Related Axioms Research Articles

Formal Security Analysis of ECC-Based RFID in Logic of Events Theory

Radio frequency identification (RFID) is a crucial component of the Internet of Things (IoT), and RFID using elliptic curve Cryptography (ECC) is a public key cryptosystem authentication approach that tackles the problem of electronic tag data encryption in RFID systems. The commercialisation and large-scale deployment of RFID systems has raised a number of security-related issues that suggest the need for security protocols. Logic of events theory (LoET) is a formal method for constructing and reasoning about distributed systems and protocols involving security concepts. This paper proposes three event classes, Compute, Retrieve, and Generate, and related axioms and inference rules to formally abstract the ECC session key generation function and formally institute the authentication process of both parties, and the ex-tended LoET is used to analyse the security properties of ECC-based RFID security protocols. Under reasonable assumptions, an ECC-based RFID mutual authentication scheme is shown to satisfy the strong mutual authentication feature. It is shown that extended logic of events theory may be used to prove the security properties of this class of ECC-based RFID protocols.

THE DIAGONAL STRONG REFLECTION PRINCIPLE AND ITS FRAGMENTS

AbstractA diagonal version of the strong reflection principle is introduced, along with fragments of this principle associated with arbitrary forcing classes. The relationships between the resulting principles and related principles, such as the corresponding forcing axioms and the corresponding fragments of the strong reflection principle, are analyzed, and consequences are presented. Some of these consequences are “exact” versions of diagonal stationary reflection principles of sets of ordinals. We also separate some of these diagonal strong reflection principles from related axioms.

Common things are common, but what is common? Incorporating probability information into differential diagnosis.

The well-known clinical axiom declaring that 'common things are common' attests to the pivotal role of probability in diagnosis. Despite the popularity of this and related axioms, there is no operationalized definition of a common disease, and no practicable way of incorporating actual disease frequencies into differential diagnosis. In this essay, we aim to disambiguate the definition of a common (or rare) disease and show that incidence-not prevalence-is the proper metric of disease frequency for differential diagnosis. We explore how numerical estimates of disease frequencies based on incidence can be incorporated into differential diagnosis as well as the inherent limitations of this method. These concepts have important implications for diagnostic decision making and medical education, and hold promise as a method to improve diagnostic accuracy.

Fair resource allocation: Using welfare-based dominance constraints

In this paper we consider the problem of supporting resource allocation decisions affecting multiple beneficiaries. Such problems inherently involve efficiency-fairness trade-offs. We introduce a new approach based on the paradigm of maximizing efficiency subject to constraints to ensure that the decision is acceptably fair. In contrast to existing literature, we incorporate fairness in the form of welfare dominance, ensuring that the resultant distribution of benefits to beneficiaries is at least as good as some reference distribution with respect to a set of social welfare functions that satisfy commonly accepted efficiency and fairness related axioms. We introduce a practical means to parameterize the problem, which allows for excluding welfare functions that are deemed insufficiently or overly sensitive to inequality. This allows for analyzing the impact of changes in inequality aversion on efficiency, thus revealing the trade-off between efficiency and fairness. We develop tractable reformulations for the resulting non-linear multi-level optimization problems. We then extend this approach for cases where resources are allocated to groups of individuals with different sizes. We demonstrate the potential use of the suggested framework on two case studies: a workload allocation problem and a healthcare provisioning problem.

Elementary inductive dichotomy: Separation of open and clopen determinacies with infinite alternatives

We introduce a new axiom called inductive dichotomy, a weak variant of the axiom of inductive definition, and analyze the relationships with other variants of inductive definition and with related axioms, in the general second order framework, including second order arithmetic, second order set theory and higher order arithmetic. By applying these results to the investigations on the determinacy axioms, we show the following. (i) Clopen determinacy is consistency-wise strictly weaker than open determinacy in these frameworks, except second order arithmetic; this is an enhancement of Schweber–Hachtman separation of open and clopen determinacy into the consistency-wise separation. (ii) Hausdorff–Kuratowski hierarchy of differences of opens is faithfully reflected by the hierarchy of consistency strengths of corresponding parameter-free determinacies in the aforementioned frameworks; this result is valid also in second order arithmetic only except clopen determinacy.

A New Version of the Generalized Krätzel-Fox Integral Operators

This article deals with some variants of Krätzel integral operators involving Fox’s H-function and their extension to classes of distributions and spaces of Boehmians. For real numbers a and b > 0 , the Fréchet space H a , b of testing functions has been identified as a subspace of certain Boehmian spaces. To establish the Boehmian spaces, two convolution products and some related axioms are established. The generalized variant of the cited Krätzel-Fox integral operator is well defined and is the operator between the Boehmian spaces. A generalized convolution theorem has also been given.

Semantic model for legal resources: Annotation and reasoning over normative provisions

A Semantic Web approach for an advanced access to legislative documents is presented in terms of a model of normative provisions and related axioms. In particular, relations between provisions are identified and modeled by introducing patterns able to describe Hohfeldian legal fundamental relations. Moreover, a query-based approach able to deal with relations between provision specific instances is described. Examples of semantic annotation of legal textual resources using RDF/OWL standards, as well as advanced access and reasoning facilities over provisions using SPARQL, are shown. The main benefit of the approach is represented by the ability to keep the complexity of the problem within a description logic computational tractability.

Intertemporal choice with different short-term and long-term discount factors

This paper proposes a new axiomatic model of intertemporal choice that allows for dynamic inconsistency. We weaken the classical assumption of stationarity into two related axioms: stationarity in the short-term and stationarity in the long-term. We obtain a model with two independent discount factors, which is flexible enough to capture different time preferences, including a greater impatience for more immediate outcomes (when a long-term discount factor exceeds a compounded short-term discount factor). Our proposed model can accommodate some experimental results that cannot be rationalized by other existing models of dynamic inconsistency (such as quasi-hyperbolic discounting and generalized hyperbolic discounting).

Intertemporal Choice with Different Short-Term and Long-Term Discount Factors

This paper proposes a new axiomatic model of intertemporal choice that allows for dynamic inconsistency. We weaken the classical assumption of stationarity into two related axioms: stationarity in the short-term and stationarity in the long-term. We obtain a model with two independent discount factors, which is flexible enough to capture different time preferences, including a greater impatience for more immediate outcomes (when a long-term discount factor exceeds a compounded short-term discount factor). Our proposed model can accommodate some experimental results that cannot be rationalized by other existing models of dynamic inconsistency (such as quasi-hyperbolic discounting and generalized hyperbolic discounting). The proposed model is applied to the problem of intertemporal consumption/savings.

A description logic framework for advanced accessing and reasoning over normative provisions

A model of normative provisions and related axioms represented by using RDF(S)/OWL are presented as a contribution to implement the semantic web in the legal domain. In particular, a pattern able to implement the Hohfeldian legal fundamental relations between provisions using OWL-DL expressivity is proposed. Moreover, a query-based approach able to deal with relations between provision instances is described. An example of advanced access and reasoning over provisions using the proposed approach, as well as a prototype architecture of a provision retrieval system, are shown. The main benefit is represented by the ability of the approach to keep the complexity of the problem within a description logic computational tractability.

Freedom as Going Off Script

In this manuscript I explore an example of an over‐privileged white woman who encounters two young Black men in a parking garage stairwell. Two related axioms are central to the oppressive script that lies before these subjects: the hetero‐patriarchal axiom that women are not safe alone at night and the racist axiom that Black men, especially young ones, are dangerous. These axioms are intended to ensure a practical conclusion—white women and Black men are supposed to avoid each other—thereby conferring legitimacy on the white male, hetero‐patriarchal order. If this is a performance of oppression, we must ask, what is the performance of freedom?Freedom, I argue, is the practice of allowing and encouraging a subject's multiple selves to interact so that one may devise and pursue courses of action that have been strategically hidden by systems of domination designed to cultivate pliant agency. My project augments accounts of multiplicitous subjectivity wherein our multiple social worlds socially constitute persons as both oppressor and oppressed, empowered and pliant. The practice of freedom conceived here acknowledges multiplicity while positioning us to seek feminist and antiracist futures that are not configured by oppression.

Generalized metrics and Caristi’s theorem

A ‘generalized metric space’ is a semimetric space which does not satisfy the triangle inequality, but which satisfies a weaker assumption called the quadrilateral inequality. After reviewing various related axioms, it is shown that Caristi’s theorem holds in complete generalized metric spaces without further assumptions. This is noteworthy because Banach’s fixed point theorem seems to require more than the quadrilateral inequality, and because standard proofs of Caristi’s theorem require the triangle inequality. MSC:54H25, 47H10.

Minimal from classical proofs

Let A be a formula without implications, and Γ consist of formulas containing disjunction and falsity only negatively and implication only positively. Orevkov (1968) and Nadathur (2000) proved that classical derivability of A from Γ implies intuitionistic derivability, by a transformation of derivations in sequent calculi. We give a new proof of this result (for minimal rather than intuitionistic logic), where the input data are natural deduction proofs in long normal form (given as proof terms via the Curry–Howard correspondence) involving stability axioms for relations; the proof gives a quadratic algorithm to remove the stability axioms. This can be of interest for computational uses of classical proofs.

Temporal Inferencing on Administrative Databases

Temporal inferencing is basic to business data processing, e.g. in such concepts as income, wealth, exchange, budgeting and contractual commitment. Time appears in numerous forms within the information system, however, in data items of varying syntax; or implicitly, in the current state of the database. Here, a uniform concept of time based on temporal intervals over a continuous calendar scale is suggested for administrative applications. Temporal operators and related axioms are proposed for logical databases.

Learning relation axioms from text: An automatic Web-based approach

Even though expressive ontology representation languages like OWL have been proposed in the last years, most available ontologies only focus on taxonomical and, in a few cases, non-taxonomical knowledge. A way to add expressivity to an ontology is to include axioms that describe the basic logical properties of the modeled relationships. However, due to the manual knowledge acquisition bottleneck, axioms are usually missing in handcrafted ontologies. Moreover, automatic or semi-automatic ontology learning approaches aimed to acquire axioms from textual resources to enrich ontologies are scarce. This paper presents a novel methodology to learn axioms associated to non-taxonomic relationships modeled in an ontology in an automatic and unsupervised way, using the Web as corpus of textual resources. The proposed method is based on the use of specially tailored linguistic patterns, the exploitation of Web search engines as massive information retrieval tools, the application of shallow natural language processing and the assessment of semantic relatedness by means of Web-scale co-occurrence statistics. The paper describes the learning algorithm and presents promising results on the assessment of the following axioms: functional, inverse, symmetrical, transitive, reflexive and inverse functional properties.

Payoffs in Nondifferentiable Perfectly Competitive TU Economies

We prove that a single-valued solution of nonatomic market games (or the perfectly competitive TU economies underling them) is uniquely determined as the Mertens value by four plausible value related axioms. Since the Mertens value is always in the core of an economy, this result provides an axiomatization of a core selection (or, alternatively, a competitive payoff selection). Previous works on this matter assumed the underlying TU economies to be either differentiable or of finite type. Our work does not assume that, thus it constitutes the first contribution to the axiomatic study of payoffs in nonatomic economies in general.

Automatic Enrichment of Semantic Relation Network and Its Application to Word Sense Disambiguation

The most fundamental step in semantic information processing (SIP) is to construct knowledge base (KB) at the human level; that is to the general understanding and conception of human knowledge. WordNet has been built to be the most systematic and as close to the human level and is being applied actively in various works. In one of our previous research, we found that a semantic gap exists between concept pairs of WordNet and those of real world. This paper contains a study on the enrichment method to build a KB. We describe the methods and the results for the automatic enrichment of the semantic relation network. A rule based method using WordNet's glossaries and an inference method using axioms for WordNet relations are applied for the enrichment and an enriched WordNet (E-WordNet) is built as the result. Our experimental results substantiate the usefulness of E-WordNet. An evaluation by comparison with the human level is attempted. Moreover, WSD-SemNet, a new word sense disambiguation (WSD) method in which E-WordNet is applied, is proposed and evaluated by comparing it with the state-of-the-art algorithm.

Ontology design patterns to disambiguate relations between genes and gene products in GENIA

MotivationAnnotated reference corpora play an important role in biomedical information extraction. A semantic annotation of the natural language texts in these reference corpora using formal ontologies is challenging due to the inherent ambiguity of natural language. The provision of formal definitions and axioms for semantic annotations offers the means for ensuring consistency as well as enables the development of verifiable annotation guidelines. Consistent semantic annotations facilitate the automatic discovery of new information through deductive inferences.ResultsWe provide a formal characterization of the relations used in the recent GENIA corpus annotations. For this purpose, we both select existing axiom systems based on the desired properties of the relations within the domain and develop new axioms for several relations. To apply this ontology of relations to the semantic annotation of text corpora, we implement two ontology design patterns. In addition, we provide a software application to convert annotated GENIA abstracts into OWL ontologies by combining both the ontology of relations and the design patterns. As a result, the GENIA abstracts become available as OWL ontologies and are amenable for automated verification, deductive inferences and other knowledge-based applications.AvailabilityDocumentation, implementation and examples are available from http://www-tsujii.is.s.u-tokyo.ac.jp/GENIA/.

Representation of preference relations on [formula omitted]-algebras of nonatomic measure spaces: Convexity and continuity

The purpose of this paper is to show how preference relations on σ -algebras can be represented by means of nonadditive set functions that satisfy appropriate requirements of convexity and continuity on σ -algebras. To this end, we introduce convex combinations of measurable sets, and quasiconcave and concave functions on σ -algebras, which conform with the standard results in convex analysis. We formulate the convexity and the continuity axioms for preference relations on σ -algebras with a metric topology and show the existence of utility functions for convex continuous preference relations. We also show that monotone continuous preference relations are representable by fuzzy measures.

A novel formal approach to program slicing

Program slicing is a well-known program analysis technique that extracts the elements of a program related to a particular computation. The current slicing methods, however, are singular (mainly based on a program or system dependence graph), and lack good reusability and flexibility. In this paper, we present a novel formal method for program slicing, modular monadic program slicing, which abstracts the computation of program slicing as a slice monad transformer, and applies it to semantic descriptions of the program analyzed in a modular way, forming the corresponding monadic slicing algorithms. The modular abstraction mechanism allows our slicing method to possess excellent modularity and language-flexibility properties. We also give the related axioms of our slice monad transformer, the proof of the correctness and the implementation of monadic slicing algorithms. We reveal the relations of our algorithms and graph-reachable slicing algorithms.