formal concepts
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2022 ◽  
Author(s):  
Micah Allen

Bruineberg and colleagues report a striking confusion, in which the formal Bayesian notion of a “Markov Blanket” has been frequently misunderstood and misapplied to phenomena of mind and life. I argue that misappropriation of formal concepts is pervasive in the “predictive processing” literature, and echo Richard Feynman in suggesting how we might resist the allure of cargo cult computationalism.





2021 ◽  
Vol 2099 (1) ◽  
pp. 012026
Author(s):  
V A Semenova ◽  
S V Smirnov

Abstract Two methodologies for formal concepts derivation are considered: the classical one, which focuses on the posterior analysis of the object’s properties of the studied knowledge domain, and non-classical, the cornerstone of which is the a priori formation of the set of measured object’s properties and the determination of existential relations on this set. In the article, firstly, a position is fixed in the technological chain of the target transformation of the source data, where the difference between considered methodologies shows itself. Secondly, the commonality of these two approaches is established in the aspect of the unity of their hypothetical-deductive basis. In this case, the cognitive activity of the subject is expressed first in a priori and then in a posteriori conceptual scaling of the measured properties. The work demonstrates the need for the joint use of the considered methodologies at processing incomplete and inconsistent empirical data about studied knowledge domain. The intermediate consolidation of these methodologies is possible only on the basis of multi-valued logic.



Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2694
Author(s):  
Amira Mouakher ◽  
Axel Ragobert ◽  
Sébastien Gerin ◽  
Andrea Ko

Formal concept analysis (FCA) is a mathematical theory that is typically used as a knowledge representation method. The approach starts with an input binary relation specifying a set of objects and attributes, finds the natural groupings (formal concepts) described in the data, and then organizes the concepts in a partial order structure or concept (Galois) lattice. Unfortunately, the total number of concepts in this structure tends to grow exponentially as the size of the data increases. Therefore, there are numerous approaches for selecting a subset of concepts to provide full or partial coverage. In this paper, we rely on the battery of mathematical models offered by FCA to introduce a new greedy algorithm, called Concise, to compute minimal and meaningful subsets of concepts. Thanks to its theoretical properties, the Concise algorithm is shown to avoid the sluggishness of its competitors while offering the ability to mine both partial and full conceptual coverage of formal contexts. Furthermore, experiments on massive datasets also underscore the preservation of the quality of the mined formal concepts through interestingness measures agreed upon by the community.



2021 ◽  
pp. 1-24
Author(s):  
Mohamed Chebel ◽  
Chiraz Latiri ◽  
Eric Gaussier

Abstract Bilingual corpora are an essential resource used to cross the language barrier in multilingual natural language processing tasks. Among bilingual corpora, comparable corpora have been the subject of many studies as they are both frequent and easily available. In this paper, we propose to make use of formal concept analysis to first construct concept vectors which can be used to enhance comparable corpora through clustering techniques. We then show how one can extract bilingual lexicons of improved quality from these enhanced corpora. We finally show that the bilingual lexicons obtained can complement existing bilingual dictionaries and improve cross-language information retrieval systems.



2021 ◽  
pp. 301-314
Author(s):  
Michael S. Pardo ◽  
Ronald J. Allen

This chapter examines the implications of the reference-class problem for attempts to model the probative value of evidence in mathematical terms. This examination makes three distinct contributions to evidence scholarship. First, and most importantly, it articulates and explains the problematic relationship between algorithmic tools and legal decision-making. Second, it points out serious pitfalls to be avoided for analytical or empirical studies of juridical proof. Third, it indicates when algorithmic tools may be more or less useful in the evidentiary process. As such, the chapter offers yet another demonstration of the very complex set of relationships involving human knowledge and rationality, on the one hand, and attempts to reduce either to a set of formal concepts, on the other.



Author(s):  
Henri Prade ◽  
Gilles Richard

This paper presents a survey of researches in analogical reasoning whose building block are analogical proportions which are statements of the form “a is to b as c is to d”. They have been developed in the last twenty years within an Artificial Intelligence perspective. After discussing their formal modeling with the associated inference mechanism, the paper reports the main results obtained in various AI domains ranging from computational linguistics to classification, including image processing, I.Q. tests, case based reasoning, preference learning, and formal concepts analysis. The last section discusses some new theoretical concerns, and the potential of analogical proportions in other areas such as argumentation, transfer learning, and XAI.





2021 ◽  
Vol 10 (6) ◽  
pp. 397
Author(s):  
Daniel G. Cole ◽  
E. Richard Hart

Indigenous maps are critical in understanding the historic and current land tenure of Indigenous groups. Furthermore, Indigenous claims to land can be seen in their connections via toponymy. European concepts of territory and political boundaries did not coincide with First Nation/American Indian views, resulting in the mistaken view that Natives did not have formal concepts of their territories. And Tribes/First Nations with cross-border territory have special jurisdictional problems. This paper illustrates how many Native residents were very spatially aware of their own lands, as well as neighboring nations’ lands, overlaps between groups, hunting territories, populations, and trade networks. Finally, the Sinixt First Nation serve as a perfect example of a case study on how an Aboriginal people are currently inputting and using a GIS representation of their territory with proper toponymy and use areas.



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