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Building theories of organizations is challenging: theories are partial and \"folk\" categories are fuzzy. The commonly used tools--first-order logic and its foundational set theory--are ill-suited for handling these complications. Here, three leading authorities rethink organization theory. Logics of Organization Theory sets forth and applies a new language for theory building based on a nonmonotonic logic and fuzzy set theory. In doing so, not only does it mark a major advance in organizational theory, but it also draws lessons for theory building elsewhere in the social sciences.

L'implication, qui est au cœur du raisonnement mathématique, est source d'importantes difficultés repérées par de nombreux auteurs. Dans cet article, nous soutenons la thèse selon laquelle ces difficultés sont dans une large mesure une conséquence de la complexité de cette notion. Pour étudier cette complexité, nous nous placerons dans la théorie sémantique de la vérité due à Tarski, ce qui nous permettra de clarifier les différents aspects de l'implication en jeu dans l'activité mathématique: relation entre propositions, implication universellement quantifiée, implication logiquement valide, règles d'inférence. Nous montrerons que pour cela, il est nécessaire d'étendre la définition classique de l'implication entre propositions pour considérer une relation entre phrases ouvertes contenant au moins une variable libre. Ceci permet de reconnaître que dans certains cas, la valeur de vérité des énoncés proposés dans la classe de mathématiques n'est pas contrainte par la situation, ceci rentrant en conflit avec la position selon laquelle, en mathématiques, un énoncé est soit vrai, soit faux. La pertinence didactique de ce cadre théorique sera illustrée par l'analyse de deux situations problématiques et par la présentation de quelques résultats expérimentaux issus de nos recherches sur la compréhension de l'implication chez des étudiants de première année universitaire. /// Implication is at the very heart of mathematical reasoning. As many authors have shown, pupils and students experience serious difficulties in using it in a suitable manner. In this paper, we support the thesis that these difficulties are closely related with the complexity of this notion. In order to study this complexity, we refer to Tarski's semantic truth theory, which contributes to clarifying the different aspects of implication: propositional connective, logically valid conditional, generalized conditional, inference rules. We will show that for this purpose, it is necessary to extend the classical definition of implication as a relation between propositions to a relation between open sentences with at least one free variable. This permits to become aware of the fact that, in some cases, the truth-value of a given mathematical statement is not constrained by the situation, contrary to the common standpoint that, in mathematics, a statement is either true or false. In the present paper, the didactic relevance of this theoretical stance will be illustrated by an analysis of two problematic situations and the presentation of some experimental results from our research on first-year university students' understanding of implication.

Issue Title: Selected Papers from the 2003 Bellingham Conference

An attempt is made to include the axioms of Mackey for probabilities of experiments in quantum mechanics into the calculus Ł_{\\aleph _{0}}$of Łukasiewicz. The obtained calculus ŁQ contains an additional modal sign Q and four modal rules of inference. The proposition Qx is read \"x is confirmed\". The most specific rule of inference may be read: for comparable observations implication is equivalent to confirmation of material implication. The semantic truth of ŁQ is established by the interpretation with the help of physical objects obeying to the rules of quantum mechanics. The embedding of the usual quantum propositional logic in ŁQ is accomplished.

Philotheus Boehner, in his paper of 1951 demonstrated that Ockham knew of material implication, and his book of 1952 translated many of Ockham's rules for simply valid consequences as tautologies (hence theorems) of PC (propositional calculus). E. A. Moody, in his book of 1953, gave a conflicting interpretation, identifying Ockham's simply valid consequences with Lewis and Langford's CSI (calculus of strict implication) and Ockham's consequences valid ut nunc with PC. It is demonstrated here that Moody was wrong and Boehner right. It is also shown that PC with propositional constants provides a framework for a truth-functional interpretation of Ockham's consequences without modal adverbs '□' and '◊' ('necessarily' and 'possibly' where '□' = df '~◊~').

Axiomatizations of two systems of modal logic are presented in this paper. The first consists of six axiom schemata and one rule of inference; this axiomatization is proved equivalent to Lewis' S3. The addition of a seventh schema, the analogue of C 10. 1, yields an axiomatization equivalent to S4. Our axiom schemata for S3 are proved mutually independent, as are our schemata for S4.

Ronald Maris' recent effort to demonstrate the logical adequacy of G. Homans' theory is itself logically inadequate. Its major problems are the trivial & contradictory conclusions which can be generated merely by extending Maris' argument & by examining the implications of unexamined premises. These problems can be resolved by eliminating extraneous propositions, placing conditions upon others, & introducing a time dimension into the analysis. However, these modifications require the adoption of a more flexible logical calculus than that with which Maris has chosen to structure his argument. AA.