Responsibility and Cross-Subsidization in Cost Sharing

We propose two axiomatic theories of cost sharing with the common premise that agents demand comparable -though perhaps different- commodities and are responsible for their own demand. Under partial responsibility the agents are not responsible for the asymmetries of the cost function: two agents consuming the same amount of output always pay the same price; this holds true under full responsibility only if the cost function is symmetric in all individual demands. If the cost function is additively separable, each agent pays her stand alone cost under full responsibility; this holds true under partial responsibility only if, in addition, the cost function is symmetric. By generalizing Moulin and Shenker’s (1999) Distributivity axiom to cost-sharing methods for heterogeneous goods, we identify in each of our two theories a different serial method. The subsidy-free serial method (Moulin, 1995) is essentially the only distributive method meeting Ranking and Dummy. The cross-subsidizing serial method (Sprumont, 1998) is the only distributive method satisfying Separability and Strong Ranking. Finally, we propose an alternative characterization of the latter method based on a strengthening of Distributivity.

Critique épistémologique de l'objectivisme de la médecine moderne : les dimensions pré-verbales de la connaissance médicale

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal

Lógica, lenguaje y significado. Lógica intensional y gramática lógica

Este texto representa el esfuerzo combinado de dos lógicos, dos filósofos y un lingüista. Esta empresa fue inspirada por la convicción de los autores de que la lógica y el lenguaje son inseparables, en particular en lo que respecta al análisis del significado. Una región interdisciplinaria emerge entre los límites de la filosofía, la lógica y la lingüística. Lógica, lenguaje y significado: lógica intensional y gramática lógica es una introducción a este campo, el cual aplica los sistemas lógico-formales al estudio del significado del lenguaje natural. El libro comienza con una introducción de los distintos principios de la semántica intensional y luego presenta varias lógicas intensionales, tales como la lógica proposicional modal, la lógica de predicados modal y la lógica temporal. También introduce la teoría de tipos, la lambda-abstracción y la sintaxis categorial.

Em direção a uma representação para equações algébricas :uma lógica equacional local

The intervalar arithmetic well-known as arithmetic of Moore, doesn't possess the same properties of the real numbers, and for this reason, it is confronted with a problem of operative nature, when we want to solve intervalar equations as extension of real equations by the usual equality and of the intervalar arithmetic, for this not to possess the inverse addictive, as well as, the property of the distributivity of the multiplication for the sum doesn t be valid for any triplet of intervals. The lack of those properties disables the use of equacional logic, so much for the resolution of an intervalar equation using the same, as for a representation of a real equation, and still, for the algebraic verification of properties of a computational system, whose data are real numbers represented by intervals. However, with the notion of order of information and of approach on intervals, introduced by Acióly[6] in 1991, the idea of an intervalar equation appears to represent a real equation satisfactorily, since the terms of the intervalar equation carry the information about the solution of the real equation. In 1999, Santiago proposed the notion of simple equality and, later on, local equality for intervals [8] and [33]. Based on that idea, this dissertation extends Santiago's local groups for local algebras, following the idea of Σ-algebras according to (Hennessy[31], 1988) and (Santiago[7], 1995). One of the contributions of this dissertation, is the theorem 5.1.3.2 that it guarantees that, when deducing a local Σ-equation E t t in the proposed system SDedLoc(E), the interpretations of t and t' will be locally the same in any local Σ-algebra that satisfies the group of fixed equations local E, whenever t and t have meaning in A. This assures to a kind of safety between the local equacional logic and the local algebras

Especificação do tipo intervalar parametrizado em CASL

The interval datatype applications in several areas is important to construct a interval type reusable, i.e., a interval constructor can be applied to any datatype and get intervals this datatype. Since the interval is, of certain form, a set of elements limited for two bounds, left and right, with a order notions, then it s reasonable that interval constructor enclose datatypes with partial order. On the order hand, what we want is work with interval of any datatype like this we work with this datatype then. it s important to guarantee the properties of the datatype when maps to interval of this datatype. Thus, the interval constructor get a theory to parametrized interval type, i.e., a interval with generics parameters (for example rational, real, complex). Sometimes, the interval application in some algebras doesn t guarantee the mainutenance of their properties, for example, when we use interval of real, that satisfies the field properties, it doesn t guarantee the distributivity propertie. A form to surpass this problem Santiago introduced the local equality theory that weakened the notion of strong equality, and thus, allowing some properties are local keeped, what can be discard before. The interval arithmetic generalization aim to apply the interval constructor on ordered algebras weakened for local equality with the purpose of the keep their properties. How the intervals are important in applications with continuous data, it s interesting specify that theory using a specification language that supply a system development using intervals of form disciplined, trustworth and safe. Currently, the algebraic specification language, based in math models, have been use to that intention often. We choose CASL (Common Algebraic Specification Language) among others languages because CASL has several characteristics excellent to parametrized interval type, such as, provide parcialiy and parametrization

Achieving completeness: from constructive set theory to large cardinals

This thesis is an exploration of several completeness phenomena, both in the constructive and the classical settings. After some introductory chapters in the first part of the thesis where we outline the background used later on, the constructive part contains a categorical formulation of several constructive completeness theorems available in the literature, but presented here in an unified framework. We develop them within a constructive reverse mathematical viewpoint, highlighting the metatheory used in each case and the strength of the corresponding completeness theorems. The classical part of the thesis focuses on infinitary intuitionistic propositional and predicate logic. We consider a propositional axiomatic system with a special distributivity rule that is enough to prove a completeness theorem, and we introduce weakly compact cardinals as the adequate metatheoretical assumption for this development. Finally, we return to the categorical formulation focusing this time on infinitary first-order intuitionistic logic. We propose a first-order system with a special rule, transfinite transitivity, that embodies both distributivity as well as a form of dependent choice, and study the extent to which completeness theorems can be established. We prove completeness using a weakly compact cardinal, and, like in the constructive part, we study disjunction-free fragments as well. The assumption of weak compactness is shown to be essential for the completeness theorems to hold.

A review of the relationships between implication, negation and aggregation functions from the point of view of material implication

Implication and aggregation functions play important complementary roles in the field of fuzzy logic. Both have been intensively investigated since the early 1980s, revealing a tight relationship between them. However, the main results regarding this relationship, published by Fodor and Demirli DeBaets in the 1990s, have been poorly disseminated and are nowadays somewhat obsolete due to the subsequent advances in the field. The present paper deals with the translation of the classical logical equivalence p → q = ¬pvq, often called material implication, to the fuzzy framework, which establishes a one-to-one correspondence between implication functions and disjunctors (the class of aggregation functions that extend the Boolean disjunction to the unit interval). The construction of implication functions from disjunctors via negation functions, and vice versa, is reviewed, stressing the properties of disjunctors (respectively, implication functions) that ensure certain properties of implication functions (disjunctors).