Graded Consequence and Some Metalogical Notions Generalized

The notion of graded consequence and some other metalogical notions like consistency, inconsistency, tautologihood and theoremhood to which grades have been introduced earlier by us are reviewed in the context of generalized operators. Some preliminary results regarding the relation between the notion of graded consequence and the notion of graded inconsistency are proved. The method of axiomatization is reconsidered in this general situation.

[1]  H. Rasiowa.  An Algebraic Approach To Non Classical Logics , 1974 .

[2]  Gerhard Gentzen,et al.  Investigations into Logical Deduction , 1970 .

[3]  Dov M. Gabbay,et al.  Handbook of Logic in Artificial Intelligence and Logic Programming: Volume 3: Nonmonotonic Reasoning and Uncertain Reasoning , 1994 .

[4]  Petr Hájek,et al.  A complete many-valued logic with product-conjunction , 1996, Arch. Math. Log..

[5]  Siegfried Gottwald,et al.  Fuzzy Sets and Fuzzy Logic , 1993 .

[6]  M. Black.  Vagueness. An Exercise in Logical Analysis , 1937, Philosophy of Science.

[7]  E. Turunen.  Algebraic structures in fuzzy logic , 1992 .

[8]  Stanisław J. Surma.  THE GROWTH OF LOGIC OUT OF THE FOUNDATIONAL RESEARCH IN MATHEMATICS , 1981 .

[9]  Brian R. Gaines,et al.  Foundations of fuzzy reasoning , 1976 .

[10]  Giangiacomo Gerla,et al.  Graded Consequence Relations and Fuzzy Closure Operators , 1996, J. Appl. Non Class. Logics.

[11]  Ladislav J. Kohout,et al.  Semantics of implication operators and fuzzy relational products , 1980 .

[12]  John P. Cleave,et al.  The Notion of Logical Consequence in the Logic of Inexact Predicates , 1974 .

[13]  Ernest Edmonds.  Lattice Fuzzy Logics , 1980, Int. J. Man Mach. Stud..

[14]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[15]  Helena Rasiowa,et al.  LT -fuzzy sets , 1992 .

[16]  Petr Hájek,et al.  Fuzzy Logic From The Logical Point of View , 1995, SOFSEM.

[17]  Mihir K. Chakraborty,et al.  Graded Consequence: Further Studies , 1995, J. Appl. Non Class. Logics.

[18]  Zvonimir Sikic.  A Proof of the Characterization Theorem for Consequence Relations , 1991, Math. Log. Q..

[19]  Vilém Novák.  On the syntactico-semantical completeness of first-order fuzzy logic. II. Main results , 1990, Kybernetika.

[20]  Witold Pedrycz,et al.  Fuzzy Sets and T-Norms in the Light of Fuzzy Logic , 1988, Int. J. Man Mach. Stud..

[21]  Giangiacomo Gerla.  An Extension Principle for Fuzzy Logics , 1994, Math. Log. Q..

[22]  D. J. Shoesmith,et al.  Multiple-Conclusion Logic , 1978 .

[23]  Juan Luis Castro,et al.  On consequence in approximate reasoning , 1994, J. Appl. Non Class. Logics.

[24]  Giangiacomo Gerla,et al.  Fuzzy natural deduction , 1990, Math. Log. Q..