In recent years, the ethical impact of AI has been increasingly scrutinized, with public scandals emerging over biased outcomes, lack of transparency, and the misuse of data. This has led to a growing mistrust of AI and increased calls for mandated ethical audits of algorithms. Current proposals for ethical assessment of algorithms are either too high level to be put into practice without further guidance, or they focus on very specific and technical notions of fairness or transparency that do not (...) consider multiple stakeholders or the broader social context. In this article, we present an auditing framework to guide the ethical assessment of an algorithm. The audit instrument itself is comprised of three elements: a list of possible interests of stakeholders affected by the algorithm, an assessment of metrics that describe key ethically salient features of the algorithm, and a relevancy matrix that connects the assessed metrics to stakeholder interests. The proposed audit instrument yields an ethical evaluation of an algorithm that could be used by regulators and others interested in doing due diligence, while paying careful attention to the complex societal context within which the algorithm is deployed. (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)

Cloud Computing is a developing field and lean toward by numerous one at current yet it's rage is part more rely upon its execution which thusly is excessively rely upon the powerful booking algorithm and load adjusting . In this paper we address this issue and propose an algorithm for private cloud which has high throughput and for open cloud which address the issue of condition awareness likewise with execution. To enhance the throughput in private cloud SJF is utilized for (...) planning and to conquer shape the issue of starvation we utilize limited pausing. For stack adjusting we screen the heap and dispatch the activity to the minimum stacked VM. To acquire advantage and to have open door for future upgrade out in the open cloud condition cognizance is the key factor and for better execution and load adjusting likewise wanted. While stack adjusting enhances the execution, the earth awareness increment the benefit of cloud suppliers. (shrink)

The problem of algorithmic structuring of proofs in the sequent calculi LK and LKB ( LK where blocks of quantifiers can be introduced in one step) is investigated, where a distinction is made between linear proofs and proofs in tree form. In this framework, structuring coincides with the introduction of cuts into a proof. The algorithmic solvability of this problem can be reduced to the question of k-l-compressibility: "Given a proof of length k , and l ≤ k (...) : Is there is a proof of length ≤ l ?" When restricted to proofs with universal or existential cuts, this problem is shown to be (1) undecidable for linear or tree-like LK-proofs (corresponds to the undecidability of second order unification), (2) undecidable for linear LKB-proofs (corresponds to the undecidability of semi-unification), and (3) decidable for tree-like LKB -proofs (corresponds to a decidable subprob- lem of semi-unification). (shrink)

Today, a consistent part of our everyday interaction with art and aesthetic artefacts occurs through digital media, and our preferences and choices are systematically tracked and analyzed by algorithms in ways that are far from transparent. Our consumption is constantly documented, and then, we are fed back through tailored information. We are therefore witnessing the emergence of a complex interrelation between our aesthetic choices, their digital elaboration, and also the production of content and the dynamics of creative processes. All are (...) involved in a process of mutual influences, and are partially determined by the invisible guiding hand of algorithms. -/- With regard to this topic, this paper will introduce some key issues concerning the role of algorithms in aesthetic domains, such as taste detection and formation, cultural consumption and production, and showing how aesthetics can contribute to the ongoing debate about the impact of today’s “algorithmic culture”. (shrink)

Abstract: The efficiency and performance of sorting algorithms play a crucial role in various applications and industries. In this research paper, we present a comprehensive comparative analysis of popular sorting algorithms on datasets of different sizes and characteristics. The aim is to evaluate the algorithms' performance and identify their strengths and weaknesses under varying scenarios. We consider six commonly used sorting algorithms: QuickSort, TimSort, MergeSort, HeapSort, RadixSort, and ShellSort. These algorithms represent a range of approaches and techniques, including divide-and-conquer, hybrid (...) sorting, and simple comparison-based methods. To assess their performance, we employ a diverse set of datasets, including the Iris dataset (1K), student dataset (5.8K), Wine dataset (6.5K), Uniform (10K), Normal (10K), Exponential (10K), Bimodal (10K), Yelp dataset (10K), MNIST dataset (42K), Uniform (100K), Normal (100K), Exponential (100K), Bimodal (100K), Uniform (500K), Normal (500K), Exponential (500K), Bimodal (500K), Uniform (1M), Normal (1M), Exponential (1M), and Bimodal (1M). These datasets cover a wide range of sizes and characteristics, allowing us to analyze the algorithms' performance across different dimensions. We measure and compare several key metrics, including execution time, memory usage, algorithmic complexity and stability. By analyzing these metrics, we gain insights into the efficiency and suitability of each algorithm for different dataset sizes and characteristics. We also discuss the implications of the findings in practical applications. Our results reveal important trade-offs among the sorting algorithms. While some algorithms excel in certain scenarios, others demonstrate better scalability or memory efficiency. We identify the best-performing algorithms for specific dataset characteristics and highlight their strengths and limitations. This research can assist developers and practitioners in selecting appropriate sorting algorithms based on their specific requirements and dataset characteristics. In conclusion, this comparative analysis provides a valuable contribution to the understanding of sorting algorithm performance. The findings contribute insights into the efficiency and suitability of popular sorting algorithms across datasets of different sizes and characteristics. By evaluating key metrics and discussing the implications, we offer guidance for selecting the most appropriate sorting algorithm in various practical scenarios. (shrink)

"Complexity" is a catchword of certain extremely popular and rapidly developing interdisciplinary new sciences, often called accordingly the sciences of complexity. It is often closely associated with another notably popular but ambiguous word, "information"; information, in turn, may be justly called the central new concept in the whole 20th century science. Moreover, the notion of information is regularly coupled with a key concept of thermodynamics, viz. entropy. And like this was not enough it is quite usual to add (...) one more at present extraordinarily popular notion, namely chaos, and wed it with the abovementioned concepts. It is my aim in this paper to critically analyse this conceptual mess from a logical and philosophical point of view concentrating on the concepts of complexity and information and the question concerning the true relation between them. (shrink)

In computational complexity theory, decision problems are divided into complexity classes based on the amount of computational resources it takes for algorithms to solve them. In theoretical computer science, it is commonly accepted that only functions for solving problems in the complexity class P, solvable by a deterministic Turing machine in polynomial time, are considered to be tractable. In cognitive science and philosophy, this tractability result has been used to argue that only functions in P can feasibly (...) work as computational models of human cognitive capacities. One interesting area of computational complexity theory is descriptive complexity, which connects the expressive strength of systems of logic with the computational complexity classes. In descriptive complexity theory, it is established that only first-order systems are connected to P, or one of its subclasses. Consequently, second-order systems of logic are considered to be computationally intractable, and may therefore seem to be unfit to model human cognitive capacities. This would be problematic when we think of the role of logic as the foundations of mathematics. In order to express many important mathematical concepts and systematically prove theorems involving them, we need to have a system of logic stronger than classical first-order logic. But if such a system is considered to be intractable, it means that the logical foundation of mathematics can be prohibitively complex for human cognition. In this paper I will argue, however, that this problem is the result of an unjustified direct use of computational complexity classes in cognitive modelling. Placing my account in the recent literature on the topic, I argue that the problem can be solved by considering computational complexity for humanly relevant problem solving algorithms and input sizes. (shrink)

This chapter uncovers the complex negotiations for authority in various representations about futures of life which have been advanced by different branches of the sciences, and have culminated in the emerging concept of life as algorithm. It charts the historical shifts in expertise and representations of life, from naturalists, to mathematical modellers, and specialists in computation, and argues that physicists, game theorists, and economists now take a leading role in explaining and projecting futures of life. The chapter identifies Richard Dawkins (...) and Max Tegmark at the forefront of the concept of life as algorithm: the first inspired by game theory as a means to study evolution; the second proposing that a materialist basis of life could place humans and artificial intelligence on an equal footing. Through close reading of their respective texts, the chapter demonstrates that both thinkers consider life as an algorithm programmed to achieve success in survival and reproduction. (shrink)

It is well known that the unpredictable speech production brought on by stress from the task at hand has a significant negative impact on the performance of speech processing algorithms. Speech therapy benefits from being able to detect stress in speech. Speech processing performance suffers noticeably when perceptually produced stress causes variations in speech production. Using the acoustic speech signal to objectively characterize speaker stress is one method for assessing production variances brought on by stress. Real-world complexity and ambiguity (...) make it difficult for decision-makers to express their conclusions with clarity in their speech. In particular, the Neutrosophic speech algorithm is used to encode the language variables because they cannot be computed directly. Neutrosophic sets are used to manage indeterminacy in a practical situation. Existing algorithms are used except for stress on Neutrosophic speech recognition. The creation of algorithms that calculate, categorize, or differentiate between different stress circumstances. Understanding stress and developing strategies to combat its effects on speech recognition and human-computer interaction system are the goals of this recognition. (shrink)

Some things look more complex than others. For example, a crenulate and richly organized leaf may seem more complex than a plain stone. What is the nature of this experience—and why do we have it in the first place? Here, we explore how object complexity serves as an efficiently extracted visual signal that the object merits further exploration. We algorithmically generated a library of geometric shapes and determined their complexity by computing the cumulative surprisal of their internal skeletons—essentially (...) quantifying the “amount of information” within each shape—and then used this approach to ask new questions about the perception of complexity. Experiments 1–3 asked what kind of mental process extracts visual complexity: a slow, deliberate, reflective process (as when we decide that an object is expensive or popular) or a fast, effortless, and automatic process (as when we see that an object is big or blue)? We placed simple and complex objects in visual search arrays and discovered that complex objects were easier to find among simple distractors than simple objects are among complex distractors—a classic search asymmetry indicating that complexity is prioritized in visual processing. Next, we explored the function of complexity: Why do we represent object complexity in the first place? Experiments 4–5 asked subjects to study serially presented objects in a self‐paced manner (for a later memory test); subjects dwelled longer on complex objects than simple objects—even when object shape was completely task‐irrelevant—suggesting a connection between visual complexity and exploratory engagement. Finally, Experiment 6 connected these implicit measures of complexity to explicit judgments. Collectively, these findings suggest that visual complexity is extracted efficiently and automatically, and even arouses a kind of “perceptual curiosity” about objects that encourages subsequent attentional engagement. (shrink)

What happens when mindless symbols of algorithmic AI encounter mindful performative rituals? I return to my criticisms of Habermas’ secularising reading of Kierkegaard’s ethics. Next, I lay out Habermas’ claim that the sacred complex of ritual and myth contains the ur-origins of postmetaphysical thinking and reflective faith. If reflective faith shares with ritual same origins as does communicative interaction, how do we access these archaic ritual sources of human solidarity in the age of AI?

In this paper, building on these previous works, we propose to go deeper into the understanding of crowd behavior by proposing an approach which integrates ontologi- cal models of crowd behavior and dedicated computer vision algorithms, with the aim of recognizing some targeted complex events happening in the playground from the observation of the spectator crowd behavior. In order to do that, we first propose an ontology encoding available knowledge on spectator crowd behavior, built as a spe- cialization of the (...) DOLCE foundational ontology, which allows the representation of categories belonging both to the physical and to the social realms. We then propose a simplified and tractable version of such ontology in a new temporal extension of a description logic, which is used for temporally coupling events happening on the play- ground and spectator crowd behavior. At last, computer vision algorithms provide the input information concerning what is observed on the stands and ontological reasoning delivers the output necessary to perform complex event recognition. (shrink)

A common criticism of the use of algorithms in criminal justice is that algorithms and their determinations are in some sense ‘opaque’—that is, difficult or impossible to understand, whether because of their complexity or because of intellectual property protections. Scholars have noted some key problems with opacity, including that opacity can mask unfair treatment and threaten public accountability. In this paper, we explore a different but related concern with algorithmic opacity, which centers on the role of public trust (...) in grounding the legitimacy of criminal justice institutions. We argue that algorithmic opacity threatens the trustworthiness of criminal justice institutions, which in turn threatens their legitimacy. We first offer an account of institutional trustworthiness before showing how opacity threatens to undermine an institution’s trustworthiness. We then explore how threats to trustworthiness affect institutional legitimacy. Finally, we offer some policy recommendations to mitigate the threat to trustworthiness posed by the opacity problem. (shrink)

Following Marr’s famous three-level distinction between explanations in cognitive science, it is often accepted that focus on modeling cognitive tasks should be on the computational level rather than the algorithmic level. When it comes to mathematical problem solving, this approach suggests that the complexity of the task of solving a problem can be characterized by the computational complexity of that problem. In this paper, I argue that human cognizers use heuristic and didactic tools and thus engage in (...) cognitive processes that make their problem solving algorithms computationally suboptimal, in contrast with the optimal algorithms studied in the computational approach. Therefore, in order to accurately model the human cognitive tasks involved in mathematical problem solving, we need to expand our methodology to also include aspects relevant to the algorithmic level. This allows us to study algorithms that are cognitively optimal for human problem solvers. Since problem solving methods are not universal, I propose that they should be studied in the framework of enculturation, which can explain the expected cultural variance in the humanly optimal algorithms. While mathematical problem solving is used as the case study, the considerations in this paper concern modeling of cognitive tasks in general. (shrink)

Big Data is a large-sized and complex dataset, which cannot be managed using traditional data processing tools. Mining process of big data is the ability to extract valuable information from these large datasets. Association rule mining is a type of data mining process, which is indented to determine interesting associations between items and to establish a set of association rules whose support is greater than a specific threshold. The classical association rules can only be extracted from binary data where an (...) item exists in a transaction, but it fails to deal effectively with quantitative attributes, through decreasing the quality of generated association rules due to sharp boundary problems. In order to overcome the drawbacks of classical association rule mining, we propose in this research a new neutrosophic association rule algorithm. The algorithm uses a new approach for generating association rules by dealing with membership, indeterminacy, and non-membership functions of items, conducting to an efficient decision-making system by considering all vague association rules. To prove the validity of the method, we compare the fuzzy mining and the neutrosophic mining. The results show that the proposed approach increases the number of generated association rules. (shrink)

We present a minimum message length (MML) framework for trajectory partitioning by point selection, and use it to automatically select the tolerance parameter ε for Douglas-Peucker partitioning, adapting to local trajectory complexity. By examining a range of ε for synthetic and real trajectories, it is easy to see that the best ε does vary by trajectory, and that the MML encoding makes sensible choices and is robust against Gaussian noise. We use it to explore the identification of micro-activities within (...) a longer trajectory. This MML metric is comparable to the TRACLUS metric – and shares the constraint of abstracting only by omission of points – but is a true lossless encoding. Such encoding has several theoretical advantages – particularly with very small segments (high frame rates) – but actual performance interacts strongly with the search algorithm. Both differ from unconstrained piecewise linear approximations, including other MML formulations. (shrink)

Contains a description of a generalized and constructive formal model for the processes of subjective and creative thinking. According to the author, the algorithm presented in the article is capable of real and arbitrarily complex thinking and is potentially able to report on the presence of consciousness.

Science is the basis for managing the affairs of life and human activities, and living without knowledge is a form of wandering and a kind of loss. Using scientific methods helps us understand the foundations of choice, decision-making, and adopting the right solutions when solutions abound and options are numerous. Operational research is considered the best that scientific development has provided because its methods depend on the application of scientific methods in solving complex issues and the optimal use of available (...) resources in various fields, private and governmental work in peace and war, in politics and economics, in planning and implementation, and in various aspects of life. Its basic essence is to use the data provided for the issue under study to build a mathematical model that is the optimal solution. It is the basis on which decision makers rely in managing institutions and companies, and when operations research methods meet with the neutrosophic teacher, we get ideal solutions that take into account all the circumstances and fluctuations that may occur in the work environment over time. One of the most important operations research methods is the linear programming method. Which prompted us to reformulate the linear models, the graphical method, and the simplex method, which are used to obtain the optimal solution for linear models using the concepts of neutrosophic science. In this research, and as a continuation of what we presented previously, we will reformulate the modified simplex algorithm that was presented to address the difficulty that we were facing when applying the direct simplex algorithm. It is the large number of calculations required to be performed in each step of the solution, which requires a lot of time and effort. (shrink)

A crucial question for artificial cognition systems is what meaning is and how it arises. In pursuit of that question, this paper extends earlier work in which we show that emergence of simple signaling in biologically inspired models using arrays of locally interactive agents. Communities of "communicators" develop in an environment of wandering food sources and predators using any of a variety of mechanisms: imitation of successful neighbors, localized genetic algorithms and partial neural net training on successful neighbors. Here we (...) focus on environmental variability, comparing results for environments with (a) constant resources, (b) random resources, and (c) cycles of "boom and bust." In both simple and complex models across all three mechanisms of strategy change, the emergence of communication is strongly favored by cycles of "boom and bust." These results are particularly intriguing given the importance of environmental variability in fields as diverse as psychology, ecology and cultural anthropology. (shrink)

The notion of representation in neuroscience has largely been predicated on localizing the components of computational processes that explain cognitive function. On this view, which I call “algorithmic homuncularism,” individual, spatially and temporally distinct parts of the brain serve as vehicles for distinct contents, and the causal relationships between them implement the transformations specified by an algorithm. This view has a widespread influence in philosophy and cognitive neuroscience, and has recently been ably articulated and defended by Shea. Still, I (...) am skeptical about algorithmic homuncularism, and I argue against it by focusing on recent methods for complex data analysis in systems neuroscience. I claim that analyses such as principle components analysis and linear discriminant analysis prevent individuating vehicles as algorithmic homuncularism recommends. Rather, each individual part contributes to a global state space, trajectories of which vary with important task parameters. I argue that, while homuncularism is false, this view still supports a kind of “vehicle realism,” and I apply this view to debates about the explanatory role of representation. (shrink)

Complexity is a relatively new field of study that is still heavily influenced by philosophy. However, with the advent of modern computing, it has become easier to conduct thorough investigations of complex systems using computational simulations. Despite significant progress, there remain certain characteristics of complex systems that are difficult to comprehend. To better understand these features, information can be applied using simple models of complex systems. The concepts of Shannon's information theory, Kolgomorov complexity, and logical depth are helpful (...) in this regard. Computational mathematical models based on recursive processes, recursive functions, and information in functions offer new insights into complexity by exploring its connection with irreversibility and the loss of information. Through these models, it is possible to see complexity as a transformation of input information through algorithmic computation, with time, logical depth, and information loss serving as key factors in understanding the process. (shrink)

This paper considers negative triggers and the interpretation of simple sentences containing more than one occurrence of those items . In the most typical interpretations those sentences have more negative expressions than negations in their semantic representation. It is first shown that this compositionality problem remains in current approaches. A principled algorithm for deriving the representation of sentences with multiple negative quantifiers in a DRT framework is then introduced. The algorithm is under the control of an on-line check-in, keeping the (...) complexity of negation auto-embedding below a threshold of complexity. This mechanism is seen as a competence limitation imposing the ‘abrogation of compositionality’ observed in the so-called negative concord readings . A solution to the compositionality problem is thus proposed, which is based on a control on the processing input motivated by a limitation of the processing mechanism itself. (shrink)

The opacity of some recent Machine Learning (ML) techniques have raised fundamental questions on their explainability, and created a whole domain dedicated to Explainable Artificial Intelligence (XAI). However, most of the literature has been dedicated to explainability as a scientific problem dealt with typical methods of computer science, from statistics to UX. In this paper, we focus on explainability as a pedagogical problem emerging from the interaction between lay users and complex technological systems. We defend an empirical methodology based on (...) field work, which should go beyond the in-vitro analysis of UX to examine in-vivo problems emerging in the field. Our methodology is also comparative, as it chooses to steer away from the almost exclusive focus on ML to compare its challenges with those faced by more vintage algorithms. Finally, it is also philosophical, as we defend the relevance of the philosophical literature to define the epistemic desiderata of a good explanation. This study was conducted in collaboration with Etalab, a Task Force of the French Prime Minister in charge of Open Data & Open Government Policies, dealing in particular with the enforcement of the right to an explanation. In order to illustrate and refine our methodology before going up to scale, we conduct a preliminary work of case studies on the main different types of algorithms used by the French administration: computation, matching algorithms and ML. We study the merits and drawbacks of a recent approach to explanation, which we baptize input-output black box reasoning or BBR for short. We begin by presenting a conceptual framework including the distinctions necessary to a study of pedagogical explainability. We proceed to algorithmic case studies, and draw model-specific and model-agnostic lessons and conjectures. (shrink)

Crossing the road within the traffic system is an example of an action human agents perform successfully day-to-day in complex systems. How do they perform such successful actions given that the behaviour of complex systems is often difficult to predict? The contemporary literature contains two contrasting approaches to the epistemology of complex systems: an analytic and a post-modern approach. We argue that neither approach adequately accounts for how successful action is possible in complex systems. Agents regularly perform successful actions without (...) obeying (explicit or implicit) algorithmic rules (as the analytic approach suggests) and without an existential leap to action (as the post-modern approach suggests). We offer an alternative: A common-sense pragmatist epistemology, one that focuses on the kind of actions making up most agents’ successful moment-to-moment actions in complex systems. Successful actions obtain when agents apply ceteris paribus rules-of-thumb during predictive and decisional practices while achieving some desired goal. (shrink)

Complex systems are difficult to manage, operate and maintain. This is why we see teams of highly specialised engineers in industries such as aerospace, nuclear and subsurface. Condition based monitoring is also employed to maximise the efficiency of extensive maintenance programmes instead of using periodic maintenance. A level of automation is often required in such complex engineering platforms in order to effectively and safely manage them. Advances in Artificial Intelligence related technologies have offered greater levels of automation but this potentially (...) pivots the weight of decision making away from the operator to the machine. Implementing AI or complex algorithms into a platform can mean that the Operators’ control over the system is diminished or removed altogether. For example, in the Boeing 737 Air Max Disaster, AI had been added to a platform and removed the operators’ control of the system. This meant that the operator could not then move outside the extremely reserved, algorithm defined, “envelope” of operation. This paper analyses the challenges of AI driven condition based monitoring where there is a potential to see similar consequences to those seen in control engineering. As the future of society becomes more about algorithm driven technology, it is prudent to ask, not only whether we should implement AI into complex systems, but how this can be achieved ethically and safely in order to reduce risk to life. (shrink)

Richard Dawkins has popularized an argument that he thinks sound for showing that there is almost certainly no God. It rests on the assumptions (1) that complex and statistically improbable things are more difficult to explain than those that are not and (2) that an explanatory mechanism must show how this complexity can be built up from simpler means. But what justifies claims about the designer’s own complexity? One comes to a different understanding of order and of simplicity (...) when one considers the psychological counterpart of information. In assessing his treatment of biological organisms as either self-programmed machines or algorithms, I show how self-generated organized complexity does not fit well with our knowledge of abduction and of information theory as applied to genetics. I also review some philosophical proposals for explaining how the complexity of the world could be externally controlled if one wanted to uphold a traditional understanding of divine simplicity. (shrink)

Synthetic biology aims at reconstructing life to put to the test the limits of our understanding. It is based on premises similar to those which permitted invention of computers, where a machine, which reproduces over time, runs a program, which replicates. The underlying heuristics explored here is that an authentic category of reality, information, must be coupled with the standard categories, matter, energy, space and time to account for what life is. The use of this still elusive category permits us (...) to interact with reality via construction of self-consistent models producing predictions which can be instantiated into experiments. While the present theory of information has much to say about the program, with the creative properties of recursivity at its heart, we almost entirely lack a theory of the information supporting the machine. We suggest that the program of life codes for processes meant to trap information which comes from the context provided by the environment of the machine. (shrink)

This paper investigates the seeming incompatibility of reductionism and non-reductionism in the context of complexity sciences. I review algorithmic information theory for this purpose. I offer two physical metaphors to form a better understanding of algorithmic complexity, and I briefly discuss its advantages, shortcomings and applications. Then, I revisit the non-reductionist approaches in philosophy of mind which are often arguments from ignorance to counter physicalism. A new approach called mild non-reductionism is proposed which reconciliates the necessities (...) of acknowledging irreducibility found in complex systems, and maintaining physicalism. (shrink)

We study the algorithmic complexity of isomorphic embeddings between computable structures.

The aim of this paper is to comprehensively question the validity of the standard way of interpreting Chaitin's famous incompleteness theorem, which says that for every formalized theory of arithmetic there is a finite constant c such that the theory in question cannot prove any particular number to have Kolmogorov complexity larger than c. The received interpretation of theorem claims that the limiting constant is determined by the complexity of the theory itself, which is assumed to be good (...) measure of the strength of the theory. I exhibit certain strong counterexamples and establish conclusively that the received view is false. Moreover, I show that the limiting constants provided by the theorem do not in any way reflect the power of formalized theories, but that the values of these constants are actually determined by the chosen coding of Turing machines, and are thus quite accidental. (shrink)

Many artificial intelligence (AI) systems currently used for decision-making are opaque, i.e., the internal factors that determine their decisions are not fully known to people due to the systems’ computational complexity. In response to this problem, several researchers have argued that human decision-making is equally opaque and since simplifying, reason-giving explanations (rather than exhaustive causal accounts) of a decision are typically viewed as sufficient in the human case, the same should hold for algorithmic decision-making. Here, I contend that (...) this argument overlooks that human decision-making is sometimes significantly more transparent and trustworthy than algorithmic decision-making. This is because when people explain their decisions by giving reasons for them, this frequently prompts those giving the reasons to govern or regulate themselves so as to think and act in ways that confirm their reason reports. AI explanation systems lack this self-regulative feature. Overlooking it when comparing algorithmic and human decision-making can result in underestimations of the transparency of human decision-making and in the development of explainable AI that may mislead people by activating generally warranted beliefs about the regulative dimension of reason-giving. (shrink)

Computational complexity is a discipline of computer science and mathematics which classifies computational problems depending on their inherent difficulty, i.e. categorizes algorithms according to their performance, and relates these classes to each other. P problems are a class of computational problems that can be solved in polynomial time using a deterministic Turing machine while solutions to NP problems can be verified in polynomial time, but we still do not know whether they can be solved in polynomial time as well. (...) A solution for the so-called NP-complete problems will also be a solution for any other such problems. Its artificial-intelligence analogue is the class of AI-complete problems, for which a complete mathematical formalization still does not exist. In this chapter we will focus on analysing computational classes to better understand possible formalizations of AI-complete problems, and to see whether a universal algorithm, such as a Turing test, could exist for all AI-complete problems. In order to better observe how modern computer science tries to deal with computational complexity issues, we present several different deep-learning strategies involving optimization methods to see that the inability to exactly solve a problem from a higher order computational class does not mean there is not a satisfactory solution using state-of-the-art machine-learning techniques. Such methods are compared to philosophical issues and psychological research regarding human abilities of solving analogous NP-complete problems, to fortify the claim that we do not need to have an exact and correct way of solving AI-complete problems to nevertheless possibly achieve the notion of strong AI. (shrink)

ABSTRACT: One important criticism of algorithmic systems is that they lack transparency. Such systems can be opaque because they are complex, protected by patent or trade secret, or deliberately obscure. In the EU, there is a debate about whether the General Data Protection Regulation (GDPR) contains a “right to explanation,” and if so what such a right entails. Our task in this chapter is to address this informational component of algorithmic systems. We argue that information access is integral (...) for respecting autonomy, and transparency policies should be tailored to advance autonomy. -/- To make this argument we distinguish two facets of agency (i.e., capacity to act). The first is practical agency, or the ability to act effectively according to one’s values. The second is what we call cognitive agency, which is the ability to exercise what Pamela Hieronymi calls “evaluative control” (i.e., the ability to control our affective states, such as beliefs, desires, and attitudes). We argue that respecting autonomy requires providing persons sufficient information to exercise evaluative control and properly interpret the world and one’s place in it. We draw this distinction out by considering algorithmic systems used in background checks, and we apply the view to key cases involving risk assessment in criminal justice decisions and K-12 teacher evaluation. -/- The link below is to an open access version of the chapter. (shrink)

This theme issue has the founding ambition of landscaping Data Ethics as a new branch of ethics that studies and evaluates moral problems related to data (including generation, recording, curation, processing, dissemination, sharing, and use), algorithms (including AI, artificial agents, machine learning, and robots), and corresponding practices (including responsible innovation, programming, hacking, and professional codes), in order to formulate and support morally good solutions (e.g. right conducts or right values). Data Ethics builds on the foundation provided by Computer and Information (...) Ethics but, at the same time, it refines the approach endorsed so far in this research field, by shifting the Level of Abstraction of ethical enquiries, from being information-centric to being data-centric. This shift brings into focus the different moral dimensions of all kinds of data, even the data that never translate directly into information but can be used to support actions or generate behaviours, for example. It highlights the need for ethical analyses to concentrate on the content and nature of computational operations — the interactions among hardware, software, and data — rather than on the variety of digital technologies that enables them. And it emphasises the complexity of the ethical challenges posed by Data Science. Because of such complexity, Data Ethics should be developed from the start as a macroethics, that is, as an overall framework that avoids narrow, ad hoc approaches and addresses the ethical impact and implications of Data Science and its applications within a consistent, holistic, and inclusive framework. Only as a macroethics Data Ethics will provide the solutions that can maximise the value of Data Science for our societies, for all of us, and for our environments. (shrink)

The mind-body problem is analyzed in a physicalist perspective. By combining the concepts of emergence and algorithmic information theory in a thought experiment employing a basic nonlinear process, it is shown that epistemically strongly emergent properties may develop in a physical system. Turning to the significantly more complex neural network of the brain it is subsequently argued that consciousness is epistemically emergent. Thus reductionist understanding of consciousness appears not possible; the mind-body problem does not have a reductionist solution. The (...) ontologically emergent character of consciousness is then identified from a combinatorial analysis relating to universal limits set by quantum mechanics, implying that consciousness is fundamentally irreducible to low-level phenomena. (shrink)

Many cognitive scientists, having discovered that some computational-level characterization f of a cognitive capacity φ is intractable, invoke heuristics as algorithmic-level explanations of how cognizers compute f. We argue that such explanations are actually dysfunctional, and rebut five possible objections. We then propose computational-level theory revision as a principled and workable alternative.

I use modal logic and transfinite set-theory to define metaphysical foundations for a general theory of computation. A possible universe is a certain kind of situation; a situation is a set of facts. An algorithm is a certain kind of inductively defined property. A machine is a series of situations that instantiates an algorithm in a certain way. There are finite as well as transfinite algorithms and machines of any degree of complexity (e.g., Turing and super-Turing machines and more). (...) There are physically and metaphysically possible machines. There is an iterative hierarchy of logically possible machines in the iterative hierarchy of sets. Some algorithms are such that machines that instantiate them are minds. So there is an iterative hierarchy of finitely and transfinitely complex minds. (shrink)

Marr’s seminal distinction between computational, algorithmic, and implementational levels of analysis has inspired research in cognitive science for more than 30 years. According to a widely-used paradigm, the modelling of cognitive processes should mainly operate on the computational level and be targeted at the idealised competence, rather than the actual performance of cognisers in a specific domain. In this paper, we explore how this paradigm can be adopted and revised to understand mathematical problem solving. The computational-level approach applies methods (...) from computational complexity theory and focuses on optimal strategies for completing cognitive tasks. However, human cognitive capacities in mathematical problem solving are essentially characterised by processes that are computationally sub-optimal, because they initially add to the computational complexity of the solutions. Yet, these solutions can be optimal for human cognisers given the acquisition and enactment of mathematical practices. Here we present diagrams and the spatial manipulation of symbols as two examples of problem solving strategies that can be computationally sub-optimal but humanly optimal. These aspects need to be taken into account when analysing competence in mathematical problem solving. Empirically informed considerations on enculturation can help identify, explore, and model the cognitive processes involved in problem solving tasks. The enculturation account of mathematical problem solving strongly suggests that computational-level analyses need to be complemented by considerations on the algorithmic and implementational levels. The emerging research strategy can help develop algorithms that model what we call enculturated cognitive optimality in an empirically plausible and ecologically valid way. (shrink)

Early work on the frequency theory of probability made extensive use of the notion of randomness, conceived of as a property possessed by disorderly collections of outcomes. Growing out of this work, a rich mathematical literature on algorithmic randomness and Kolmogorov complexity developed through the twentieth century, but largely lost contact with the philosophical literature on physical probability. The present chapter begins with a clarification of the notions of randomness and probability, conceiving of the former as a property (...) of a sequence of outcomes, and the latter as a property of the process generating those outcomes. A discussion follows of the nature and limits of the relationship between the two notions, with largely negative verdicts on the prospects for any reduction of one to the other, although the existence of an apparently random sequence of outcomes is good evidence for the involvement of a genuinely chancy process. (shrink)

The mind-body problem is analyzed in a physicalist perspective. By combining the concepts of emergence and algorithmic information theory in a thought experiment employing a basic nonlinear process, it is argued that epistemically strongly emergent properties may develop in a physical system. A comparison with the significantly more complex neural network of the brain shows that also consciousness is epistemically emergent in a strong sense. Thus reductionist understanding of consciousness appears not possible; the mind-body problem does not have a (...) reductionist solution. The ontologically emergent character of consciousness is then identified from a combinatorial analysis relating to system limits set by quantum mechanics, implying that consciousness is fundamentally irreducible to low-level phenomena. In the perspective of a modified definition of free will, the character of the physical interactions of the brain's neural system is subsequently studied. As an ontologically open system, it is asserted that its future states are undeterminable in principle. We argue that this leads to freedom of the will. (shrink)

Ludwig Wittgenstein, in the "Remarks on the Foundation of Mathematics", often refers to contradictions as deserving special study. He is said to have predicted that there will be mathematical investigations of calculi containing contradictions and that people will pride themselves on having emancipated themselves from consistency. This paper examines a way of taking this prediction seriously. It starts by demonstrating that the easy way of understanding the role of contradictions in a discourse, namely in terms of pure convention within a (...) specific linguistic community, is naive and therefore to be avoided. A number of steps will then be taken to formulate and justify what will be called a ‘containment-account’ of contradiction. This term refers to a way of understanding how a contradiction in a discourse can be contained without allowing it to infect the entire discourse with inconsistency. The account builds on work done by N. Rescher and involves complex ontologies that are either over-determined or under-determined at some points. These worlds are such that, for some P, they allow us to deny simultaneously both that P and that -P. They likewise allow us to hold both that P and that -P. The ontological status of P and that of -P are considered independent issues, so as to block the inference from P and -P to the conjunction (P & -P). In this way, the task of containment is carried out by the complexity of the ontology determining the possible worlds under consideration. The paper proceeds by countering the objection that such possible worlds are useless fictions. This is carried out by highlighting three significant areas of application, one in philosophy of science, one in philosophy of religion, and one in the area of epistemology. In general, one may say that, in some language-games, a contradiction can be a useful instrument to attest that rationality goes beyond ratiocination, in other words to indicate that there is more to discourse and practice than what can be expressed in precise algorithmic trees. The upshot of the entire argument is that the proposed ‘containment-account’ of contradiction can be an adequate illustration of how Wittgenstein’s prediction is not sterile, but a possible source of inspiration. (shrink)

Many of the benefits and burdens we might experience in our lives — from bank loans to bail terms — are increasingly decided by institutions relying on algorithms. In a sense, this is nothing new: algorithms — instructions whose steps can, in principle, be mechanically executed to solve a decision problem — are at least as old as allocative social institutions themselves. Algorithms, after all, help decision-makers to navigate the complexity and variation of whatever domains they are designed for. (...) In another sense, however, this development is startlingly new: not only are algorithms being deployed in ever more social contexts, they are being mechanically executed not merely in principle, but pervasively in practice. Due to recent advances in computing technology, the benefits and burdens we experience in our lives are now increasingly decided by automata, rather than each other. How are we to morally assess these technologies? In this chapter, I propose a preliminary conceptual schema for identifying and locating the various injustices of automated, algorithmic social decision systems, from a broadly liberal perspective. (shrink)

Review of "Exploring Randomness" (200) and "The Unknowable" (1999) by Gregory Chaitin.

There are (at least) three approaches to quantifying information. The first, algorithmic information or Kolmogorov complexity, takes events as strings and, given a universal Turing machine, quantifies the information content of a string as the length of the shortest program producing it [1]. The second, Shannon information, takes events as belonging to ensembles and quantifies the information resulting from observing the given event in terms of the number of alternate events that have been ruled out [2]. The third, (...) statistical learning theory, has introduced measures of capacity that control (in part) the expected risk of classifiers [3]. These capacities quantify the expectations regarding future data that learning algorithms embed into classifiers. Solomonoff and Hutter have applied algorithmic information to prove remarkable results on universal induction. Shannon information provides the mathematical foundation for communication and coding theory. However, both approaches have shortcomings. Algorithmic information is not computable, severely limiting its practical usefulness. Shannon information refers to ensembles rather than actual events: it makes no sense to compute the Shannon information of a single string – or rather, there are many answers to this question depending on how a related ensemble is constructed. Although there are asymptotic results linking algorithmic and Shannon information, it is unsatisfying that there is such a large gap – a difference in kind – between the two measures. This note describes a new method of quantifying information, effective information, that links algorithmic information to Shannon information, and also links both to capacities arising in statistical learning theory [4, 5]. After introducing the measure, we show that it provides a non-universal analog of Kolmogorov complexity. We then apply it to derive basic capacities in statistical learning theory: empirical VC-entropy and empirical Rademacher complexity. A nice byproduct of our approach is an interpretation of the explanatory power of a learning algorithm in terms of the number of hypotheses it falsifies [6], counted in two different ways for the two capacities. We also discuss how effective information relates to information gain, Shannon and mutual information. (shrink)

This Thesis presents a model of cognitive development inspired by Piaget's "Genetic Epistemology". It is observed that the epigenetic process described by Piaget posess mechanisms and behaviour that characterise complex adaptive systems. A model of bipedal motion based around the "Bucket Brigade" algorithm of Holland is presened to explore this relationship.

Applying the concepts of Kolmogorov-Chaitin complexity and Turing’s uncomputability from the computability and algorithmic information theories to the irreducible and incomputable randomness of quantum mechanics, a novel argument for the existence of God is presented. Concepts of ‘transintelligence’ and ‘transcausality’ are introduced, and from them, it is posited that our universe must be epistemologically and ontologically an open universe. The proposed idea also proffers a new perspective on the nonlocal nature and the infamous wave-function-collapse problem of quantum mechanics.

Products made from animal fur and skin have been a major part of human civilization. However, in modern society, the unsustainable consumption of these products – often considered luxury goods – has many negative environmental impacts. This study explores how people’s perceptions of biodiversity affect their attitudes and behaviors toward consumption. To investigate the information process deeper, we add the moderation of beliefs about biodiversity loss. Following the Bayesian Mindsponge Framework (BMF) analytics, we use mindsponge-based reasoning for constructing conceptual models (...) and employ Bayesian analysis aided by Markov Chain Monte Carlo (MCMC) algorithms on a dataset of 535 Vietnamese urban residents. The results show that people’s preference for using products made from animal skin/fur is negatively associated with perceived consequences of biodiversity loss when they believe biodiversity loss is real and a major problem. In contrast, if urban residents believe biodiversity loss is unreal or not a significant issue, the association between perceived consequences of biodiversity loss and personal preference happens in the opposite direction. The same effects of biodiversity loss perception on people’s possession of skin/fur products was not found, indicating a more complex information process on behaviors compared to attitudes. Nevertheless, in the scenario that people believe biodiversity loss is not a significant issue, the higher the perceived consequences of biodiversity loss are, the greater number of animal-based products they likely own. Our results suggest that policymakers should not neglect the factor of personal belief besides knowledge and awareness in environmental campaigns. (shrink)

Personal AI assistants are now nearly ubiquitous. Every leading smartphone operating system comes with a personal AI assistant that promises to help you with basic cognitive tasks: searching, planning, messaging, scheduling and so on. Usage of such devices is effectively a form of algorithmic outsourcing: getting a smart algorithm to do something on your behalf. Many have expressed concerns about this algorithmic outsourcing. They claim that it is dehumanising, leads to cognitive degeneration, and robs us of our freedom (...) and autonomy. Some people have a more subtle view, arguing that it is problematic in those cases where its use may degrade important interpersonal virtues. In this article, I assess these objections to the use of AI assistants. I will argue that the ethics of their use is complex. There are no quick fixes or knockdown objections to the practice, but there are some legitimate concerns. By carefully analysing and evaluating the objections that have been lodged to date, we can begin to articulate an ethics of personal AI use that navigates those concerns. In the process, we can locate some paradoxes in our thinking about outsourcing and technological dependence, and we can think more clearly about what it means to live a good life in the age of smart machines. (shrink)

Products made from animal fur and skin have been a major part of human civilization. However, in modern society, the unsustainable consumption of these products – often considered luxury goods – has many negative environmental impacts. This study explores how people’s perceptions of biodiversity affect their attitudes and behaviors toward consumption. To investigate the information process deeper, we add the moderation of beliefs about biodiversity loss. Following the Bayesian Mindsponge Framework (BMF) analytics, we use mindsponge-based reasoning for constructing conceptual models (...) and employ Bayesian analysis aided by Markov Chain Monte Carlo (MCMC) algorithms on a dataset of 535 Vietnamese urban residents. The results show that people’s preference for using products made from animal skin/fur is negatively associated with perceived consequences of biodiversity loss when they believe biodiversity loss is real and a major problem. In contrast, if urban residents believe biodiversity loss is unreal or not a significant issue, the association between perceived consequences of biodiversity loss and personal preference happens in the opposite direction. The same effects of biodiversity loss perception on people’s possession of skin/fur products was not found, indicating a more complex information process on behaviors compared to attitudes. Nevertheless, in the scenario that people believe biodiversity loss is not a significant issue, the higher the perceived consequences of biodiversity loss are, the greater number of animal-based products they likely own. Our results suggest that policymakers should not neglect the factor of personal belief besides knowledge and awareness in environmental campaigns. (shrink)