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1、TheLogicofEquilibriumandAbelianLatticeOrderedGroupsAdrianaGalli¤DepartamentodeMatem´aticasUniversidadNacionaldeLaPlataLaPlata,ARGENTINARenatoA.LewinyFacultaddeMatem´aticasPontificiaUniversidadCat´olicadeChileCasilla306Correo22,Santiago,CHILEMartaSagastume¤DepartamentodeMatem´
2、aticasUniversidadNacionaldeLaPlataLaPlata,ARGENTINAAbstractWeintroduceadeductivesystemBalwhichmodelsthelogicofbalanceofopposingforcesorofbalancebetweenconflictingevidenceorinfluences.“Truthvalues”areinterpretedasdeviationsFromastateofequilibrium,sointhissense,thetheoremsofBala
3、retobeinterpretedasbalancedstatements,forwhichreasonthereisonlyonedistinguishedtruthvalue,namelytheonethatrepresentsequilibrium.ThemainresultsarethatthesystemBalisalgebraizableinthesenseof[5]anditsequivalentalgebraicsemanticsBALisdefinitionally¤Fundingforthefirstandthirdauthor
4、hasbeenprovidedbyFOMEC.yFundingforthesecondauthorhasbeenprovidedbyFONDECYT1020621,FacultaddeCienciasExactas,U.N.deLaPlata,andFOMEC.1equivalenttothevarietyofabelianlatticeorderedgroups,thatis,thecategoriesofthealgebrasinBALandof`–groupsareisomorphic(see[10],Ch.4,4).Wealsoprov
5、ethedeductiontheoremforBalandwestudydifferentkindsofsemanticconsequenceassociatedtoBal.Finally,weprovetheco-NP-completenessofthetautologyproblemofBal.1IntroductionInthispaperwewanttomodelsomeaspectsofargumentsinwhichconflict-ingpiecesofevidence,suchasthosethatappearinapolicein
6、vestigation,creditrecords,politicalinfluences,andeveninscientificresearch,arecon-fronted.Inallthesecases,thepiecesofevidencecanbeassignedadegreeofrelevancetothecaseathand.Itappearsnaturalthentoassignpositivedegreestosomebitsofevidenceandnegativedegreestothosethatopposethem.Nee
7、dlesstosay,thepositivenessisarbitrary,itissimplyafixedpriv-ilegeddirection.Evidencecanpileup,butitisobviousthatnoamountofitwillprovethatsomefactiseithertrueorfalse,soweshouldnottalkabouttruthorfalsehood,insteadourstatementstalkaboutpotentiallyunboundedevidencefororagainstsome
8、fact.Inthisscenario,itisnaturaltopayattentiontothosestatementswhichdonotpro
