In this note, we answer a question raised by Johnson and Schechtman [7], about the hypercontractive semigroup on {−1, 1}. More generally, we prove the theorem below. 2000 Math. Subject Classification: Primary 47D20. Seconday 47L20. In this note, we answer a question raised by Johnson and Schechtman [7]. We refer to their paper for motivation and background. In addition, we refer the reader to [...

This study examines the issue of norm construction in al-Ghazālī’s thought focusing on grounds advanced to support his radical infallibilist position. To fulfill such end, al-Ghazālī, I explain, relies two types arguments, first one relates presumptive nature legal texts order highlight their fundamental indeterminacy and second links interpreter show impossibility fall into error. buttress the...

There exists infinitely many ways to extend the classical propositional connectives to the set [0, 1] such that the behavior in its extremes is as in the classical logic. Still, it is a consensus that it is not sufficient, demanding that these extensions also preserve some minimal logical properties of the classical connectives. Thus, the notions of t-norms, t-conorms, fuzzy negations, and fuzz...

Modus Ponens is a key property for fuzzy implication functions that are going to be used in fuzzy inference processes. In this paper it is investigated when fuzzy implication functions derived from uninorms via residuation, usually called RU implications, satisfy the modus ponens with respect to a continuous t-norm T , or equivalently, when they are T -conditionals. For RU -implications it is p...

The definition and the general methods of construction of non-statistical association measures on different domains are discussed. An association measure is a function of two variables defined on a set X with involutive operation and satisfying the properties similar to the properties of the Pearson’s correlation coefficient. Such measure can be used for analysis of the possible positive and ne...