Equivalences andtranslations between consequence relations abound inlogic. The notion ofequivalencecanbedefinedsyntactically,intermsoftranslationsofformulas,andorder-theoretically,in terms ofthe associated lattices oftheories. W.BlokandD.Pigozziproved in(4)that the twodefinitions coincideinthecaseofanalgebraizablesententialdeductivesystem. Arefinedtreatmentofthisequivalence was provided by W. Blok and B. J´ onsson in (3). Other authors have extended this result to thecases ofk-deductive systems and of consequence relations on associative, commutative, multiple conclusion sequents. Ourmainresultsubsumesallexistingresultsintheliteratureandrevealstheircommoncharacter. Theproofsareoforder-theoretic andcategoricalnature.
['Nikolaos Galatos', 'Constantine Tsinakis']
EQUIVALENCE OF CONSEQUENCE RELATIONS: AN ORDER-THEORETIC AND CATEGORICAL PERSPECTIVE