  Denial Logic DL, a system of justification 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. Using
Artemov's natural semantics for justification logic JL, 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 the internalization property, are
inconsistent with DL. In contrast, we define negative constant specifications,
which can be used in DL to model agents 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 algebraic fibring of Denial Logic with the
Logic of Proofs to model envatted brains who can justify and check tautologies
and who can avow their propositional attitudes. Denial Logic was inspired by
online debates over anthropogenic global warming.

Logic