Search results for "Axiom"
showing 10 items of 91 documents
Introduction to generalized topological spaces
2011
[EN] We introduce the notion of generalized topological space (gt-space). Generalized topology of gt-space has the structure of frame and is closed under arbitrary unions and finite intersections modulo small subsets. The family of small subsets of a gt-space forms an ideal that is compatible with the generalized topology. To support the definition of gt-space we prove the frame embedding modulo compatible ideal theorem. Weprovide some examples of gt-spaces and study key topological notions (continuity, separation axioms, cardinal invariants) in terms of generalized spaces.
Uncertainty Measures, Realizations and Entropies*
1997
This paper presents the axiomatic foundations of uncertainty theories arising in quantum theory and artificial intelligence. Plausibility measures and additive uncertainty measures are investigated. The representation of uncertainty measures by random sets in spaces of events forms a common base for the treatment of an appropriate integration theory as well as for a reasonable decision theory.
A Pedagogical Proof of Arrow's Impossibility Theorem
1999
In this note I consider a simple proof of Arrow's Impossibility Theorem (Arrow 1963). I start with the case of three individuals who have preferences on three alternatives. In this special case there are 133=2197 possible combinations of the three individuals' rational preferences. However, by considering the subset of linear preferences, and employing the full strength of the IIA axiom, I reduce the number of cases necessary to completely describe the SWF to a small number, allowing an elementary proof suitable for most undergraduate students. This special case conveys the nature of Arrow's result. It is well known that the restriction to three options is not really limiting (any larger se…
L -valued bornologies on powersets
2016
In M. Abel and A. ostak (2011) [1], the concept of an L-fuzzy bornology was introduced. Actually, an L-fuzzy bornology on a set X is a certain ideal in the family LX of L-fuzzy subsets of a set X. Here we propose an alternative approach to fuzzification of the concept of bornology. We define an L-valued bornology on a set X as an L-fuzzy subset B of the powerset 2X satisfying L-valued analogues of the axioms of a bornology. Basic properties of L-valued bornological spaces are studied. Our special interest concerns L-valued bornologies induced by fuzzy metrics and relative compactness-type L-valued bornologies in ChangGoguen L-topological spaces.
Collection Principles in Dependent Type Theory
2002
We introduce logic-enriched intuitionistic type theories, that extend intuitionistic dependent type theories with primitive judgements to express logic. By adding type theoretic rules that correspond to the collection axiom schemes of the constructive set theory CZF we obtain a generalisation of the type theoretic interpretation of CZF. Suitable logic-enriched type theories allow also the study of reinterpretations of logic. We end the paper with an application to the double-negation interpretation.
Rejected axioms for the “nonsense-logic” W and the k-valued logic of Sobociński
2009
In this paper rejection systems for the “nonsense-logic” W and the k-valued implicational-negational sentential calculi of Sobocinski are given. Considered systems consist of computable sets of rejected axioms and only one rejection rule: the rejection version of detachment rule.
Axiomatic characterization of the weighted solidarity values
2014
Abstract We define and characterize the class of all weighted solidarity values . Our first characterization employs the classical axioms determining the solidarity value (except symmetry ), that is, efficiency , additivity and the A-null player axiom , and two new axioms called proportionality and strong individual rationality . In our second axiomatization, the additivity and the A-null player axioms are replaced by a new axiom called average marginality .
Measuring freedom of choice: An alternative view of a recent literature
2004
A recent literature has emerged in social choice theory which attributes intrinsic importance to freedom in the evaluation of states of affairs. The literature’s philosophical basis lies in Berlin’s notion of positive liberty. Accordingly, axiomatic measures of availability of choices are developed and the information they convey used for ranking states on the basis of the extent of liberty they offer to individuals. This paper argues that the literature’s contributions have taken Berlin’s analytical framework for granted exceedingly narrowing the philosophical terms of the debate. It is shown that, once freedom is analyzed from the perspective of an alternative structure, the triadic synta…
Car following: Comparing distance-oriented vs. inertia-oriented driving techniques
2018
The rationale behind most car-following (CF) models is the possibility to appraise and formalize how drivers naturally follow each other. Characterizing and parametrizing Normative Driving Behavior (NDB) became major goals, especially during the last 25 years. Most CF models assumed driver propensity for constant, safe distance is axiomatic. This paper challenges the idea of safety distance as the main parameter defining a unique (or natural) NDB. Instead, it states drivers can adapt to reactive and proactive car following. Drawing on recent CF models close to the Nagoya paradigm and on other phenomena (e.g., wave movement in Nature), we conceived car following by Driving to keep Inertia (D…
Finite Model Reasoning in Expressive Fragments of First-Order Logic
2017
Over the past two decades several fragments of first-order logic have been identified and shown to have good computational and algorithmic properties, to a great extent as a result of appropriately describing the image of the standard translation of modal logic to first-order logic. This applies most notably to the guarded fragment, where quantifiers are appropriately relativized by atoms, and the fragment defined by restricting the number of variables to two. The aim of this talk is to review recent work concerning these fragments and their popular extensions. When presenting the material special attention is given to decision procedures for the finite satisfiability problems, as many of t…