Uninorm logic with the n-potency axiom

This paper investigates a class of extensions C"nUL of uninorm logic UL, which is obtained by adding the n-potency axiom to UL. The main result of this paper is that by generalizing Jenei and Montagna-style approach for proving standard completeness for monoidal t-norm based logic MTL, we obtain the standard completeness for C"nUL. In addition, we present the suitable analytic hypersequent calculi for C"nUL.

[1]  R. Mesiar,et al.  ”Aggregation Functions”, Cambridge University Press , 2008, 2008 6th International Symposium on Intelligent Systems and Informatics.

[2]  San-Min Wang.  Involutive uninorm logic with the n-potency axiom , 2013, Fuzzy Sets Syst..

[3]  Agata Ciabattoni,et al.  Bounded Contraction in Systems with Linearity , 1999, TABLEAUX.

[4]  Harold Schellinx,et al.  Extending Intuitionistic Linear Logic with Knotted Structural Rules , 1994, Notre Dame J. Formal Log..

[5]  Andreja Prijatelj.  Connectification forn-contraction , 1995, Stud Logica.

[6]  Lluis Godo,et al.  Monoidal t-norm based logic: towards a logic for left-continuous t-norms , 2001, Fuzzy Sets Syst..

[7]  Franco Montagna,et al.  Substructural fuzzy logics , 2007, Journal of Symbolic Logic.

[8]  D. Gabbay,et al.  Proof Theory for Fuzzy Logics , 2008 .

[9]  Arnon Avron,et al.  Hypersequents, logical consequence and intermediate logics for concurrency , 1991, Annals of Mathematics and Artificial Intelligence.

[10]  Arnon Avron,et al.  A constructive analysis of RM , 1987, Journal of Symbolic Logic.

[11]  Enrico Marchioni,et al.  Interpolation Properties for Uninorm Based Logics , 2010, 2010 40th IEEE International Symposium on Multiple-Valued Logic.

[12]  Bin Zhao,et al.  HpsUL is not the logic of pseudo-uninorms and their residua , 2009, Log. J. IGPL.

[13]  Franco Montagna,et al.  On the Standard and Rational Completeness of some Axiomatic Extensions of the Monoidal T-norm Logic , 2002, Stud Logica.

[14]  Franco Montagna,et al.  A Proof of Standard Completeness for Esteva and Godo's Logic MTL , 2002, Stud Logica.

[15]  Ronald R. Yager,et al.  Uninorm aggregation operators , 1996, Fuzzy Sets Syst..

[16]  Petr Cintula,et al.  Logics with disjunction and proof by cases , 2008, Arch. Math. Log..

[17]  Carles Noguera,et al.  On n ‐contractive fuzzy logics , 2007, Math. Log. Q..

[18]  Franco Montagna,et al.  n-Contractive BL-logics , 2011, Arch. Math. Log..

[19]  Andreja Prijatelj,et al.  Bounded contraction and Gentzen-style formulation of Łukasiewicz logics , 1996, Stud Logica.

[20]  D. Gabbay,et al.  Proof theory for fuzzy logics. Applied Logic Series, vol. 36 , 2010 .