Handbook of Mathematical Fuzzy Logic. Volume 1

Originatingasanattempttoprovidesolidlogicalfoundationsforfuzzysettheory,andmotivatedalsobyphilosophicalandcomputationalproblemsofvaguenessandimprecision,MathematicalFuzzyLogic(MFL)hasbecomeasignificantsubfieldofmathematicallogic.Researchinthisareafocusesonmany-valuedlogicswithlinearlyorderedtruthvaluesandhasyieldedelegantanddeepmathematicaltheoriesandchallengingproblems,thuscontinuingtoattractaneverincreasingnumberofresearchers.Thistwo-volumehandbookprovidesanup-to-datesystematicpresentationofthebest-developedareasofMFL.ItsintendedaudienceisresearchersworkingonMFLorrelatedfields,whomayusethetextasareferencebook,andanyonelookingforacomprehensiveintroductiontoMFL.Despitebeinglocatedintherealmofpuremathematicallogic,thishandbookwillalsobeusefulforreadersinterestedinlogicalfoundationsoffuzzysettheoryorinamathematicalapparatussuitablefordealingwithsomephilosophicalandlinguisticissuesrelatedtovagueness.ThefirstvolumecontainsagentleintroductiontoMFL,apresentationofanabstractalgebraicframeworkforMFL,chaptersonprooftheoryandalgebraicsemanticsoffuzzylogics,and,finally,analgebraicstudyofHajek'slogicBL.ThesecondvolumeisdevotedtoLukasiewiczlogicandMValgebras,Godel-Dummettlogicanditsvariants,fuzzylogicsinexpandedpropositionallanguages,studiesoffunctionalrepresentationsforfuzzylogicsandtheirfreealgebras,computationalcomplexityofpropositionallogics,andarithmeticalcomplexityoffirst-orderlogics.