In this paper, I evaluate the claim that the equivalence of multiple intensionally distinct definitions of random sequence provides evidence for the claim that these definitions capture the intuitive conception of randomness, concluding that the former claim is false. I then develop an alternative account of the significance of randomness-theoretic equivalence results, arguing that they are instances of a phenomenon I refer to as schematic equivalence. On my account, this alternative approach has the virtue of providing the plurality (...) of definitions of randomness with conceptual unity and a rationale for certain investigations that are carried out in the field. (shrink)

Although information content is invariant up to an additive constant, the range of possible additive constants applicable to programming languages is so large that in practice it plays a major role in the actual evaluation of K(s), the Kolmogorov complexity of a string s. We present a summary of the approach we've developed to overcome the problem by calculating its algorithmic probability and evaluating the algorithmic complexity via the coding theorem, thereby providing a stable framework for Kolmogorov complexity even for (...) short strings. We also show that reasonable formalisms produce reasonable complexity classifications. (shrink)

This article introduces definitions for direct, means-end, oblique (or indirect) and ulterior intent which can be used to test for intent in an algorithmic actor. These definitions of intent are informed by legal theory from common law jurisdictions. Certain crimes exist where the harm caused is dependent on the reason it was done so. Here the actus reus or performative element of the crime is dependent on the mental state or mens rea of the actor. The ability to (...) prosecute these crimes is dependent on the ability to identify and diagnose intentional states in the accused. A certain class of auto didactic algorithmic actor can be given broad objectives without being told how to meet them. Without a definition of intent, they cannot be told not to engage in certain law breaking behaviour nor can they ever be identified as having done it. This ambiguity is neither positive for the owner of the algorithm or for society. The problem exists over and above more familiar debates concerning the eligibility of algorithms for culpability judgements that mens rea is usually associated with. Aside from inchoate offences, many economic crimes with elements of fraud or deceit fall into this category of crime. Algorithms operate in areas where these crimes could be plausibly undertaken depending on whether the intent existed in the algorithm or not. (shrink)

In the article the basic procedures for finding of connective elements and resolving conflicts of references is analyzed. On the basis of this, a generalized algorithm is proposed that combines advantages of existing procedures for search for connective elements between phrases. The advantages of the selected procedures and their sequence are described, the formal description of input data and the results of the algorithm are presented. To optimize the procedure for scanning the text, the algorithm is performed as an iterative (...) reduction of the candidates for communication elements. This is achieved through the confirmation of non-conflict links and the gradual resolution of conflicts. (shrink)

This is a review of some of the definitions of the concept of a stable model that have been proposed in the literature. These definitions are equivalent to each other, at least when applied to traditional Prologstyle programs, but there are reasons why each of them is valuable and interesting. A new characterization of stable models can suggest an alternative picture of the intuitive meaning of logic programs; or it can lead to new algorithms for generating stable (...) models; or it can work better than others when we turn to generalizations of the traditional syntax that are important from the perspective of answer set programming; or it can be more convenient for use in proofs; or it can be interesting simply because it demonstrates a relationship between seemingly unrelated ideas. (shrink)

Part of understanding the meaning and power of algorithms means asking what new demands they might make of ethical frameworks, and how they might be held accountable to ethical standards. I develop a definition of networked information algorithms as assemblages of institutionally situated code, practices, and norms with the power to create, sustain, and signify relationships among people and data through minimally observable, semiautonomous action. Starting from Merrill’s prompt to see ethics as the study of “what we ought (...) to do,” I examine ethical dimensions of contemporary NIAs. Specifically, in an effort to sketch an empirically grounded, pragmatic ethics of algorithms, I trace an algorithmic assemblage’s power to convene constituents, suggest actions based on perceived similarity and probability, and govern the timing and timeframes of ethical action. (shrink)

The concept of “life” certainly is of some use to distinguish birds and beavers from water and stones. This pragmatic usefulness has led to its construal as a categorical predicate that can sift out living entities from non-living ones depending on their possessing specific properties—reproduction, metabolism, evolvability etc. In this paper, we argue against this binary construal of life. Using text-mining methods across over 30,000 scientific articles, we defend instead a degrees-of-life view and show how these methods can contribute to (...) experimental philosophy of science and concept explication. We apply topic-modeling algorithms to identify which specific properties are attributed to a target set of entities (bacteria, archaea, viruses, prions, plasmids, phages and the molecule of adenine). Eight major clusters of properties were identified together with their relative relevance for each target entity (two that relate to metabolism and catalysis, one to genetics, one to evolvability, one to structure, and—rather unexpectedly—three that concern interactions with the environment broadly construed). While aligning with intuitions—for instance about viruses being less alive than bacteria—these quantitative results also reveal differential degrees of performance that have so far remained elusive or overlooked. Taken together, these analyses provide a conceptual “lifeness space” that makes it possible to move away from a categorical construal of life by empirically assessing the relative lifeness of more-or-less alive entities. (shrink)

In this paper, we point out that explainability is useful but not sufficient to ensure the legitimacy of algorithmic decision systems. We argue that the key requirements for high-stakes decision systems should be justifiability and contestability. We highlight the conceptual differences between explanations and justifications, provide dual definitions of justifications and contestations, and suggest different ways to operationalize justifiability and contestability.

This article responds to recent debates in critical algorithm studies about the significance of the term “algorithm.” Where some have suggested that critical scholars should align their use of the term with its common definition in professional computer science, I argue that we should instead approach algorithms as “multiples”—unstable objects that are enacted through the varied practices that people use to engage with them, including the practices of “outsider” researchers. This approach builds on the work of Laura Devendorf, Elizabeth (...) Goodman, and Annemarie Mol. Different ways of enacting algorithms foreground certain issues while occluding others: computer scientists enact algorithms as conceptual objects indifferent to implementation details, while calls for accountability enact algorithms as closed boxes to be opened. I propose that critical researchers might seek to enact algorithms ethnographically, seeing them as heterogeneous and diffuse sociotechnical systems, rather than rigidly constrained and procedural formulas. To do so, I suggest thinking of algorithms not “in” culture, as the event occasioning this essay was titled, but “as” culture: part of broad patterns of meaning and practice that can be engaged with empirically. I offer a set of practical tactics for the ethnographic enactment of algorithmic systems, which do not depend on pinning down a singular “algorithm” or achieving “access,” but which rather work from the partial and mobile position of an outsider. (shrink)

We propose a test based on the theory of algorithmic complexity and an experimental evaluation of Levin's universal distribution to identify evidence in support of or in contravention of the claim that the world is algorithmic in nature. To this end statistical comparisons are undertaken of the frequency distributions of data from physical sources--repositories of information such as images, data stored in a hard drive, computer programs and DNA sequences--and the output frequency distributions generated by purely algorithmic means--by running abstract (...) computing devices such as Turing machines, cellular automata and Post Tag systems. Statistical correlations were found and their significance measured. (shrink)

I examine the classical idea of ‘algorithm’ as a sequential, step-by-step, deterministic procedure (i.e., the idea of ‘algorithm’ that was already in use by the 1930s), with respect to three themes, its relation to the notion of an ‘effective procedure’, its different roles and uses in logic, computer science, and mathematics (focused on numerical analysis), and its different formal definitions proposed by practitioners in these areas. I argue that ‘algorithm’ has been conceptualized and used in contrasting ways in the (...) above areas, and discuss challenges and prospects for adopting a final foundational theory of (classical) ‘algorithms’. (shrink)

Fairness is one of the most prominent values in the Ethics and Artificial Intelligence (AI) debate and, specifically, in the discussion on algorithmic decision-making (ADM). However, while the need for fairness in ADM is widely acknowledged, the very concept of fairness has not been sufficiently explored so far. Our paper aims to fill this gap and claims that an ethically informed re-definition of fairness is needed to adequately investigate fairness in ADM. To achieve our goal, after an introductory section aimed (...) at clarifying the aim and structure of the paper, in section “Fairness in algorithmic decision-making” we provide an overview of the state of the art of the discussion on fairness in ADM and show its shortcomings; in section “Fairness as an ethical value”, we pursue an ethical inquiry into the concept of fairness, drawing insights from accounts of fairness developed in moral philosophy, and define fairness as an ethical value. In particular, we argue that fairness is articulated in a distributive and socio-relational dimension; it comprises three main components: fair equality of opportunity, equal right to justification, and fair equality of relationship; these components are grounded in the need to respect persons both as persons and as particular individuals. In section “Fairness in algorithmic decision-making revised”, we analyze the implications of our redefinition of fairness as an ethical value on the discussion of fairness in ADM and show that each component of fairness has profound effects on the criteria that ADM ought to meet. Finally, in section “Concluding remarks”, we sketch some broader implications and conclude. (shrink)

Efforts to promote equitable public policy with algorithms appear to be fundamentally constrained by the “impossibility of fairness” (an incompatibility between mathematical definitions of fairness). This technical limitation raises a central question about algorithmic fairness: How can computer scientists and policymakers support equitable policy reforms with algorithms? In this article, I argue that promoting justice with algorithms requires reforming the methodology of algorithmic fairness. First, I diagnose the problems of the current methodology for algorithmic fairness, which (...) I call “formal algorithmic fairness.” Because formal algorithmic fairness restricts analysis to isolated decision-making procedures, it leads to the impossibility of fairness and to models that exacerbate oppression despite appearing “fair.” Second, I draw on theories of substantive equality from law and philosophy to propose an alternative methodology, which I call “substantive algorithmic fairness.” Because substantive algorithmic fairness takes a more expansive scope of analysis, it enables an escape from the impossibility of fairness and provides a rigorous guide for alleviating injustice with algorithms. In sum, substantive algorithmic fairness presents a new direction for algorithmic fairness: away from formal mathematical models of “fair” decision-making and toward substantive evaluations of whether and how algorithms can promote justice in practice. (shrink)

Algorithmic decision making is used in an increasing number of fields. Letting automated processes take decisions raises the question of their accountability. In the field of computational journalism, the algorithmic accountability framework proposed by Diakopoulos formalizes this challenge by considering algorithms as objects of human creation, with the goal of revealing the intent embedded into their implementation. A consequence of this definition is that ensuring accountability essentially boils down to a transparency question: given the appropriate reverse-engineering tools, it should (...) be feasible to extract design criteria and to identify intentional biases. General limitations of this transparency ideal have been discussed by Ananny and Crawford :973–989, 2018). We further focus on its technical limitations. We show that even if reverse-engineering concludes that the criteria embedded into an algorithm correspond to its publicized intent, it may be that adversarial behaviors make the algorithm deviate from its expected operation. We illustrate this issue with an automated news recommendation system, and show how the classification algorithms used in such systems can be fooled with hard-to-notice modifications of the articles to classify. We therefore suggest that robustness against adversarial behaviors should be taken into account in the definition of algorithmic accountability, to better capture the risks inherent to algorithmic decision making. We finally discuss the various challenges that this new technical limitation raises for journalism practice. (shrink)

Two definitions of algorithm, their uses, and their implied models of computing in society, are reviewed. The first, termed the structural programming definition, aligns more with usage in computer science, and as the name suggests, the intellectual project of structured programming. The second, termed the systemic definition, is more informal and emerges from ethnographic observations of discussions of software in both professional and everyday settings. Specific examples of locating algorithms within modern codebases are shared, as well as code (...) directly impacting social and ethical concerns. The structural distinction between algorithms and social concerns is explained as mirroring the engineering construct of algorithms and data structures. It is proposed that, rather than this separation being an attempt to enforce a professional boundary and evade social responsibility, it is a crucial technical distinction within code which makes it clearer and more transparent. The power structures reinforced by the broader, cultural interpretations of algorithm are reconsidered, along with what it would mean for software to have an inclusive design culture. (shrink)

This article is a set of reflections on the question: ‘what is completely new in algorithmic governmentality compared to capitalism and neoliberalism?’ The following text is thus some preliminary, temporary and definitively uncertain intuitions in response to this question.

The rhetoric of algorithmic neutrality is more alive than ever-why? This volume explores key moments in the historical emergence of algorithmic practices and in the constitution of their credibility and authority since 1500. If algorithms are historical objects and their associated meanings and values are situated and contingent-and if we are to push back against rhetorical claims of otherwise-then the genealogical investigation this book offers is essential to understand the power of the algorithm. The fact that algorithms create (...) the conditions for many of our encounters with social reality contrasts starkly with their relative invisibility. More than other artifacts, algorithms are easily black-boxed. Rather than contingent and modifiable, they are widely seen as obvious and unproblematic-without context and without history. As an antidote, this volume keeps a clear focus on the emergence and continuous reconstitution of algorithmic practices alongside the ascendance of modernity. Its essays highlight the trajectory of an algorithmic modernity, one characterized by attitudes and practices that are best emblematized by the modernist aesthetic and inhuman efficacy of the algorithm. The volume moves from early modern algorithmic practices, centered on heuristics for arithmetic operations, emphasizing ruptures, shifts, and variations across times and cultures. By the age of Enlightenment, the term algorithm had come to signify any process of systematic calculation that could be carried out mechanically, but its meaning and implications are still distant from those familiar to us. It's in the nineteenth and twentieth century that the meaning of algorithm is sharpened through a new discipline and by adding sets of specific conditions-such as the condition of finiteness-which acquire new and crucial significance in the age of digital computing. Throughout, the connection between algorithms and modernity is one of our central concerns. Through detailed historical reconstructions of specific moments, thinkers, and cultural phenomena over the last five hundred years, these essays lead us to the definitions of algorithm most legible today and to the pervasiveness of both algorithmic procedures and rhetoric. This volume contributes a multi-faceted exploration of the genealogies of algorithms, of algorithmic thinking, and of the distinctly modernist faith in algorithms as neutral tools that merely illuminate the natural and social world. (shrink)

The computational approach to psychiatric disorders, including delusions, promises explanation and treatment. Here, we argue that an information processing approach might be misleading to understand psychopathology and requires further refinement. We explore the claim of computational psychiatry being a bridge between phenomenology and physiology while focussing on the ontological commitments and corresponding methodology computational psychiatry is based on. Interconnecting ontological claims and methodological practices, the paper illustrates the structure of theory-building and testing in computational psychiatry.First, we will explain the ontological (...) commitments computational psychiatry is grounded in, theBayesian Brain hypothesis(BBH) of unconscious inference, paired with normative deontic approaches applied to gauge psychopathology. We then turn to the steps taken in empirical paradigms, from definitions, which are used as starting points, to the operationalisation and isolation of cognitive processes and hypothesis testing based on algorithmic models, to consecutive interpretations regarding the aetiology of psychiatric disorders. We outline how experimental paradigms in computational psychiatry are specifically designed to confirm aberrations in assumed inferential processes, which are thought of as being the underlyingcore invariant features.We will illustrate a gap between the ontological commitments of computational psychiatry and the operationalisation and testing of the cognition assumed to be relevant for psychopathology. This conceptual gap is of utmost importance when designing computational paradigms and may impede a crisp understanding of the approach. Lastly, in evaluating the conceptual gap, it becomes apparent that the information processing formalism used in computational psychiatry is still grounded in rational cognitive psychology. (shrink)

Over the past decade, scholars, institutions, and activists have voiced strong concerns about the potential of automated decision systems to indirectly discriminate against vulnerable groups. This article analyses the ethics of algorithmic indirect discrimination, and argues that we can explain what is morally bad about such discrimination by reference to the fact that it causes harm. The article first sketches certain elements of the technical and conceptual background, including definitions of direct and indirect algorithmic differential treatment. It next introduces (...) three prominent accounts of fairness as potential explanations if the badness of algorithmic indirect discrimination, but argues that all three are vulnerable to powerful levelling-down-style objections. Instead, the article demonstrates how proper attention to the way differences in decision-scenarios affect the distribution of harms can help us account for intuitions in prominent cases. Finally, the article considers a potential objection based on the fact that certain forms of algorithmic indirect discrimination appear to distribute rather than cause harm, and notes that we can explain how such distributions cause harm by attending to differences in individual and group vulnerability. (shrink)

In this APA blog, I appeal to two 2020 cases of algorithms gone wrong to motivate philosophical attention to algorithmic oppression. I offer a simple definition, then describe a few of the ways it is engendered. References and extends work by Safiya Noble, Cathy O'Neil, Ruha Benjamin, Virginia Eubanks, Sara Wachter-Boettcher, Michael Kearns & Aaron Roth.

This article is both a comment on Neyland’s ‘On organizing algorithms’ and a supplementary note to our ‘The concept of algorithm as an interpretative key of modern rationality’. In the first part we discuss the concepts of algorithm and recursive function from a different perspective from that of our previous article. Our cultural reference for these concepts is once again computability theory. We give additional arguments in support of the idea that a culture informed by an algorithmic logic has (...) promoted modern rationality both in science and in society. We stress again the importance of distinguishing between algorithms applied to quantifiable entities such as space, time and value and those applied to ontological entities such as human actions. In the second case, the algorithm is applied outside its domain of definition and leads to social disaggregation. (shrink)

Sequential decision theory formally solves the problem of rational agents in uncertain worlds if the true environmental prior probability distribution is known. Solomonoff's theory of universal induction formally solves the problem of sequence prediction for unknown prior distribution. We combine both ideas and get a parameter-free theory of universal Artificial Intelligence. We give strong arguments that the resulting AIXI model is the most intelligent unbiased agent possible. We outline how the AIXI model can formally solve a number of problem classes, (...) including sequence prediction, strategic games, function minimization, reinforcement and supervised learning. The major drawback of the AIXI model is that it is uncomputable. To overcome this problem, we construct a modified algorithm AIXItl that is still effectively more intelligent than any other time t and length l bounded agent. The computation time of AIXItl is of the order t x 2^l. The discussion includes formal definitions of intelligence order relations, the horizon problem and relations of the AIXI theory to other AI approaches. (shrink)

To address the rising concern that algorithmic decision-making may reinforce discriminatory biases, researchers have proposed many notions of fairness and corresponding mathematical formalizations. Each of these notions is often presented as a one-size-fits-all, absolute condition; however, in reality, the practical and ethical trade-offs are unavoidable and more complex. We introduce a new approach that considers fairness—not as a binary, absolute mathematical condition—but rather, as a relational notion in comparison to alternative decisionmaking processes. Using US mortgage lending as an example use (...) case, we discuss the ethical foundations of each definition of fairness and demonstrate that our proposed methodology more closely captures the ethical trade-offs of the decision-maker, as well as forcing a more explicit representation of which values and objectives are prioritised. (shrink)

This comprehensive compendium provides a rigorous framework to tackle the daunting challenges of designing correct and efficient algorithms. It gives a uniform approach to the design, analysis, optimization, and verification of algorithms. The volume also provides essential tools to understand algorithms and their associated data structures. This useful reference text describes a way of thinking that eases the task of proving algorithm correctness. Working through a proof of correctness reveals an algorithm's subtleties in a way that a (...) typical description does not. Algorithm analysis is presented using careful definitions that make the analyses mathematically rigorous. (shrink)

There is growing concern that decision-making informed by machine learning (ML) algorithms may unfairly discriminate based on personal demographic attributes, such as race and gender. Scholars have responded by introducing numerous mathematical definitions of fairness to test the algorithm, many of which are in conflict with one another. However, these reductionist representations of fairness often bear little resemblance to real-life fairness considerations, which in practice are highly contextual. Moreover, fairness metrics tend to be implemented in narrow and targeted (...) toolkits that are difficult to integrate into an algorithm’s broader ethical assessment. In this paper, we derive lessons from ethical philosophy and welfare economics as they relate to the contextual factors relevant for fairness. In particular we highlight the debate around acceptability of particular inequalities and the inextricable links between fairness, welfare and autonomy. We propose Key Ethics Indicators (KEIs) as a way towards providing a more holistic understanding of whether or not an algorithm is aligned to the decision-maker’s ethical values. (shrink)

This study investigates to what extent the amount of variation in a visual scene causes speakers to mention the attribute color in their definite target descriptions, focusing on scenes in which this attribute is not needed for identification of the target. The results of our three experiments show that speakers are more likely to redundantly include a color attribute when the scene variation is high as compared with when this variation is low (even if this leads to overspecified descriptions). We (...) argue that these findings are problematic for existing algorithms that aim to automatically generate psychologically realistic target descriptions, such as the Incremental Algorithm, as these algorithms make use of a fixed preference order per domain and do not take visual scene variation into account. (shrink)

Data-driven algorithms are currently deployed in several fields, leading to a rapid increase in the importance algorithms have in decision-making processes. Over the last years, several instances of discrimination by algorithms were observed. A new branch of research emerged to examine the concept of “algorithmic fairness.” No consensus currently exists on a single operationalization of fairness, although causal-based definitions are arguably more aligned with the human conception of fairness. The aim of this article is to investigate (...) the degree of this alignment in a case study inspired by a recent ruling of an Italian court on the reputational-ranking algorithm used by a food delivery platform. I relied on the documentation of the legal dispute to discuss the applicability, intuitiveness and appropriateness of causal models in evaluating fairness, with a specific focus on a causal-based fairness definition called “counterfactual fairness.” I first describe the details of the dispute and the arguments presented to the court, as well as the court’s final decision, to establish the context of the case study. Then, I translate the dispute into a formal simplified problem using a causal diagram, which represents the main aspects of the data generation process in the case study. I identify the criteria used by the court in ruling that the algorithm was unfair and compare them with the counterfactual fairness definition. The definition of counterfactual fairness was found to be well aligned with the human conception of fairness in this case study, using the court order rationale as a gold standard. (shrink)

In this paper, we build upon Bruno Latour’s political writings to address the current impasse regarding algorithms in public life. We assert that the increasing difficulties at governing algorithms—be they qualified as “machine learning,” “big data,” or “artificial intelligence”—can be related to their current ontological thinness: deriving from constricted views on theoretical practices, algorithms’ standard definition as problem-solving computerized methods provides poor grips for affective dissensions. We then emphasize on the role historical and ethnographic studies of (...) class='Hi'>algorithms can potentially play in the politicization of algorithms. By both digging into the genealogy of algorithms’ constricted definition and by making their contemporary constitutive relationships more visible, both historical and ethnographic studies can contribute to vascularizing algorithms and making them objects of enlarged disputes. We conclude by giving a flavor of the political potential of the vascularization efforts we call for, using materials from an ethnographic study conducted in a computer science laboratory. (shrink)

In this position paper, we introduce a new epistemic lens for analyzing algorithmic harm. We argue that the epistemic lens we propose herein has two key contributions to help reframe and address some of the assumptions underlying inquiries into algorithmic fairness. First, we argue that using the framework of epistemic injustice helps to identify the root causes of harms currently framed as instances of representational harm. We suggest that the epistemic lens offers a theoretical foundation for expanding approaches to algorithmic (...) fairness in order to address a wider range of harms not recognized by existing technical or legal definitions. Second, we argue that the epistemic lens helps to identify the epistemic goals of inquiries into algorithmic fairness. There are two distinct contexts within which we examine algorithmic harm: at times, we seek to understand and describe the world as it is, and, at other times, we seek to build a more just future. The epistemic lens can serve to direct our attention to the epistemic frameworks that shape our interpretations of the world as it is and the ways we envision possible futures. Clarity with respect to which epistemic context is relevant in a given inquiry can further help inform choices among the different ways of measuring and addressing algorithmic harms. We introduce this framework with the goal of initiating new research directions bridging philosophical, legal, and technical approaches to understanding and mitigating algorithmic harms. (shrink)

The accurate annotation of an unknown protein sequence depends on extant data of template sequences. This could be empirical or sets of reference sequences, and provides an exhaustive pool of probable functions. Individual methods of predicting dominant function possess shortcomings such as varying degrees of inter-sequence redundancy, arbitrary domain inclusion thresholds, heterogeneous parameterization protocols, and ill-conditioned input channels. Here, I present a rigorous theoretical derivation of various steps of a generic algorithm that integrates and utilizes several statistical methods to predict (...) the dominant function in unknown protein sequences. The accompanying mathematical proofs, interval definitions, analysis, and numerical computations presented are meant to offer insights not only into the specificity and accuracy of predictions, but also provide details of the operatic mechanisms involved in the integration and its ensuing rigor. The algorithm uses numerically modified raw hidden markov model scores of well defined sets of training sequences and clusters them on the basis of known function. The results are then fed into an artificial neural network, the predictions of which can be refined using the available data. This pipeline is trained recursively and can be used to discern the dominant principal function, and thereby, annotate an unknown protein sequence. Whilst, the approach is complex, the specificity of the final predictions can benefit laboratory workers design their experiments with greater confidence. -/- . (shrink)

In user cluster analysis, users with the same or similar behavior characteristics are divided into the same group by iterative update clustering, and the core and larger user groups are detected. In this paper, we present the formulation and data mining of the correlation rules based on the clustering algorithm through the definition and procedure of the algorithm. In addition, based on the idea of the K-mode clustering algorithm, this paper proposes a clustering method combining related rules with multivalued discrete (...) features. In this paper, we construct a method to calculate the similarity between users using Jaccard distance and combine correlation rules with Jaccard distances to improve the similarity between users. Next, we propose a clustering method suitable for MDF. Finally, the basic K-mode algorithm is improved by the similarity measure method combining the correlation rule with the Jaccard distance and the cluster center update method which is the ARMDKM algorithm proposed in this paper. This method solves the problem that the MDF cannot be effectively processed in the traditional model and demonstrates its theoretical correctness. This experiment verifies the correctness of the new method by clustering purity, entropy, contour, and other indicators. (shrink)

To address the rising concern that algorithmic decision-making may reinforce discriminatory biases, researchers have proposed many notions of fairness and corresponding mathematical formalizations. Each of these notions is often presented as a one-size-fits-all, absolute condition; however, in reality, the practical and ethical trade-offs are unavoidable and more complex. We introduce a new approach that considers fairness—not as a binary, absolute mathematical condition—but rather, as a relational notion in comparison to alternative decision-making processes. Using U.S. mortgage lending as an example use (...) case, we discuss the ethical foundations of each definition of fairness and demonstrate that our proposed methodology more closely captures the ethical trade-offs of the decision-maker. (shrink)

In the paper, a detailed analysis of some new logical aspects of Cantor’s diagonal proof of the uncountability of continuum is presented. For the first time, strict formal, axiomatic, and algorithmic definitions of the notions of potential and actual infinities are presented. It is shown that the actualization of infinite sets and sequences used in Cantor’s proof is a necessary, but hidden, condition of the proof. The explication of the necessary condition and its factual usage within the framework of (...) Cantor’s proof makes, Cantor’s proof invalid. It’s shown that traditional Cantor’s proof has a second necessary, but hidden as well, condition which is teleological by its nature, i.e., is not mathematical. The explication of the second necessary condition makes Cantor’s statement on the uncountability of continuum unprovable from the point of view of classical logic.One of the most dramatic facts in history of science is connected just with the notion of actual infinity and consists in the following. On the one hand, Aristotle, Berkeley, Locke, Descartes, Spinoza, Gauss, Kant, Cauchy, Kronecker, Hermite, Poincaré, Bair, Borel, Brouwer, Quine, Wittgenstein, Weyl, Luzin, and a lot of other outstanding creators of classical logic and classical mathematics, during millenniums, stated categorically and insistently warned about that the actual infinity is a self-contradictory notion and its usage in mathematics is inadmissible (e.g., according to Poincare, “There is no actual infinity. - Cantorians forgot that and fell into contradictions. Later generations will regard Mengenlehre (set theory) as a disease from which one has recovered”). On the other hand, a lot of outstanding scientists of the XX c.c., such as Hilbert, Church, Turing, Gödel, etc., and modern axiomatic set theory as a whole ignored this (intuitive though) opinion of genii and accepted Cantor’s “transfinite paradise”, based on the actual infinity. In the paper some logical, philosophical, and psychological aspects of this historical “favorable opposition” are analyzed, and the fact that the scientific intuition of genii has won the historical battle against the mytho-’logic’ of Cantor’s transfinite ‘paradise’ is explained and logically justified. (shrink)

In the paper, a detailed analysis of some new logical aspects of Cantor’s diagonal proof of the uncountability of continuum is presented. For the first time, strict formal, axiomatic, and algorithmic definitions of the notions of potential and actual infinities are presented. It is shown that the actualization of infinite sets and sequences used in Cantor’s proof is a necessary, but hidden, condition of the proof. The explication of the necessary condition and its factual usage within the framework of (...) Cantor’s proof makes, Cantor’s proof invalid. It’s shown that traditional Cantor’s proof has a second necessary, but hidden as well, condition which is teleological by its nature, i.e., is not mathematical. The explication of the second necessary condition makes Cantor’s statement on the uncountability of continuum unprovable from the point of view of classical logic.One of the most dramatic facts in history of science is connected just with the notion of actual infinity and consists in the following. On the one hand, Aristotle, Berkeley, Locke, Descartes, Spinoza, Gauss, Kant, Cauchy, Kronecker, Hermite, Poincaré, Bair, Borel, Brouwer, Quine, Wittgenstein, Weyl, Luzin, and a lot of other outstanding creators of classical logic and classical mathematics, during millenniums, stated categorically and insistently warned about that the actual infinity is a self-contradictory notion and its usage in mathematics is inadmissible (e.g., according to Poincare, “There is no actual infinity. - Cantorians forgot that and fell into contradictions. Later generations will regard Mengenlehre (set theory) as a disease from which one has recovered”). On the other hand, a lot of outstanding scientists of the XX c.c., such as Hilbert, Church, Turing, Gödel, etc., and modern axiomatic set theory as a whole ignored this (intuitive though) opinion of genii and accepted Cantor’s “transfinite paradise”, based on the actual infinity. In the paper some logical, philosophical, and psychological aspects of this historical “favorable opposition” are analyzed, and the fact that the scientific intuition of genii has won the historical battle against the mytho-’logic’ of Cantor’s transfinite ‘paradise’ is explained and logically justified. (shrink)

This paper deals with Gärdenfors’ theory of conceptual spaces. Let \({\mathcal {S}}\) be a conceptual space consisting of 2-type fuzzy sets equipped with several kinds of metrics. Let a finite set of prototypes \(\tilde{P}_1,\ldots,\tilde{P}_n\in \mathcal {S}\) be given. Our main result is the construction of a classification algorithm. That is, given an element \({\tilde{A}}\in \mathcal {S},\) our algorithm classifies it into the conceptual field determined by one of the given prototypes \(\tilde{P}_i.\) The construction of our algorithm uses some physical analogies (...) and the Newton potential plays a significant role here. Importantly, the resulting conceptual fields are not convex in the Euclidean sense, which we believe is a reasonable departure from the assumptions of Gardenfors’ original definition of the conceptual space. A partitioning algorithm of the space \(\mathcal {S}\) is also considered in the paper. In the application section, we test our classification algorithm on real data and obtain very satisfactory results. Moreover, the example we consider is another argument against requiring convexity of conceptual fields. (shrink)

A wave of recent scholarship has warned about the potential for discriminatory harms of algorithmic systems, spurring an interest in algorithmic accountability and regulation. Meanwhile, parallel concerns about surveillance practices have already led to multiple successful regulatory efforts of surveillance technologies—many of which have algorithmic components. Here, we examine municipal surveillance regulation as offering lessons for algorithmic oversight. Taking the 2017 Seattle Surveillance Ordinance as our primary case study and surveying efforts across five other cities, we describe the features of (...) existing surveillance regulation; including procedures for describing surveillance technologies in detail, requirements for public engagement, and processes for establishing acceptable uses. Although the Seattle Surveillance Ordinance was not intended to address algorithmic accountability, we find these considerations to be relevant to the law’s aim of surfacing disparate impacts of systems in use. We also find that in notable cases government employees did not identify regulated algorithmic surveillance technologies as reliant on algorithmic or machine learning systems, highlighting definitional gaps that could hinder future efforts toward algorithmic regulation. We argue that finer-grained distinctions between types of information systems in the language of law and policy, and risk assessment tools integrated into their implementation would strengthen future regulatory efforts by rendering underlying algorithmic components more legible and accountable to political and community stakeholders. (shrink)

There are writers in both metaphysics and algorithmic information theory (AIT) who seem to think that the latter could provide a formal theory of the former. This paper is intended as a step in that direction. It demonstrates how AIT might be used to define basic metaphysical notions such as *object* and *property* for a simple, idealized world. The extent to which these definitions capture intuitions about the metaphysics of the simple world, times the extent to which we think (...) the simple world is analogous to our own, will determine a lower bound for basing a metaphysics for *our* world on AIT. (shrink)

Our aim is to discover whether the notion of algorithmic orbit-complexity can serve to define “chaos” in a dynamical system. We begin with a mostly expository discussion of algorithmic complexity and certain results of Brudno, Pesin, and Ruelle (BRP theorems) which relate the degree of exponential instability of a dynamical system to the average algorithmic complexity of its orbits. When one speaks of predicting the behavior of a dynamical system, one usually has in mind one or more variables in the (...) phase space that are of particular interest. To say that the system is unpredictable is, roughly, to say that one cannot feasibly determine future values of these variables from an approximation of the initial conditions of the system. We introduce the notions of restrictedexponential instability and conditionalorbit-complexity, and announce a new and rather general result, similar in spirit to the BRP theorems, establishing average conditional orbit-complexity as a lower bound for the degree of restricted exponential instability in a dynamical system. The BRP theorems require the phase space to be compact and metrizable. We construct a noncompact kicked rotor dynamical system of physical interest, and show that the relationship between orbit-complexity and exponential instability fails to hold for this system. We conclude that orbit-complexity cannot serve as a general definition of “chaos.”. (shrink)

Describing an algorithm can provide a formalization of a specific process. However, different ways of conceptualizing algorithms foreground certain issues while obscuring others. This article attempts to define an algorithm in a broad sense as a cultural activity of key importance to make sense of socio-cognitive structures. It also attempts to develop a sharper account on the interaction between humans and tools, symbols and technologies. Rather than human or machine-centered analyses, I draw upon sociological and anthropological theories that underline (...) social practices to propose expanding our understanding of an algorithm through the notion of ‘collective intentionalities’. To make this term clear, a brief historical review is presented, followed by an argumentation on how to incorporate it in an integral perspective. The article responds to recent debates in critical algorithm studies about the significance of the term. It develops a discussion along the lines of cognitive anthropology and the cognitive sciences, therefore advancing a definition that is grounded in observed practices as well as in modeled descriptions. The benefit of this approach is that it encourages scholars to explore cognitive structures via archaeologies of technological assemblages, where intentionalities play a defining role in understanding socio-structured practices and cognitive ecologies. (shrink)

Modern society makes extensive use of automated algorithmic decisions, fueled by advances in artificial intelligence. However, since these systems are not perfect, questions about fairness are increasingly investigated in the literature. In particular, many authors take a Rawlsian approach to algorithmic fairness. This article aims to identify some complications with this approach: Under which circumstances can Rawls’s original position reasonably be applied to algorithmic fairness decisions? First, it is argued that there are important differences between Rawls’s original position and a (...) parallel algorithmic fairness original position with respect to risk attitudes. Second, it is argued that the application of Rawls’s original position to algorithmic fairness faces a boundary problem in defining relevant stakeholders. Third, it is observed that the definition of the least advantaged, necessary for applying the difference principle, requires some attention in the context of algorithmic fairness. Finally, it is argued that appropriate deliberation in algorithmic fairness contexts often require more knowledge about probabilities than the Rawlsian original position allows. Provided that these complications are duly considered, the thought-experiment of the Rawlsian original position can be useful in algorithmic fairness decisions. (shrink)

Liquidity risk arises from the inability to unwind or hedge trading positions at the prevailing market prices. The risk of liquidity is a wide and complex topic as it depends on several factors and causes. While much has been written on the subject, there exists no clear-cut mathematical description of the phenomena and typical market risk modeling methods fail to identify the effect of illiquidity risk. In this paper, we do not propose a definitive one either, but we attempt to (...) derive novel mathematical algorithms for the dynamic modeling of trading volumes during the closeout period from the perspective of multiple-asset portfolio, as well as for financial entities with different subsidiary firms and multiple agents. The robust modeling techniques are based on the application of initial-value-problem differential equations technique for portfolio selection and risk management purposes. This paper provides some crucial parameters for the assessment of the trading volumes of multiple-asset portfolio during the closeout period, where the mathematical proofs for each theorem and corollary are provided. Based on the new developed econophysics theory, this paper presents for the first time a closed-form solution for key parameters for the estimation of trading volumes and liquidity risk, such as the unwinding constant, half-life, and mean lifetime and discusses how these novel parameters can be estimated and incorporated into the proposed techniques. The developed modeling algorithms are appealing in terms of theory and are promising for practical econophysics applications, particularly in developing dynamic and robust portfolio management algorithms in light of the 2007–2009 global financial crunch. In addition, they can be applied to artificial intelligence and machine learning for the policymaking process, reinforcement machine learning techniques for the Internet of Things data analytics, expert systems in finance, FinTech, and within big data ecosystems. (shrink)