Propositional Calculus for Associatively Tied Implications
Nehad N. Morsi, Wafik Boulos Lotfallah, Moataz El-Zekey, Maritime Transport · 2005
Recently, Morsi [28] has developed a complete syntax for the semantical domain of all adjointness algebras. In [1], Abdel-Hamid and Morsi enrich adjointness algebras with one more conjunction, this time a t-norm T (T need not be commutative) that ties an implication A in the following sense: A(T(a, b), z) = A(a, A(b, z)). In this paper, we develop a new complete syntax for quite a general multiple-valued logic whose semantics is based on this type of algebra. Such a formal system serves as a combined calculus for two, possibly different, types of uncertainty. 1 Tied Adjointness Algebras We here compile basics on implications and their adjoints that will be needed in this work. Throughout, P and L