Normalisation for Some Quite Interesting Many-Valued Logics
Nils Kürbis, Yaroslav Petrukhin
Abstract
In this paper, we consider a set of quite interesting three- and four-valued logics and prove the normalisation theorem for their natural deduction formulations. Among the logics in question are the Logic of Paradox, First Degree Entailment, Strong Kleene logic, and some of their implicative extensions, including RM3 and RM3⊃. Also, we present a detailed version of Prawitz’s proof of Nelson’s logic N4 and its extension by intuitionist negation.
Topics & Concepts
IntuitionismNegationExtension (predicate logic)MathematicsLogical consequenceIntuitionistic logicNatural deductionSet (abstract data type)T-norm fuzzy logicsAlgebra over a fieldDiscrete mathematicsCalculus (dental)Pure mathematicsPropositional calculusAlgorithmComputer scienceProgramming languageFuzzy logicArtificial intelligenceFuzzy setGeometryMembership functionMedicineDentistryAdvanced Algebra and LogicLogic, Reasoning, and KnowledgeLogic, programming, and type systems