%0 Generic %1 lengyel2012denial %A Lengyel, Florian %A St-Pierre, Benoit %D 2012 %K denial logic %T Denial Logic %U http://arxiv.org/abs/1203.0389 %X We define Denial Logic DL, a system of justification logic that models an agent whose justified beliefs are false, who cannot avow his own propositional attitudes and who can believe contradictions but not tautologies of classical propositional logic. 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 prove soundness and completeness results for DL. Some logical notions developed for JL, such as constant specifications and the internalization property, are inconsistent with DL. This leads us to define negative constant specifications for DL, which can be used to model agents with justified false beliefs. Denial logic can therefore be relevant to philosophical skepticism. We use DL with what we call coherent negative constant specifications to model a Putnamian brain in a vat with the justified false belief that it is not a brain in a vat, and derive a model of JL in which "I am a brain in a vat" is false. We define the fusion of Denial Logic with the Logic of Proofs to model an agent who can justify and check tautologies and who can believe his justified false beliefs. Denial Logic was inspired by the contemporary debate over anthropogenic global warming.

@misc{lengyel2012denial, abstract = {We define Denial Logic DL, a system of justification logic that models an agent whose justified beliefs are false, who cannot avow his own propositional attitudes and who can believe contradictions but not tautologies of classical propositional logic. 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 prove soundness and completeness results for DL. Some logical notions developed for JL, such as constant specifications and the internalization property, are inconsistent with DL. This leads us to define negative constant specifications for DL, which can be used to model agents with justified false beliefs. Denial logic can therefore be relevant to philosophical skepticism. We use DL with what we call coherent negative constant specifications to model a Putnamian brain in a vat with the justified false belief that it is not a brain in a vat, and derive a model of JL in which "I am a brain in a vat" is false. We define the fusion of Denial Logic with the Logic of Proofs to model an agent who can justify and check tautologies and who can believe his justified false beliefs. Denial Logic was inspired by the contemporary debate over anthropogenic global warming.}, added-at = {2012-03-09T08:39:01.000+0100}, author = {Lengyel, Florian and St-Pierre, Benoit}, biburl = {https://www.bibsonomy.org/bibtex/20e9bdb789a7edeab7a7b143c90baf738/adriangroza}, description = {[1203.0389] Denial Logic}, interhash = {603dac6b0069b873a6c438fb21e0ad2a}, intrahash = {0e9bdb789a7edeab7a7b143c90baf738}, keywords = {denial logic}, note = {cite arxiv:1203.0389 Comment: 18 pages}, timestamp = {2012-03-09T08:39:01.000+0100}, title = {Denial Logic}, url = {http://arxiv.org/abs/1203.0389}, year = 2012 }