In this paper we analyze methodological and philosophical implications of algorithmic aspects of unconventional computation. At first, we describe how the classical algorithmic universe developed and analyze why it became closed in the conventional approach to computation. Then we explain how new models of algorithms turned the classical closed algorithmic universe into the open world of algorithmic constellations, allowing higher flexibility and expressive power, supporting constructivism and creativity in mathematical modeling. As Goedels undecidability theorems (...) demonstrate, the closed algorithmic universe restricts essential forms of mathematical cognition. In contrast, the open algorithmic universe, and even more the open world of algorithmic constellations, remove such restrictions and enable new, richer understanding of computation. (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)

Algorithmic probability and friends: Proceedings of the Ray Solomonoff 85th memorial conference is a collection of original work and surveys. The Solomonoff 85th memorial conference was held at Monash University's Clayton campus in Melbourne, Australia as a tribute to pioneer, Ray Solomonoff, honouring his various pioneering works - most particularly, his revolutionary insight in the early 1960s that the universality of Universal Turing Machines could be used for universal Bayesian prediction and artificial intelligence. This work continues to increasingly influence (...) and under-pin statistics, econometrics, machine learning, data mining, inductive inference, search algorithms, data compression, theories of intelligence and philosophy of science - and applications of these areas. Ray not only envisioned this as the path to genuine artificial intelligence, but also, still in the 1960s, anticipated stages of progress in machine intelligence which would ultimately lead to machines surpassing human intelligence. Ray warned of the need to anticipate and discuss the potential consequences - and dangers - sooner rather than later. Possibly foremostly, Ray Solomonoff was a fine, happy, frugal and adventurous human being of gentle resolve who managed to fund himself while electing to conduct so much of his paradigm-changing research outside of the university system. The volume contains 35 papers pertaining to the abovementioned topics in tribute to Ray Solomonoff and his legacy. (shrink)

The increase in the size of universities has greatly increased the number of teachers, students, and courses and has also increased the difficulty of scheduling courses. This study used coevolution to improve the genetic algorithm and applied it to solve the course scheduling problem in universities. Finally, simulation experiments were conducted on the traditional and improved genetic algorithms in MATLAB software. The results showed that the improved genetic algorithm converged faster and produced better solutions than the traditional genetic algorithm under (...) the same crossover and mutation probability. As the mutation probability in the algorithm increased, the fitness values of both genetic algorithms gradually decreased, and the computation time increased. With the increase in crossover probability in the algorithm, the fitness value of the two genetic algorithms increased first and then decreased, and the computational time decreased first and then increased. (shrink)

The traditional recognition method of whitewash behavior of accounting statements needs to analyze a large number of special data samples. The learning rate of the algorithm is low, resulting in low recognition accuracy. To solve the aforementioned problems, this article proposes a method to identify the whitewash behavior of university accounting statements based on the FCM clustering algorithm. This article analyzes the motivation of university accounting statement whitewashing behavior, studies the common means of statement whitewashing, and establishes a fuzzy set (...) for the identification of university accounting statement whitewashing behavior. By calculating the fuzzy partition coefficient, the membership matrix of whitewash behavior recognition is established, and the whitewash behavior is classified through the iteration of the FCM algorithm. The comparative experimental results show that the recognition method has good recognition performance, low recognition error rate, and recognition accuracy of 82%. (shrink)

Neutrosophic theory and its applications have been expanding in all directions at an astonishing rate especially after of the introduction the journal entitled “Neutrosophic Sets and Systems”. New theories, techniques, algorithms have been rapidly developed. One of the most striking trends in the neutrosophic theory is the hybridization of neutrosophic set with other potential sets such as rough set, bipolar set, soft set, hesitant fuzzy set, etc. The different hybrid structures such as rough neutrosophic set, single valued neutrosophic rough set, (...) bipolar neutrosophic set, single valued neutrosophic hesitant fuzzy set, etc. are proposed in the literature in a short period of time. Neutrosophic set has been an important tool in the application of various areas such as data mining, decision making, e-learning, engineering, law, medicine, social science, and some more. -/- This book explores the emerging field of Neutrosophic Algebraic Structures, focusing on both their theoretical foundations and practical applications. We apply innovative algorithmic methods to investigate the complex interactions of neutrosophic elements, such as neutrosophic numbers, sets, and functions, within algebraic systems. Our goal is to show how neutrosophic structures challenge and expand traditional algebraic approaches, offering solutions to problems across diverse fields like computer science, engineering, artificial intelligence, and decision-making. (shrink)

In this paper, we will analyze the relationships among three important philosophical theses in Kuhn’s thought: the plurality of worlds thesis, the no universal algorithm thesis, and the niche-construction analogy. We will do that by resorting to a hitherto neglected notion employed by Kuhn: the idea of a feedback loop. We will show that this notion captures an important structural aspect of the epistemic dynamics at work in each of the three theses, therefore allowing us to read them as constituting (...) a virtuous epistemic cycle. Finally, we will apply our unified interpretation of the three theses to scientific practice to sketch a novel neo-Kuhnian picture of theory choice. (shrink)

In order to better improve the teaching quality of university teachers, an effective method should be adopted for evaluation and analysis. This work studied the machine learning algorithms and selected the support vector machine (SVM) algorithm to evaluate teaching quality. First, the principles of selecting evaluation indexes were briefly introduced, and 16 evaluation indexes were selected from different aspects. Then, the SVM algorithm was used for evaluation. A genetic algorithm (GA)-SVM algorithm was designed and experimentally analyzed. It was found that (...) the training time and testing time of the GA-SVM algorithm were 23.21 and 7.25 ms, both of which were shorter than the SVM algorithm. In the evaluation of teaching quality, the evaluation value of the GA-SVM algorithm was closer to the actual value, indicating that the evaluation result was more accurate. The average accuracy of the GA-SVM algorithm was 11.64% higher than that of the SVM algorithm (98.36 vs 86.72%). The experimental results verify that the GA-SVM algorithm can have a good application in evaluating and analyzing teaching quality in universities with its advantages in efficiency and accuracy. (shrink)

William Dembski claims to have established a decision process to determine when highly unlikely events observed in the natural world are due to Intelligent Design. This article argues that, as no implementable randomness test is superior to a universal Martin-Löf test, this test should be used to replace Dembski's decision process. Furthermore, Dembski's decision process is flawed, as natural explanations are eliminated before chance. Dembski also introduces a fourth law of thermodynamics, his “law of conservation of information,” to argue that (...) information cannot increase by natural processes. However, this article, using algorithmic information theory, shows that this law is no more than the second law of thermodynamics. The article concludes that any discussions on the possibilities of design interventions in nature should be articulated in terms of the algorithmic information theory approach to randomness and its robust decision process. (shrink)

Nowadays, innovation and entrepreneurship courses occupy a very important place in universities and colleges and have also become an important teaching position in the process of building a new science. Colleges and universities actively respond to the challenge of “mass entrepreneurship and innovation” and define the goals and specifications of the talent training mechanism based on data fusion algorithms to cultivate as much high-quality applied talent as possible. In view of some shortcomings and problems in the current talent training mechanism (...) in universities and colleges, this paper proposes a data fusion algorithm based on information fusion theory and proof theory. The aim is to verify the feasibility of establishing a talent training mechanism for innovation and entrepreneurship education in universities and colleges. And this paper analyzes and explores the data fusion algorithm and the elements of innovation and entrepreneurial talent training, and forms an operating mechanism for entrepreneurial talent training according to social needs. Among them, the efficiency of the data fusion algorithm used by the GM model plays a significant role in the final result, and the minimum relative error value is 3.2%. Finally, it is concluded that we should focus on establishing a perfect talent training system for college students’ innovation and entrepreneurship education to improve students’ own comprehensive quality and various abilities, and to solve some social problems that are difficult to find employment in essence. (shrink)

How should we incorporate algorithms into humanistic scholarship? The typical approach is to clone what humans have done but faster, extrapolating expert insights to landfills of source material. But creative scholars do not clone tradition; instead, they produce readings that challenge closely held understandings. We theorize and then illustrate how to construct bad robots trained to surprise and provoke. These robots aren’t the most human but rather the most alien—not tame but dangerous. We explore the relationship between the reproduction of (...) tradition and the generation of surprise and then show how formalizing a particular humanistic theory as a Bayesian prior allows us to identify readings that disrupt it through a process of algorithmic abduction. Among the exploding universe of surprising (and mostly ridiculous) possible readings, algorithmic efficiency allows us to select readings that nonetheless garner substantial support from the total archive and so merit interpretation and engagement. It is in such interaction between alien and human readers that meaning is made and understanding disturbed; it is by extending alien readings to novel texts that the scholarly community tests the value of those readings. (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.

In philosophy of mind, zombies are imaginary creatures that are exact physical duplicates of conscious subjects but for whom there is no first-personal experience. Zombies are meant to show that physicalism—the theory that the universe is made up entirely out of physical components—is false. In this paper, I apply the zombie thought experiment to the realm of morality to assess whether moral agency is something independent from sentience. Algorithms, I argue, are a kind of functional moral zombie, such that (...) thinking about the latter can help us better understand and regulate the former. I contend that the main reason why algorithms can be neither autonomous nor accountable is that they lack sentience. Moral zombies and algorithms are incoherent as moral agents because they lack the necessary moral understanding to be morally responsible. To understand what it means to inflict pain on someone, it is necessary to have experiential knowledge of pain. At most, for an algorithm that feels nothing, ‘values’ will be items on a list, possibly prioritised in a certain way according to a number that represents weightiness. But entities that do not feel cannot value, and beings that do not value cannot act for moral reasons. (shrink)

An a priori semimeasure (also known as “algorithmic probability” or “the Solomonoff prior” in the context of inductive inference) is defined as the transformation, by a given universal monotone Turing machine, of the uniform measure on the infinite strings. It is shown in this paper that the class of a priori semimeasures can equivalently be defined as the class of transformations, by all compatible universal monotone Turing machines, of any continuous computable measure in place of the uniform measure. Some (...) consideration is given to possible implications for the association of algorithmic probability with certain foundational principles of statistics. (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)

I will propose the notion that the universe is digital, not as a claim about what the universe is made of but rather about the way it unfolds. Central to the argument will be the concepts of symmetry breaking and algorithmic probability, which will be used as tools to compare the way patterns are distributed in our world to the way patterns are distributed in a simulated digital one. These concepts will provide a framework for a discussion (...) of the informational nature of reality. I will argue that if the universe were analog, then the world would likely be random, making it largely incomprehensible. The digital model has, however, an inherent beauty in its imposition of an upper limit and in the convergence in computational power to a maximal level of sophistication. Even if deterministic, that it is digital doesnít mean that the world is trivial or predictable, but rather that it is built up from operations that at the lowest scale are very simple but that at a higher scale look complex and even random, though only in appearance. (shrink)

The algorithmic theory of laws claims that the laws of nature are the algorithms in the best possible compression of all empirical data. This position assumes that the universe is compressible and that data received from observing it is easily reproducible using a simple set of rules. However, there are three sources of evidence that suggest that the universe as a whole is incompressible. The first comes from the practice of science. The other two come from the (...) nature of the universe itself: the presence of chaotic behavior and the nature of quantum systems also suggests that the universe is incompressible. This paper evaluates these sources and argues that none provides a convincing case to reject the algorithmic theory of laws. (shrink)

This article investigates the hypothesis of creating non-linear audio-visual narratives, through an unanticipated use of traditional print-based games, enriched with videos, via augmented reality (AR) possibilities. A ludic system has been created and presented. Based on a traditional card game, a non-linear cinematic narrative occurs. We attempt to examine the following questions: in which way can we bring together different forms of visual communication, such as graphic design and video? Can the above forms create a complex narrative whole and what (...) kind of rules will be needed for this? How can we enrich traditional forms of gaming with the potentials of AR? Gaming itself demands a set of rules. Can these rules play the role of algorithms in the combined universe that we have designed and created? In which way can the designer on the one hand and the user on the other influence the overall output of the system? What will the user experience be like? The printed card system chosen for this is Tarot and more precisely the Great Arcana, which makes use of the 22 fundamental Tarot figures. (shrink)

: Lately there is more attention paid to technological development in intelligent tutoring systems. This field is becoming an interesting topic to many researchers. In this paper, we are presenting an intelligent tutoring system for teaching DES Information Security Algorithm called DES-Tutor. The DES-Tutor target the students enrolled in cryptography course in the department Information Technology in Al-Azhar University in Gaza. Through DES-Tutor the student will be able to study course material and try the exercises of each lesson. An evaluation (...) of the DES-Tutor was carried out and the results were promising. (shrink)

The problem of data privacy is to verify that confidential information stored in an information system is not provided to unauthorized users and, therefore, personal and other sensitive data remain private. One way to guarantee this is to distort a knowledge base such that it does not reveal sensitive information. In the present paper we will give a universal definition of the problem of knowledge base distortion. It is universal in the sense that is independent of any particular knowledge representation (...) formalism. We will then present a basic and general algorithm for knowledge base distortion to guarantee data privacy. This algorithm provides us with upper bounds for the complexity of the distortion problem. Moreover, we examine heuristics to improve its average performance. (shrink)

Algorithmic systems are increasingly used by state agencies to inform decisions about humans. They produce scores on risks of recidivism in criminal justice, indicate the probability for a job seeker to find a job in the labor market, or calculate whether an applicant should get access to a certain university program. In this contribution, we take an interdisciplinary perspective, provide a bird’s eye view of the different key decisions that are to be taken when state actors decide to use (...) an algorithmic system, and illustrate these decisions with empirical examples from case studies. Building on these insights, we discuss the main pitfalls and promises of the use of algorithmic system by the state and focus on four levels: The most basic question whether an algorithmic system should be used at all, the regulation and governance of the system, issues of algorithm design, and, finally, questions related to the implementation of the system on the ground and the human–machine-interaction that comes with it. Based on our assessment of the advantages and challenges that arise at each of these levels, we propose a set of crucial questions to be asked when such intricate matters are addressed. (shrink)

Suppose that we have a method which estimates the conditional probabilities of some unknown stochastic source and we use it to guess which of the outcomes will happen. We want to make a correct guess as often as it is possible. What estimators are good for this? In this work, we consider estimators given by a familiar notion of universal coding for stationary ergodic measures, while working in the framework of algorithmic randomness, i.e., we are particularly interested in prediction (...) of Martin-Löf random points. We outline the general theory and exhibit some counterexamples. Completing a result of Ryabko from 2009 we also show that universal probability measure in the sense of universal coding induces a universal predictor in the prequential sense. Surprisingly, this implication holds true provided the universal measure does not ascribe too low conditional probabilities to individual symbols. As an example, we show that the Prediction by Partial Matching measure satisfies this requirement with a large reserve. (shrink)

Health, such as the industry, university or city, is immersed in a process of digital transformation generated by the possibility and technological convergence of the Internet of Things (IoT), Big Data and Artificial Intelligence on the one hand and their consequences on the other: hyperconnectivity, datafication and algorithmization. This is a process of transformation towards what has come to be called Smart Health, Health 4.0 or mHealth. However, despite the enormous potential that underlies the digitization of the healthcare sector, this (...) process can have very negative effects both for the sector and its organizations and for the system’s user. One of the most worrying questions at this moment is the aspect and the force that bioethification is taking; that is, the process by which mass data on the opinions, preferences and behaviors of the hyperconnected users of the cyber-physical assistance system are stored, crossed and processed, on the basis of an utilitarian criterion, to determine through mathematical models what is morally valid. The aim of the present study is to analyze the present and future consequences of bioethification in the health field, as well as to propose guidelines to undertake a socially responsible and morally valid digitalization. Key words: bioethification, moral deliberation, discursive ethics, clinical practice, smart health, smart hospital. (shrink)

J. B. Predd S. R. Kulkarni H. V. Poor D. N. Osherson Department of Electrical Engineering Department of Psychology Princeton University Princeton University Princeton, NJ 08544 Princeton, NJ 08544 {jpredd,kulkarni,poor}@princeton.edu osherson@princeton.edu..

Over the years, companies have adopted hiring algorithms because they promise wider job candidate pools, lower recruitment costs and less human bias. Despite these promises, they also bring perils. Using them can inflict unintentional harms on individual human rights. These include the five human rights to work, equality and nondiscrimination, privacy, free expression and free association. Despite the human rights harms of hiring algorithms, the AI ethics literature has predominantly focused on abstract ethical principles. This is problematic for two reasons. (...) First, AI principles have been criticized for being vague and not actionable. Second, the use of vague ethical principles to discuss algorithmic risks does not provide any accountability. This lack of accountability creates an algorithmic accountability gap. Closing this gap is crucial because, without accountability, the use of hiring algorithms can lead to discrimination and unequal access to employment opportunities. This paper makes two contributions to the AI ethics literature. First, it frames the ethical risks of hiring algorithms using international human rights law as a universal standard for determining algorithmic accountability. Second, it evaluates four types of algorithmic impact assessments in terms of how effectively they address the five human rights of job applicants implicated in hiring algorithms. It determines which of the assessments can help companies audit their hiring algorithms and close the algorithmic accountability gap. (shrink)

Concerns over epistemic opacity abound in contemporary debates on Artificial Intelligence (AI). However, it is not always clear to what extent these concerns refer to the same set of problems. We can observe, first, that the terms 'transparency' and 'opacity' are used either in reference to the computational elements of an AI model or to the models to which they pertain. Second, opacity and transparency might either be understood to refer to the properties of AI systems or to the epistemic (...) situation of human agents with respect to these systems. While these diagnoses are independently discussed in the literature, juxtaposing them and exploring possible interrelations will help to get a view of the relevant distinctions between conceptions of opacity and their empirical bearing. In pursuit of this aim, two pertinent conditions affecting computer models in general and contemporary AI in particular are outlined and discussed: opacity as a problem of computational tractability and opacity as a problem of the universality of the computational method. (shrink)

The study of Martin‐Löf randomness on a computable metric space with a computable measure has seen much progress recently. In this paper we study Martin‐Löf randomness on a more general space, that is, a computable topological space with a computable measure. On such a space, Martin‐Löf randomness may not be a natural notion because there is no universal test, and Martin‐Löf randomness and complexity randomness (defined in this paper) do not coincide in general. We show that SCT3 is a sufficient (...) condition for the existence and coincidence, and study how much we can weaken this condition. (shrink)

The multimedia technology and computer technology supported by the development of modern science and technology provide an important platform for the development of college physical education teaching activities. To better play the role of network auxiliary teaching platform in college sports teaching and improve the effectiveness of college sports teaching, the construction method of multimedia auxiliary teaching effect evaluation model based on the random number forest algorithm is proposed. Through the specification of the random forest algorithm and the optimization of (...) the teaching quality evaluation index, the auxiliary teaching level of the college physical education network is analyzed, and the evaluation of the multimedia auxiliary teaching effect of the physical education courses is completed. The experimental results verify the effectiveness of the evaluation model designed in this article, with a user satisfaction of 72%. Teachers and students can use the evaluation model to improve the teaching quality and teaching efficiency, improve the management work, and promote the scientific, standardization, and specialization of physical education teaching management in colleges and universities. (shrink)

Independence of Conditionals (IC) has recently been proposed as a basic rule for causal structure learning. If a Bayesian network represents the causal structure, its Conditional Probability Distributions (CPDs) should be algorithmically independent. In this paper we compare IC with causal faithfulness (FF), stating that only those conditional independences that are implied by the causal Markov condition hold true. The latter is a basic postulate in common approaches to causal structure learning. The common spirit of FF and IC is to (...) reject causal graphs for which the joint distribution looks ‘non-generic’. The difference lies in the notion of genericity: FF sometimes rejects models just because one of the CPDs is simple, for instance if the CPD describes a deterministic relation. IC does not behave in this undesirable way. It only rejects a model when there is a non-generic relation between different CPDs although each CPD looks generic when considered separately. Moreover, it detects relations between CPDs that cannot be captured by conditional independences. IC therefore helps in distinguishing causal graphs that induce the same conditional independences (i.e., they belong to the same Markov equivalence class). The usual justification for FF implicitly assumes a prior that is a probability density on the parameter space. IC can be justified by Solomonoff’s universal prior, assigning non-zero probability to those points in parameter space that have a finite description. In this way, it favours simple CPDs, and therefore respects Occam’s razor. Since Kolmogorov complexity is uncomputable, IC is not directly applicable in practice. We argue that it is nevertheless helpful, since it has already served as inspiration and justification for novel causal inference algorithms. (shrink)

The representation of public and private partnership in higher education management as a mechanism of forming the added value of human capital is specified. An algorithm of economic effect calculation of universities and entrepreneurs cooperation at training undergraduates is given. As shown in the article the economic effect is achieved by developing wide cooperation with entrepreneurs in public and private partnership and widening the undergraduates’ flow at conducting practices and independent work in individual education.

The Fairness, Accountability, and Transparency (FAccT) literature tends to focus on bias as a problem that requires ex post solutions (e.g. fairness metrics), rather than addressing the underlying social and technical conditions that (re)produce it. In this article, we propose a complementary strategy that uses genealogy as a constructive, epistemic critique to explain algorithmic bias in terms of the conditions that enable it. We focus on XAI feature attributions (Shapley values) and counterfactual approaches as potential tools to gauge these (...) conditions and offer two main contributions. One is constructive: we develop a theoretical framework to classify these approaches according to their relevance for bias as evidence of social disparities. We draw on Pearl’s ladder of causation (Causality: models, reasoning, and inference. Cambridge University Press, Cambridge, 2000, Causality, 2nd edn. Cambridge University Press, Cambridge, 2009. doi:10.1017/CBO9780511803161) to order these XAI approaches concerning their ability to answer fairness-relevant questions and identify fairness-relevant solutions. The other contribution is critical: we evaluate these approaches in terms of their assumptions about the role of protected characteristics in discriminatory outcomes. We achieve this by building on Kohler-Hausmann’s (Northwest Univ Law Rev 113(5):1163–1227, 2019) constructivist theory of discrimination. We derive three recommendations for XAI practitioners to develop and AI policymakers to regulate tools that address algorithmic bias in its conditions and hence mitigate its future occurrence. (shrink)

Cities, such as industry or the universities, are immersed in a process of digital transformation generated by the possibility and technological convergence of the Internet of Things, Big Data and Artificial Intelligence and its consequences: hyperconnectivity, datafication and algorithmization. A process of transformation towards what has come to be called as Smart Cities. The aim of this paper is to show the impacts and consequences of digital connectivity, algorithmization and the datafication of urban digital society to outline possible ways of (...) resolving the underlying moral conflicts. (shrink)

ACMES is a multidisciplinary conference series that focuses on epistemological and mathematical issues relating to computation in modern science. This volume includes a selection of papers presented at the 2015 and 2016 conferences held at Western University that provide an interdisciplinary outlook on modern applied mathematics that draws from theory and practice, and situates it in proper context. These papers come from leading mathematicians, computational scientists, and philosophers of science, and cover a broad collection of mathematical and philosophical topics, including (...) numerical analysis and its underlying philosophy, computer algebra, reliability and uncertainty quantification, computation and complexity theory, combinatorics, error analysis, perturbation theory, experimental mathematics, scientific epistemology, and foundations of mathematics. By bringing together contributions from researchers who approach the mathematical sciences from different perspectives, the volume will further readers' understanding of the multifaceted role of mathematics in modern science, informed by the state of the art in mathematics, scientific computing, and current modeling techniques. (shrink)

In this thesis I investigate the theoretical possibility of a universal method of prediction. A prediction method is universal if it is always able to learn from data: if it is always able to extrapolate given data about past observations to maximally successful predictions about future observations. The context of this investigation is the broader philosophical question into the possibility of a formal specification of inductive or scientific reasoning, a question that also relates to modern-day speculation about a fully automatized (...) data-driven science. I investigate, in particular, a proposed definition of a universal prediction method that goes back to Solomonoff and Levin. This definition marks the birth of the theory of Kolmogorov complexity, and has a direct line to the information-theoretic approach in modern machine learning. Solomonoff's work was inspired by Carnap's program of inductive logic, and the more precise definition due to Levin can be seen as an explicit attempt to escape the diagonal argument that Putnam famously launched against the feasibility of Carnap's program. The Solomonoff-Levin definition essentially aims at a mixture of all possible prediction algorithms. An alternative interpretation is that the definition formalizes the idea that learning from data is equivalent to compressing data. In this guise, the definition is often presented as an implementation and even as a justification of Occam's razor, the principle that we should look for simple explanations. The conclusions of my investigation are negative. I show that the Solomonoff-Levin definition fails to unite two necessary conditions to count as a universal prediction method, as turns out be entailed by Putnam's original argument after all; and I argue that this indeed shows that no definition can. Moreover, I show that the suggested justification of Occam's razor does not work, and I argue that the relevant notion of simplicity as compressibility is already problematic itself. (shrink)

ABSTRACT: How can we think about a universal ethics that could be adopted by any intelligent being, including the rising population of cyborgs, intelligent machines, intelligent algorithms or even potential extraterrestrial life? We generally give value to complex structures, to objects resulting from a long work, to systems with many elements and with many links finely adjusted. These include living beings, books, works of art or scientific theories. Intuitively, we want to keep, multiply, and share such structures, as well as (...) prevent their destruction. Such objects have value not because more information would simply mean more value. Instead, they have value because they require a long computational history, numerous interactions for their construction that we can assimilate to a computation, and they display what we call organized complexity. To propose the foundations of a universal ethics based on the intrinsic value of organized complexity, we first discuss conceptions of complexity, and argue that Charles Bennett’s logical depth is certainly a first approximation of what we are looking for. We then put forward three fundamental imperatives: to preserve, augment and recursively promote organized complexity. We show a broad range of applications with human, non-human and non-living examples. Finally, we discuss some specific issues of our framework such as the distribution of complexity, of managing copies and erasures, and how our universal ethics tackles classical ethical issues. In sum, we propose a clear, homogenous and consistent ethical foundation that can integrate many universal ethics desiderata. (shrink)

This note presents a point of view upon the notions of programsubstitution which are the tools for proving properties of programs of algorithmic logics [5], [3] being sufficiently strong and universal to comprise almost all previously introduced theories of programming, and the so-called extended algorithmic logic [1], [2] and algorithmic logic with nondeterministic programs [4]. It appears that the mentioned substitution rule allows us to examine more deeply algorithmic properties of terms, formulas and programs. Besides the (...) problem of Post-completeness and structural completeness of algorithmic logics strengthened additionally by the rule of substitution is raised. (shrink)

The concept of polarity is pervasive in natural language. It relates syntax, semantics and pragmatics narrowly, Semantics: an international handbook of natural language meaning, De Gruyter Mouton, Berlin, 2011; Israel in The grammar of polarity: pragmatics, sensitivity, and the logic of scales, Cambridge studies in linguistics, Cambridge University Press, Cambridge, 2014), it refers to items of many syntactic categories such as nouns, verbs and adverbs. Neutral polarity items appear in affirmative and negative sentences, negative polarity items cannot appear in affirmative (...) sentences, and positive polarity items cannot appear in negative sentences. A way of reasoning in Natural Language is through Natural Logic. This logic is based on the concept of polarity in order to make the meaning of a sentence weaker o stronger without changing its truth value. There exist many proposals to compute polarity in the Natural Logic context, the most widely known are the ones by: van Benthem, Sánchez-Valencia, Dowty, and van Eijck, 6th international Tbilisi symposium on logic, language, and computation, Batumi, Georgia, Springer, 2007). If Natural Logic is going to be used, as an inferential mechanism between text fragments, in Natural Language Processing applications such as text summarization, question answering, and information extraction, it is a priority to know what the existing relationship among the aforementioned algorithms is; for example, to implement the most general. We show in this paper the equivalence among the analyzed algorithms, filling a gap in Natural Logic research, particularly in computing polarity, and the soundness of their algorithms. (shrink)

This paper is going to focus on the problem of emotions in technology, in particular in reference to the case of algorithms developed to track early rehospitalizations. In this paper I am going to discuss how phenomenology can support the integration of emotions in technology and how this integration can improve our chances for that “decent survival” that the founder of bioethics, Potter, has envisioned as the main goal of this discipline (Natl Cancer Inst Monogr 13:111–116, 1964; Bioethics, bridge to (...) the future. Prentice Hall, Inc., Englewood Cliffs, p 24, 1971; Ann N Y Acad Sci 196(Art. 4):200–205, 1972; Cancer Res 35:2297–2306, 1975; Global bioethics. Michigan University, 1988). I believe that descriptive phenomenology can be a useful philosophical and psychological approach to improve the moral and emotional intelligence behind machine learning programming (Dreyfus, What computers can’t do: the limits of artificial intelligence. HarperCollins, 1978; The Socratic and platonic basis of cognitivism. AI & Society, Springer, Berlin, 1988) and overcome the risk of ethical opacity implied in programming (Casacuberta, Ethical and technical aspects of emotions to create empathy in medical machines. In Van Rysewik SP, Pontier M (eds) Machine in medical ethics. Springer, New York/Dordrecht, 2015). On the one hand, the ethical aspect of phenomenology would allow us to grasp the predicative and pre-predicative facie of the lived-experiences and their emotional contents. On the other hand, the phenomenological method of research applied in psychology would offer a way to transcribe and interpret data in a responsible and contextualized way. (shrink)

We survey concepts at the frontier of research connecting artificial, animal, and human cognition to computation and information processing—from the Turing test to Searle’s Chinese room argument, from integrated information theory to computational and algorithmic complexity. We start by arguing that passing the Turing test is a trivial computational problem and that its pragmatic difficulty sheds light on the computational nature of the human mind more than it does on the challenge of artificial intelligence. We then review our proposed (...) algorithmic information-theoretic measures for quantifying and characterizing cognition in various forms. These are capable of accounting for known biases in human behavior, thus vindicating a computational algorithmic view of cognition as first suggested by Turing, but this time rooted in the concept of algorithmic probability, which in turn is based on computational universality while being independent of computational model, and which has the virtue of being predictive and testable as a model theory of cognitive behavior. (shrink)

In previous works we have established that the spacetime probabilistic organization of the quantum theory is determined by the spacetime characteristics of the operations by which the observer produces the objects to be studied (“states” of microsystems) and obtains qualifications of these. Guided by this first conclusion, we have then built a “general syntax of relativized conceptualization” where any description is explicitly and systematically referred to the two basic epistemic operations by which the conceptor introduces the object to be qualified (...) and then obtains qualifications of it. Inside this syntax there emerges a general typology of the relativized descriptions. Here we show that with respect to this typology the type of the predictive quantum mechanical descriptions acquires a precise definition. It appears that the quantum mechanical formalism has captured and has expressed directly in a mathematical language the most complex form in which can occur a first descriptional phase that lies universally at the bottom of any chain of conceptualization. The main features of the Hilbert-Dirac algorithms are decoded in terms of the general syntax of relativized conceptualization. This renders explicit the semantical contents of the quantum mechanical representations relating each one of these to its mathematical quantum mechanical expression. Basic insufficiencies are thus identified and, correlatively, false problems as well as answers to these, or guides toward answers. Globally the results obtained provide a basis for future attempts at a general mathematical representation of the processes of conceptualization. “Il pourrait, en effet, être dangereux pour l'avenir de la Physique qu'elle se contente trop facilement de purs formalismes, d'images floues et d'explications toutes verbales s'exprimant par des mots à signification imprécise”—Louis de Broglie,Certitudes et Incertitudes de la Science (Albin Michel, Paris, 1965). (shrink)

The paper studies the logic TL(NBox+-wC) – logic of discrete linear time with current time point clusters. Its language uses modalities Diamond+ (possible in future) and Diamond- (possible in past) and special temporal operations, – Box+w (weakly necessary in future) and Box-w (weakly necessary in past). We proceed by developing an algorithm recognizing theorems of TL(NBox+-wC), so we prove that TL(NBox+-wC) is decidable. The algorithm is based on reduction of formulas to inference rules and converting the rules in special reduced (...) normal form, and, then, on checking validity of such rules in models of singleexponential size in the rules. Also we consider the admissibility problem for TL(NBox+-wC) and show how to reduce the problem for admissibility to the decidability of TL(NBox+-wC) itself using definable universal modalities. (shrink)

A wide-ranging history of the intellectual developments that produced the modern idea of the algorithm. Bringing together the histories of mathematics, computer science, and linguistic thought, Language and the Rise of the Algorithm reveals how recent developments in artificial intelligence are reopening an issue that troubled mathematicians long before the computer age. How do you draw the line between computational rules and the complexities of making systems comprehensible to people? Here Jeffrey M. Binder offers a compelling tour of four visions (...) of universal computation that addressed this issue in very different ways: G. W. Leibniz's calculus ratiocinator; a universal algebra scheme Nicolas de Condorcet designed during the French Revolution; George Boole's nineteenth-century logic system; and the early programming language ALGOL, whose name is short for algorithmic language. These episodes show that symbolic computation has repeatedly become entangled in debates about the nature of communication. To what extent can meaning be controlled by individuals, like the values of a and b in algebra, and to what extent is meaning inevitably social? By attending to this long-neglected question, we come to see that the modern idea of the algorithm is implicated in a long history of attempts to maintain a disciplinary boundary separating technical knowledge from the languages people speak day to day. Machine learning, in its increasing dependence on words, now places this boundary in jeopardy, making its stakes all the more urgent to understand. The idea of the algorithm is a levee holding back the social complexity of language, and it is about to break. This book is about the flood that inspired its construction. (shrink)

A central concern of generative grammar is the relationship between hierarchy and word order, traditionally understood as two dimensions of a single syntactic representation. A related concern is directionality in the grammar. Traditional approaches posit process-neutral grammars, embodying knowledge of language, put to use with infinite facility both for production and comprehension. This has crystallized in the view of Merge as the central property of syntax, perhaps its only novel feature. A growing number of approaches explore grammars with different directionalities, (...) often with more direct connections to performance mechanisms. This paper describes a novel model of universal grammar as a one-directional, universal parser. Mismatch between word order and interpretation order is pervasive in comprehension; in the present model, word order is language-particular and interpretation order (i.e., hierarchy) is universal. These orders are not two dimensions of a unified abstract object (e.g., precedence and dominance in a single tree); rather, both are temporal sequences, and UG is an invariant real-time procedure (based on Knuth's stack-sorting algorithm) transforming word order into hierarchical order. This shift in perspective has several desirable consequences. It collapses linearization, displacement, and composition into a single performance process. The architecture provides a novel source of brackets (labeled unambiguously and without search), which are understood not as part-whole constituency relations, but as storage and retrieval routines in parsing. It also explains why neutral word order within single syntactic cycles avoids 213-like permutations. The model identifies cycles as extended projections of lexical heads, grounding the notion of phase. This is achieved with a universal processor, dispensing with parameters. The empirical focus is word order in noun phrases. This domain provides some of the clearest evidence for 213-avoidance as a cross-linguistic word order generalization. Importantly, recursive phrase structure “bottoms out” in noun phrases, which are typically a single cycle (though further cycles may be embedded, e.g., relative clauses). By contrast, a simple transitive clause plausibly involves two cycles (vP and CP), embedding further nominal cycles. In the present theory, recursion is fundamentally distinct from structure-building within a single cycle, and different word order restrictions might emerge in larger domains like clauses. (shrink)

A Computable Universe is a collection of papers discussing computation in nature and the nature of computation, a compilation of the views of the pioneers in the contemporary area of intellectual inquiry focused on computational and informational theories of the world. This volume is the definitive source of informational/computational views of the world, and of cutting-edge models of the universe, both digital and quantum, discussed from a philosophical perspective as well as in the greatest technical detail. The book (...) discusses the foundations of computation in relation to nature. It focuses on two main questions: What is computation? How does nature compute? The contributors are world-renowned experts who have helped shape a cutting-edge computational understanding of the universe. They discuss computation in the world from a variety of perspectives, ranging from foundational concepts to pragmatic models to ontological conceptions and their philosophical implications. The volume provides a state-of-the-art collection of technical papers and non-technical essays representing a field that takes information and computation to be key to understanding and explaining the basic structure underpinning physical reality. It also includes a new edition of Konrad Zuse's "Calculating Space", and a panel discussion transcription on the topic, featuring worldwide experts (including a Nobel prize) in quantum mechanics, physics, cognition, computation and algorithmic complexity.A Computable Universe is a collection of papers discussing computation in nature and the nature of computation, a compilation of the views of the pioneers in the contemporary area of intellectual inquiry focused on computational and informational theories of the world. This volume is the definitive source of informational/computational views of the world, and of cutting-edge models of the universe, both digital and quantum, discussed from a philosophical perspective as well as in the greatest technical detail. The book discusses the foundations of computation in relation to nature. It focuses on two main questions: What is computation? How does nature compute? The contributors are world-renowned experts who have helped shape a cutting-edge computational understanding of the universe. They discuss computation in the world from a variety of perspectives, ranging from foundational concepts to pragmatic models to ontological conceptions and their philosophical implications. The volume provides a state-of-the-art collection of technical papers and non-technical essays representing a field that takes information and computation to be key to understanding and explaining the basic structure underpinning physical reality. It also includes a new edition of Konrad Zuse's "Calculating Space", and a panel discussion transcription on the topic, featuring worldwide experts (including a Nobel prize) in quantum mechanics, physics, cognition, computation and algorithmic complexity. (shrink)