JL in which "I am a brain in a vat" is false. We extend DL to the multi-modal logic DL ⊕JL LP to model envatted brains who can justify and check tautologies and avow their own propositional attitudes. Denial Logic was inspired by online debates over anthropogenic global warming.