Axiomatization of Inconsistency Indicators for Pairwise Comparisons

This study proposes revised axioms for defining inconsistency indicators in pairwise comparisons. It is based on the new findings that "PC submatrix cannot have a worse inconsistency indicator than the PC matrix containing it" and that there must be a PC submatrix with the same inconsistency as the given PC matrix. This study also provides better reasoning for the need of normalization. It is a revision of axiomatization by Koczkodaj and Szwarc, 2014 which proposed axioms expressed informally with some deficiencies addressed in this study.Comment: This paper should have been withdrawn by the first author a long time ago. The work has been finished with another researcher, I have been pushed out the projec

LOGICAL AND PSYCHOLOGICAL PARTITIONING OF MIND: DEPICTING THE SAME MAP?

The aim of this paper is to demonstrate that empirically delimited structures of mind are also differentiable by means of systematic logical analysis. In the sake of this aim, the paper first summarizes Demetriou's theory of cognitive organization and growth. This theory assumes that the mind is a multistructural entity that develops across three fronts: the processing system that constrains processing potentials, a set of specialized structural systems (SSSs) that guide processing within different reality and knowledge domains, and a hypecognitive system that monitors and controls the functioning of all other systems. In the second part the paper focuses on the SSSs, which are the target of our logical analysis, and it summarizes a series of empirical studies demonstrating their autonomous operation. The third part develops the logical proof showing that each SSS involves a kernel element that cannot be reduced to standard logic or to any other SSS. The implications of this analysis for the general theory of knowledge and cognitive development are discussed in the concluding part of the paper

Empirical Similarity

An agent is asked to assess a real-valued variable Y_{p} based on certain characteristics X_{p} = (X_{p}^{1},...,X_{p}^{m}), and on a database consisting (X_{i}^{1},...,X_{i}^{m},Y_{i}) for i = 1,...,n. A possible approach to combine past observations of X and Y with the current values of X to generate an assessment of Y is similarity-weighted averaging. It suggests that the predicted value of Y, Y_{p}^{s}, be the weighted average of all previously observed values Y_{i}, where the weight of Y_{i}, for every i =1,...,n, is the similarity between the vector X_{p}^{1},...,X_{p}^{m}, associated with Y_{p}, and the previously observed vector, X_{i}^{1},...,X_{i}^{m}. We axiomatize this rule. We assume that, given every database, a predictor has a ranking over possible values, and we show that certain reasonable conditions on these rankings imply that they are determined by the proximity to a similarity-weighted average for a certain similarity function. The axiomatization does not suggest a particular similarity function, or even a particular functional form of this function. We therefore proceed to suggest that the similarity function be estimated from past observations. We develop tools of statistical inference for parametric estimation of the similarity function, for the case of a continuous as well as a discrete variable. Finally, we discuss the relationship of the proposed method to other methods of estimation and prediction.Similarity, estimation

Keynes’s missing axioms

Between Keynes’s verbalized theory and its formal basis persists a lacuna. The conceptual groundwork is too small and not general. The quest for a comprehensive formal basis is guided by the question: what is the minimum set of foundational propositions for a consistent reconstruction of the money economy? We start with three structural axioms. The claim of generality entails that it should be possible to prove that Keynes’s formalism is a subset of the structural axiom set. The axioms are applied to a central part of the General Theory in order to achieve consistency and generality

Invisible Hand in the Process of Making Economics or on the Method and Scope of Economics

As a social science, economics cannot be reduced to simply an a priori science or an ideology. In addition economics cannot be solely an empirical or a historical science. Economics is a research field which studies only one dimension of human behavior, with the four fields of mathematics, econometrics, ethics and history intersecting one another. The purpose of this paper is to discuss the two parts of the proposition above, in connection with the controversies surrounding the method and the scope of economics: economics as an applied mathematics and economics as a predictive/empirical science.Invisible hand, Scope and method in economics, Economics as an applied mathematics, Economics as an empirical science, Economics as ideology.

Formalizing structured file services for the data storage and retrieval subsystem of the data management system for Spacestation Freedom

A brief example of the use of formal methods techniques in the specification of a software system is presented. The report is part of a larger effort targeted at defining a formal methods pilot project for NASA. One possible application domain that may be used to demonstrate the effective use of formal methods techniques within the NASA environment is presented. It is not intended to provide a tutorial on either formal methods techniques or the application being addressed. It should, however, provide an indication that the application being considered is suitable for a formal methods by showing how such a task may be started. The particular system being addressed is the Structured File Services (SFS), which is a part of the Data Storage and Retrieval Subsystem (DSAR), which in turn is part of the Data Management System (DMS) onboard Spacestation Freedom. This is a software system that is currently under development for NASA. An informal mathematical development is presented. Section 3 contains the same development using Penelope (23), an Ada specification and verification system. The complete text of the English version Software Requirements Specification (SRS) is reproduced in Appendix A

Reconstructing the Quantity Theory (I)

The quantity theory is disjunct to the hard core of general equilibrium theory. It does not relate to the formal foundations of standard economics and, vice versa, from the behavioral axioms of standard economics a rationale for using money cannot be derived. The present paper leaves the standard axioms aside and reconstructs the quantity theory from entirely new structural axiomatic foundations. This gives a coherent view of the interrelations of quantity of money, transaction money, saving–dissaving, liquidity–illiquidity, rates of interest, leverage, allocation, prices, profits, unit of account, and employment