Consequences of a Goedel's misjudgment

The fundamental aim of the paper is to correct an harmful way to interpret a Goedel's erroneous remark at the Congress of Koenigsberg in 1930. Despite the Goedel's fault is rather venial, its misreading has produced and continues to produce dangerous fruits, as to apply the incompleteness Theorems to the full second-order Arithmetic and to deduce the semantic incompleteness of its language by these same Theorems. The first three paragraphs are introductory and serve to define the languages inherently semantic and its properties, to discuss the consequences of the expression order used in a language and some question about the semantic completeness: in particular is highlighted the fact that a non-formal theory may be semantically complete despite using a language semantically incomplete. Finally, an alternative interpretation of the Goedel's unfortunate comment is proposed. KEYWORDS: semantic completeness, syntactic incompleteness, categoricity, arithmetic, second-order languages, paradoxesComment: English version, 19 pages. Fixed and improved terminolog

Practical Model-Based Diagnosis with Qualitative Possibilistic Uncertainty

An approach to fault isolation that exploits vastly incomplete models is presented. It relies on separate descriptions of each component behavior, together with the links between them, which enables focusing of the reasoning to the relevant part of the system. As normal observations do not need explanation, the behavior of the components is limited to anomaly propagation. Diagnostic solutions are disorders (fault modes or abnormal signatures) that are consistent with the observations, as well as abductive explanations. An ordinal representation of uncertainty based on possibility theory provides a simple exception-tolerant description of the component behaviors. We can for instance distinguish between effects that are more or less certainly present (or absent) and effects that are more or less certainly present (or absent) when a given anomaly is present. A realistic example illustrates the benefits of this approach.Comment: Appears in Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence (UAI1995

Objective and Subjective Rationality in a Multiple Prior Model

A decision maker is characterized by two binary relations. The first reflects decisions that are rational in an “objective” sense: the decision maker can convince others that she is right in making them. The second relation models decisions that are rational in a “subjective” sense: the decision maker cannot be convinced that she is wrong in making them. We impose axioms on these relations that allow a joint representation by a single set of prior probabilities. It is “objectively rational” to choose f in the presence of g if and only if the expected utility of f is at least as high as that of g given each and every prior in the set. It is “subjectively rational” to choose f rather than g if and only if the minimal expected utility of f (relative to all priors in the set) is at least as high as that of g.Rationality, Multiple Priors.

Mathematical proofs and scientific discovery

The idea that science can be automated is so deeply related to the view that the method of mathematics is the axiomatic method, that confuting the claim that mathematical knowledge can be extended by means of the axiomatic method is almost equivalent to confuting the claim that science can be automated. I argue that the axiomatic view is inadequate as a view of the method of mathematics and that the analytic view is to be preferred. But, if the method of mathematics and natural sciences is the analytic method, then the advancement of knowledge cannot be mechanized, since non-deductive reasoning plays a crucial role in the analytic method, and non-deductive reasoning cannot be fully mechanized

A qualitative assessment of machine learning support for detecting data completeness and accuracy issues to improve data analytics in big data for the healthcare industry

Tackling Data Quality issues as part of Big Data can be challenging. For data cleansing activities, manual methods are not efficient due to the potentially very large amount of data. This paper aims to qualitatively assess the possibilities for using machine learning in the process of detecting data incompleteness and inaccuracy, since these two data quality dimensions were found to be the most significant by a previous research study conducted by the authors. A review of existing literature concludes that there is no unique machine learning algorithm most suitable to deal with both incompleteness and inaccuracy of data. Various algorithms are selected from existing studies and applied against a representative big (healthcare) dataset. Following experiments, it was also discovered that the implementation of machine learning algorithms in this context encounters several challenges for Big Data quality activities. These challenges are related to the amount of data particular machine learning algorithms can scale to and also to certain data type restrictions imposed by some machine learning algorithms. The study concludes that 1) data imputation works better with linear regression models, 2) clustering models are more efficient to detect outliers but fully automated systems may not be realistic in this context. Therefore, a certain level of human judgement is still needed

Metalogic and the Overgeneration Argument

A prominent objection against the logicality of second-order logic is the so-called Overgeneration Argument. However, it is far from clear how this argument is to be understood. In the first part of the article, we examine the argument and locate its main source, namely, the alleged entanglement of second-order logic and mathematics. We then identify various reasons why the entanglement may be thought to be problematic. In the second part of the article, we take a metatheoretic perspective on the matter. We prove a number of results establishing that the entanglement is sensitive to the kind of semantics used for second-order logic. These results provide evidence that by moving from the standard set-theoretic semantics for second-order logic to a semantics which makes use of higher-order resources, the entanglement either disappears or may no longer be in conflict with the logicality of second-order logic