Difference between revisions of "On the scope of some formulas defining additive connectives in fuzzy logics"

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== Abstract ==
 
== Abstract ==
  
 
In (Fuzzy Sets and Systems 149(2005) 297) [[San-min Wang|Wang]] et al. defined a new fuzzy logic called NMG. They also introduced new formulas to define the additive connectives from multiplicative conjunction, residuated implication and bottom in NMG. However, they did not study the scope of these formulas in the general framework of fuzzy logics. This is the aim of this paper. Therefore, we add the definability formulas to known fuzzy logics as new axioms, following the method used in (Beyond Two: Theory and Applications of Multiple-Valued Logic, 2003, 251.), and we obtain some families of logics presented in a simpler language. Finally, we discuss the standard completeness of these new logics.
 
In (Fuzzy Sets and Systems 149(2005) 297) [[San-min Wang|Wang]] et al. defined a new fuzzy logic called NMG. They also introduced new formulas to define the additive connectives from multiplicative conjunction, residuated implication and bottom in NMG. However, they did not study the scope of these formulas in the general framework of fuzzy logics. This is the aim of this paper. Therefore, we add the definability formulas to known fuzzy logics as new axioms, following the method used in (Beyond Two: Theory and Applications of Multiple-Valued Logic, 2003, 251.), and we obtain some families of logics presented in a simpler language. Finally, we discuss the standard completeness of these new logics.

Revision as of 16:35, 30 September 2008

{{Paper| author=Àngel García-Cerdaña| author2=Carles Noguera| author3=Francesc Esteva| title=On the scope of some formulas defining additive connectives in fuzzy logics| journal=Fuzzy Sets and Systems| volume=154| number=1| pages=56-75| year=2005}| preprint=http://www.carlesnoguera.cat/draft1.dvi}

Abstract

In (Fuzzy Sets and Systems 149(2005) 297) Wang et al. defined a new fuzzy logic called NMG. They also introduced new formulas to define the additive connectives from multiplicative conjunction, residuated implication and bottom in NMG. However, they did not study the scope of these formulas in the general framework of fuzzy logics. This is the aim of this paper. Therefore, we add the definability formulas to known fuzzy logics as new axioms, following the method used in (Beyond Two: Theory and Applications of Multiple-Valued Logic, 2003, 251.), and we obtain some families of logics presented in a simpler language. Finally, we discuss the standard completeness of these new logics.