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J. Font, R. Jansana (2001)
Leibniz filters and the strong version of a protoalgebraic logicArchive for Mathematical Logic, 40
J. Raftery (2006)
The equational definability of truth predicatesReports Math. Log., 41
A. Wronski (1983)
BCK-algebras do not form a varietyMathematica japonicae, 28
(2001)
Implicación estricta y lógicas subintuicionistas
J. Font, Gonzalo Rodríguez (1994)
Algebraic Study of Two Deductive Systems of Relevance LogicNotre Dame J. Formal Log., 35
J. Font (2003)
An abstract algebraic logic view of some multiple-valued logics
Félix Bou, F. Esteva, J. Font, À. Gil, L. Godo, A. Torrell, V. Verdú (2008)
Logics Preserving Degrees of Truth from Varieties of Residuated LatticesJ. Log. Comput., 22
J. Font, R. Jansana, D. Pigozzi (2003)
A Survey of Abstract Algebraic LogicStudia Logica, 74
AlgS ≤ is pointed, the interpretation of the constant term 1 on every A ∈ AlgS ≤ is the ≤ A -greatest element, and S is the 1-assertional logic of AlgS and the 1-assertional logic of AlgS ≤
⇒( p, q) is a set of protoimplication formulas for S
A. Pynko (1999)
Definitional Equivalence and Algebraizability of Generalized Logical SystemsAnn. Pure Appl. Log., 98
J. Raftery (2006)
Correspondences between gentzen and hilbert systemsJournal of Symbolic Logic, 71
J. Czelakowski (2003)
The Suszko Operator. Part I.Studia Logica, 74
P. Cintula, C. Noguera (2010)
Implicational (semilinear) logics I: a new hierarchyArchive for Mathematical Logic, 49
R. Jansana (2003)
Leibniz Filters RevisitedStudia Logica, 75
W. Blok, D. Pigozzi (1986)
Protoalgebraic logicsStudia Logica, 45
J.M. Font (2004)
Beyond Two: Theory and Algebraization of Multiple-Valued Logic
J. Font (2011)
On semilattice-based logics with an algebraizable assertional companionReports Math. Log., 46
for every A ∈ AlgS ≤ , the least S ≤ -filter of A is an S-filter, 2. S is strongly algebraizable and S ≤ and S have the same theorems
R. Jansana (2006)
Selfextensional Logics with a ConjunctionStudia Logica, 84
The best known algebraizable logics with a conjunction and an implication have the property that the conjunction defines a meet semi-lattice in the algebras of their algebraic counterpart. This property makes it possible to associate with them a semi-lattice based deductive system as a companion. Moreover, the order of the semi-lattice is also definable using the implication. This makes that the connection between the properties of the logic and the properties of its semi-lattice based companion is strong. We introduce a class of algebraizable deductive systems that includes those systems, and study some of their properties and of their semi-lattice based companions. We also study conditions which, when satisfied by a deductive system in the class, imply that it is strongly algebraizable. This brings some information on the open area of research of Abstract Algebraic Logic which consists in finding interesting characterizations of classes of algebraizable logics that are strongly algebraizable.
Archive for Mathematical Logic – Springer Journals
Published: Aug 24, 2012
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