On nearness measures in fuzzy relational data models

AbstractIt has been widely recognized that the imprecision and incompleteness inherent in real-world data suggest a fuzzy extension for information management systems. Various attempts to enhance these systems by fuzzy extensions can be found in the literature. Varying approaches concerning the fuzzification of the concept of a relation are possible, two of which are referred to in this article as the generalized fuzzy approach and the fuzzy-set relation approach. In these enhanced models, items can no longer be retrieved by merely using equality-check operations between constants; instead, operations based on some kind of nearness measures have to be developed. In fact, these models require such a nearness measure to be established for each domain for the evaluation of queries made upon them. An investigation of proposed nearness measures, often fuzzy equivalences, is conducted. The unnaturalness and impracticality of these measures leads to the development of a new measure: the resemblance relation, which is defined to be a fuzzified version of a tolerance relation. Various aspects of this relation are analyzed and discussed. It is also shown how the resemblance relation can be used to reduce redundancy in fuzzy relational database systems

Pure patterns of order 2

We provide mutual elementary recursive order isomorphisms between classical ordinal notations, based on Skolem hulling, and notations from pure elementary patterns of resemblance of order $2$, showing that the latter characterize the proof-theoretic ordinal of the fragment $\Pi^1_1$-$\mathrm{CA}_0$ of second order number theory, or equivalently the set theory $\mathrm{KPl}_0$. As a corollary, we prove that Carlson's result on the well-quasi orderedness of respecting forests of order $2$ implies transfinite induction up to the ordinal of $\mathrm{KPl}_0$. We expect that our approach will facilitate analysis of more powerful systems of patterns.Comment: corrected Theorem 4.2 with according changes in section 3 (mainly Definition 3.3), results unchanged. The manuscript was edited, aligned with reference [14] (moving former Lemma 3.5 there), and argumentation was revised, with minor corrections in (the proof of) Theorem 4.2; results unchanged. Updated revised preprint; to appear in the APAL (2017

Implementing imperfect information in fuzzy databases

Information in real-world applications is often vague, imprecise and uncertain. Ignoring the inherent imperfect nature of real-world will undoubtedly introduce some deformation of human perception of real-world and may eliminate several substantial information, which may be very useful in several data-intensive applications. In database context, several fuzzy database models have been proposed. In these works, fuzziness is introduced at different levels. Common to all these proposals is the support of fuzziness at the attribute level. This paper proposes first a rich set of data types devoted to model the different kinds of imperfect information. The paper then proposes a formal approach to implement these data types. The proposed approach was implemented within a relational object database model but it is generic enough to be incorporated into other database models.ou

Survival benefits in mimicry: a quantitative framework

Mimicry is a resemblance between species that benefits at least one of the species. It is a ubiquitous evolutionary phenomenon particularly common among prey species, in which case the advantage involves better protection from predation. We formulate a mathematical description of mimicry among prey species, to investigate benefits and disadvantages of mimicry. The basic setup involves differential equations for quantities representing predator behavior, namely, the probabilities for attacking prey at the next encounter. Using this framework, we present new quantitative results, and also provide a unified description of a significant fraction of the quantitative mimicry literature. The new results include `temporary' mutualism between prey species, and an optimal density at which the survival benefit is greatest for the mimic. The formalism leads naturally to extensions in several directions, such as the evolution of mimicry, the interplay of mimicry with population dynamics, etc. We demonstrate this extensibility by presenting some explorations on spatiotemporal pattern dynamics.Comment: 9 pages, 7 figure

Eligibility and inscrutability

The philosophy of intentionality asks questions such as: in virtue of what does a sentence, picture, or mental state represent that the world is a certain way? The subquestion I focus upon here concerns the semantic properties of language: in virtue of what does a name such as ‘London’ refer to something or a predicate such as ‘is large’ apply to some object? This essay examines one kind of answer to this “metasemantic”1 question: interpretationism, instances of which have been proposed by Donald Davidson, David Lewis, and others. I characterize the “twostep” form common to such approaches and briefl y say how two versions described by David Lewis fi t this pattern. Then I describe a fundamental challenge to this approach: a “permutation argument” that contends, by interpretationist lights, there can be no fact of the matter about lexical content (e.g., what individual words refer to). Such a thesis cannot be sustained, so the argument threatens a reductio of interpretationism. In the second part of the article, I will give what I take to be the best interpretationist response to the inscrutability paradox: David Lewis’s appeal to the differential “eligibility” of semantic theories. I contend that, given an independently plausible formulation of interpretationism, the eligibility response is an immediate consequence of Lewis’s general analysis of the theoretical virtue of simplicity. In the fi nal sections of the article, I examine the limitations of Lewis’s response. By focusing on an alternative argument for the inscrutability of reference, I am able to describe conditions under which the eligibility result will deliver the wrong results. In particular, if the world is complex enough and our language suffi ciently simple, then reference may be determinately secured to the wrong things

Content Recarving as Subject Matter Restriction

In this article I offer an explicating interpretation of the procedure of content recarving as described by Frege in §64 of the Foundations of Arithmetic. I argue that the procedure of content recarving may be interpreted as an operation that while restricting the subject matter of a sentence, performs a generalization on what the sentence says about its subject matter. The characterization of the recarving operation is given in the setting of Yablo’s theory of subject matter and it is based on the relation of determination between properties. The main advantage of the proposal is its generality, for it is applicable not just to the case of abstraction principle

Partial Perception and Approximate Understanding

What is discussed in the present paper is the assumption concerning a human narrowed sense of perception of external world and, resulting from this, a basically approximate nature of concepts that are to portray it. Apart from the perceptual vagueness, other types of vagueness are also discussed, involving both the nature of things, indeterminacy of linguistic expressions and psycho-sociological conditioning of discourse actions in one language and in translational contexts. The second part of the paper discusses the concept of conceptual and linguistic resemblance (similarity, equivalence) and discourse approximating strategies and proposes a Resemblance Matrix, presenting ways used to narrow the approximation gap between the interacting parties in monolingual and translational discourses