Issues on adjointness in multiple-valued logics Nehad N. Morsi a, * , Elewa M. Roshdy b a Department of Basic Sciences, Arab Academy for Science, Technology and Maritime Transport, P.O. Box 2033, Al-Horraya, Heliopolis, Cairo, Egypt b Department of Mathematics, Military Technical College, Cairo, Egypt Received 2 April 2005; received in revised form 16 August 2005; accepted 29 August 2005 Abstract Wecontributetothetheoryofimplicationsandconjunctionsrelatedbyadjointness, in multiple-valued logics. We suggest their use in ZadehÕs compositional rule of infer- ence, to interpret generalized modus ponens inference schemata. We provide new com- plete characterizations of implications that distinguish left arguments, implications that satisfy the exchange principle, divisible conjunctions, commutative conjunctions, asso- ciative conjunctions and triangular norms. We also introduce and characterize pseudo-strict and pseudo-continuous implications and conjunctions, and we explore the close relationship between these two notions. Ó 2005 Elsevier Inc. All rights reserved. Keywords: Non-classical logics; Implication; Conjunction; Adjointness; Generalized modus ponens 0020-0255/$ - see front matter Ó 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.ins.2005.08.005 * Corresponding author. Tel.: +20 2 4035460. E-mail address: nehadmorsi@cairo.aast.edu (N.N. Morsi). Information Sciences xxx (2005) xxx–xxx www.elsevier.com/locate/ins ARTICLE IN PRESS