Search results for "Axiom"
showing 10 items of 91 documents
Foundations for the formalization of metamathematics and axiomatizations of consequence theories
2004
Abstract This paper deals with Tarski's first axiomatic presentations of the syntax of deductive system. Andrzej Grzegorczyk's significant results which laid the foundations for the formalization of metalogic, are touched upon briefly. The results relate to Tarski's theory of concatenation, also called the theory of strings, and to Tarski's ideas on the formalization of metamathematics. There is a short mention of author's research in the field. The main part of the paper surveys research on the theory of deductive systems initiated by Tarski, in particular research on (i) the axiomatization of the general notion of consequence operation, (ii) axiom systems for the theories of classic conse…
Measuring autonomy freedom
2006
In the measurement of autonomy freedom, the admissible potential preference relations are elicited by means of the concept of ‘reasonableness’. In this paper we argue for an alternative criterion based on information about the decision maker’s ‘awareness’ of his available opportunities. We argue that such an inter- pretation of autonomy fares better than that based on reasonableness. We then introduce some axioms that capture this intuition and study their logical impli- cations. In the process, a new measure of autonomy freedom is characterized, which generalizes some of the measures so far constructed in the literature.
Rapid construction of algebraic axioms from samples
1991
Abstract An axiom is called reliable if it is confirmed in several places in a given sample of algebra. A very effective algorithm for enumerating such axioms is described.
Finiteness in a Minimalist Foundation
2008
We analyze the concepts of finite set and finite subset from the perspective of a minimalist foundational theory which has recently been introduced by Maria Emilia Maietti and the second author. The main feature of that theory and, as a consequence, of our approach is compatibility with other foundational theories such as Zermelo-Fraenkel set theory, Martin-Lof's intuitionistic Type Theory, topos theory, Aczel's CZF, Coquand's Calculus of Constructions. This compatibility forces our arguments to be constructive in a strong sense: no use is made of powerful principles such as the axiom of choice, the power-set axiom, the law of the excluded middle.
Three Wives Problem and Shapley Value
2014
We examine the Talmudic three wives problem, which is a generalization of the Talmudic contested garment problem solved by Aumann and Maschler (1985) using coalitional procedure. This problem has many practical applications. In an attempt to unify all Talmudic methods, Guiasu (2010, 2011) asserts that it can be explained in terms of “run-to-the-bank”, that is, of Shapley value in a “cumulative game”. It can be challenged because the coalitional procedure yields the same result as the nucleolus, which corresponds to a “dual game”. As Guiasu’s solution is paradoxical (it has all the appearances of truth), my contribution consists in explaining the concepts, particularly truncation, that play …
The Calm Before the Storm: Hilbert’s Early Views on Foundations
2000
In recent years there has been a growing interest among historians and philosophers of mathematics in the history of logic, set theory, and foundations.1 This trend has led to a major reassessment of early work undertaken in these fields, particularly when seen in the light of motivations that animated the leading actors. The present volume may thus be seen as a reflection of this renewed fascination with the work of Hilbert, Brouwer, Weyl, Bernays, and others, an interest that stems in part from the desire to understand the historical and intellectual context that inspired their investigations. With regard to Hilbert, it has been my contention for some time that his stance in the acrimonio…
Use of Geospatial Analyses for Semantic Reasoning
2010
International audience; This work focuses on the integration of the spatial analyses for semantic reasoning in order to compute new axioms of an existing OWL ontology. To make it concrete, we have defined Spatial Built-ins, an extension of existing Built-ins of the SWRL rule language. It permits to run deductive rules with the help of a translation rule engine. Thus, the Spatial SWRL rules are translated to standard SWRL rules. Once the spatial functions of the Spatial SWRL rules are computed with the help of a spatial database system, the resulting translated rules are computed with a reasoning engine such as Racer, Jess or Pellet.
The Foundations of Projective Geometry in Italy from De Paolis to Pieri
2002
In this paper we examine the contributions of the Italian geometrical school to the Foundations of Projective Geometry. Starting from De Paolis' work we discuss some papers by Segre, Peano, Veronese, Fano and Pieri. In particular we try to show how a totally abstract and general point of view was clearly adopted by the Italian scholars many years before the publication of Hilbert's Grundlagen. We are particularly interested in the interrelations between the Italian and the German schools (mainly the influence of Staudt's and Klein's works). We try also to understand the reason of the steady decline of the Italian school during the twentieth century.
The Obstacle Problem in a Non-Linear Potential Theory
1988
M. Brelot gave rise to the concept harmonic space when he extended classical potential theory on ℝn to an axiomatic system on a locally compact space. I have recently constructed1 a non-linear harmonic space by dropping the assumption that the sum of two harmonic functions is harmonic and considering some other axioms instead. This approach has its origin in the work of O. Martio, P. Lindqvist and S. Granlund2,3,4, who have developed a non-linear potential theory on ℝn connected with variational integrals of the type ∫ F(x,∇u(x)) dm(x), where F(x, h) ≈ |h|p.
A Measure of Polarization for Tourism: Evidence from Italian Destinations
2011
This paper proposes an index of polarization for tourism which links the axiomatic theory of Esteban and Ray with the classical hierarchical agglomerative clustering techniques. The index is aimed at analyzing the dynamics of the average length of stay across Italian destinations, and more specifically to detect whether the polarization within the set of clusters of places with similar values of the indicator has varied over time.