In [3], two different effective versions of Borel embedding are defined. The first, called computable embedding, is based on uniform enumeration reducibility, while the second, called Turing computable embedding, is based on uniform Turing reducibility. While [3] focused mainly on computable embeddings, the present paper considers Turing computable embeddings. Although the two notions are not equivalent, we can show that they behave alike on the mathematically interesting classes chosen for investigation in [3]. We (...) give a “Pull-back Theorem”, saying that if Φ is a Turing computable embedding of K into K’, then for any computable infinitary sentence φ in the language of K’, we can find a computable infinitary sentence φ* in the language of K such that for all. (shrink)

Here we prove that if T and T′ are strongly minimal theories, where T′ satisfies a certain property related to triviality and T does not, and T′ is model complete, then there is no computable embedding of Mod(T) into Mod(T′). Using this, we answer a question from [4], showing that there is no computable embedding of VS into ZS, where VS is the class of infinite vector spaces over Q, and ZS is the class of models (...) of Th(Z, S). Similarly, we show that there is no computable embedding of ACF into ZS, where ACF is the class of algebraically closed fields of characteristic 0. (shrink)

We study what the existence of a classical embedding between computable structures implies about the existence of computable embeddings. In particular, we consider the effect of fixing and varying the computable presentations of the computable structures.

We solve a longstanding question of Rosenstein, and make progress toward solving a longstanding open problem in the area of computable linear orderings by showing that every computable ƞ-like linear ordering without an infinite strongly ƞ-like interval has a computable copy without nontrivial computable self-embedding. The precise characterization of those computable linear orderings which have computable copies without nontrivial computable self-embedding remains open.

We study the computational content of various theorems with reverse mathematical strength around Arithmetical Transfinite Recursion (ATR_0) from the point of view of computability-theoretic reducibilities, in particular Weihrauch reducibility. Our main result states that it is equally hard to construct an embedding between two given well-orderings, as it is to construct a Turing jump hierarchy on a given well-ordering. This answers a question of Marcone. We obtain a similar result for Fraïssé's conjecture restricted to well-orderings.

The Local Computation Framework has been used to improve the efficiency of computation in various uncertainty formalisms. This paper shows how the framework can be used for the computation of logical deduction in two different ways; the first way involves embedding model structures in the framework; the second, and more direct, way involves embedding sets of formulae. This work can be applied to many of the logics developed for different kinds of reasoning, including predicate calculus, modal logics, possibilistic (...) logics, probabilistic logics and non-monotonic logics. (shrink)

The Connes Embedding Problem asks whether every separable II1 factor embeds into an ultrapower of the hyperfinite II1 factor. We show that the CEP is equivalent to the statement that every type II1 tracial von Neumann algebra has a computable universal theory.

We divide the class of infinite computable trees into three types. For the first and second types, 0' computes a nontrivial self-embedding while for the third type 0'' computes a nontrivial self-embedding. These results are optimal and we obtain partial results concerning the complexity of nontrivial self-embeddings of infinite computable trees considered up to isomorphism. We show that every infinite computable tree must have either an infinite computable chain or an infinite Π01 antichain. This (...) result is optimal and has connections to the program of reverse mathematics. (shrink)

We show that the lattice L 20 is not embeddable into the lattice of ideals of computably enumerable Turing degrees (J). We define a structure called a pseudolattice that generalizes the notion of a lattice, and show that there is a Π 2 necessary and sufficient condition for embedding a finite pseudolattice into J.

Embedding ethics modules within computer science courses has become a popular response to the growing recognition that CS programs need to better equip their students to navigate the ethical dimensions of computing technologies like AI, machine learning, and big data analytics. However, the popularity of this approach has outpaced the evidence of its positive outcomes. To help close that gap, this empirical study reports positive results from Northeastern’s program that embeds values analysis modules into CS courses. The resulting data (...) suggest that such modules have a positive effect on students’ moral attitudes and that students leave the modules believing they are more prepared to navigate the ethical dimensions they’ll likely face in their eventual careers. Importantly, these gains were accomplished at an institution without a philosophy doctoral program, suggesting this strategy can be effectively employed by a wider range of institutions than many have thought. (shrink)

We prove two embedding and extension theorems in the context of the constructive theory of metric spaces. The first states that Cantor space embeds in any inhabited complete separable metric space (CSM) without isolated points, X, in such a way that every sequentially continuous function from Cantor space to ℤ extends to a sequentially continuous function from X to ℝ. The second asserts an analogous property for Baire space relative to any inhabited locally non‐compact CSM. Both results rely on (...) having careful constructive formulations of the concepts involved.As a first application, we derive new relationships between “continuity principles” asserting that all functions between specified metric spaces are pointwise continuous. In particular, we give conditions that imply the failure of the continuity principle “all functions from X to ℝ are continuous”, when X is an inhabited CSM without isolated points, and when X is an inhabited locally non‐compact CSM. One situation in which the latter case applies is in models based on “domain realizability”, in which the failure of the continuity principle for any inhabited locally non‐compact CSM, X, generalizes a result previously obtained by Escardó and Streicher in the special case X = C[0, 1].As a second application, we show that, when the notion of inhabited complete separable metric space without isolated points is interpreted in a recursion‐theoretic setting, then, for any such space X, there exists a Banach‐Mazur computable function from X to the computable real numbers that is not Markov computable. This generalizes a result obtained by Hertling in the special case that X is the space of computable real numbers. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim). (shrink)

We prove two embedding and extension theorems in the context of the constructive theory of metric spaces. The first states that Cantor space embeds in any inhabited complete separable metric space without isolated points, X, in such a way that every sequentially continuous function from Cantor space to ℤ extends to a sequentially continuous function from X to ℝ. The second asserts an analogous property for Baire space relative to any inhabited locally non-compact CSM. Both results rely on having (...) careful constructive formulations of the concepts involved.As a first application, we derive new relationships between “continuity principles” asserting that all functions between specified metric spaces are pointwise continuous. In particular, we give conditions that imply the failure of the continuity principle “all functions from X to ℝ are continuous”, when X is an inhabited CSM without isolated points, and when X is an inhabited locally non-compact CSM. One situation in which the latter case applies is in models based on “domain realizability”, in which the failure of the continuity principle for any inhabited locally non-compact CSM, X, generalizes a result previously obtained by Escardó and Streicher in the special case X = C[0, 1].As a second application, we show that, when the notion of inhabited complete separable metric space without isolated points is interpreted in a recursion-theoretic setting, then, for any such space X, there exists a Banach-Mazur computable function from X to the computable real numbers that is not Markov computable. This generalizes a result obtained by Hertling in the special case that X is the space of computable real numbers. (shrink)

The Dushnik–Miller Theorem states that every infinite countable linear ordering has a nontrivial self-embedding. We examine computability-theoretical aspects of this classical theorem.

The purpose of this paper is to show that there exist star-finite tree-structured sets in which the computations of parallel programs can be faithfully embedded, and that the theory of star-finite sets and relations therefore provides a new tool for the analysis of non-deterministic computations.

Organizations such as the EU High-Level Expert Group on AI and the IEEE have recently formulated ethical principles and (moral) values that should be adhered to in the design and deployment of artificial intelligence (AI). These include respect for autonomy, non-maleficence, fairness, transparency, explainability, and accountability. But how can we ensure and verify that an AI system actually respects these values? To help answer this question, I propose an account for determining when an AI system can be said to embody (...) certain values. This account understands embodied values as the result of design activities intended to embed those values in such systems. AI systems are here understood as a special kind of sociotechnical system that, like traditional sociotechnical systems, are composed of technical artifacts, human agents, and institutions but—in addition—contain artificial agents and certain technical norms that regulate interactions between artificial agents and other elements of the system. The specific challenges and opportunities of embedding values in AI systems are discussed, and some lessons for better embedding values in AI systems are drawn. (shrink)

The computer distance teaching system teaches through the network, and there is no entrance threshold. Any student who is willing to study can log in to the network computer distance teaching system for study at any free time. Neural network has a strong self-learning ability and is an important part of artificial intelligence research. Based on this study, a neural network-embedded architecture based on shared memory and bus structure is proposed. By looking for an alternative method of exp function to (...) improve the speed of radial basis function algorithm, and then by analyzing the judgment conditions in the main loop during the algorithm process, these judgment conditions are modified conditionally to reduce the calculation scale, which can double the speed of the algorithm. Finally, this article verifies the function, performance, and interface of the computer distance education system. (shrink)

In this study, we use temporally aligned word embeddings and a large diachronic corpus of English to quantify language change in a data-driven, scalable way, which is grounded in language use. We show a unique and reliable relation between measures of language change and age of acquisition (AoA) while controlling for frequency, contextual diversity, concreteness, length, dominant part of speech, orthographic neighborhood density, and diachronic frequency variation. We analyze measures of language change tackling both the change in lexical representations and (...) the change in the relation between lexical representations and the words with the most similar usage patterns, showing that they capture different aspects of language change. Our results show a unique relation between language change and AoA, which is stronger when considering neighborhood-level measures of language change: Words with more coherent diachronic usage patterns tend to be acquired earlier. The results support theories positing a link between ontogenetic and ethnogenetic processes in language. (shrink)

We define a class of finite partial lattices which admit a notion of rank compatible with embedding constructions, and present a necessary and sufficient condition for the embeddability of a finite ranked partial lattice into the computably enumerable degrees.

Computational models of infant word‐finding typically operate over transcriptions of infant‐directed speech corpora. It is now possible to test models of word segmentation on speech materials, rather than transcriptions of speech. We propose that such modeling efforts be conducted over the speech of the experimental stimuli used in studies measuring infants' capacity for learning from spoken sentences. Correspondence with infant outcomes in such experiments is an appropriate benchmark for models of infants. We demonstrate such an analysis by applying the DP‐Parser (...) model of Algayres and colleagues to auditory stimuli used in infant psycholinguistic experiments by Pelucchi and colleagues. The DP‐Parser model takes speech as input, and creates multiple overlapping embeddings from each utterance. Prospective words are identified as clusters of similar embedded segments. This allows segmentation of each utterance into possible words, using a dynamic programming method that maximizes the frequency of constituent segments. We show that DP‐Parse mimics American English learners' performance in extracting words from Italian sentences, favoring the segmentation of words with high syllabic transitional probability. This kind of computational analysis over actual stimuli from infant experiments may be helpful in tuning future models to match human performance. (shrink)

Every second-countable regular topological space X is metrizable. For a given “computable” topological space satisfying an axiom of computable regularity M. Schröder [10] has constructed a computable metric. In this article we study whether this metric space can be considered computationally as a subspace of some computable metric space [15]. While Schröder's construction is “pointless”, i. e., only sets of a countable base but no concrete points are known, for a computable metric space a concrete (...) dense set of computable points is needed. But there may be no computable points in X. By converging sequences of basis sets instead of Cauchy sequences of points we construct a metric completion of a space together with a canonical representation equation image, equation image. We show that there is a computable embedding of in with computable inverse. Finally, we construct a notation of a dense set of points in with computable mutual distances and prove that the Cauchy representation of the resulting computable metric space is equivalent to equation image. Therefore, every computably regular space has a computable homeomorphic embedding in a computable metric space, which topologically is its completion. By the way we prove a computable Urysohn lemma. (shrink)

We present a necessary and sufficient condition for the embeddability of a principally decomposable finite lattice into the computably enumerable degrees. This improves a previous result which required that, in addition, the lattice be ranked. The same condition is also necessary and sufficient for a finite lattice to be embeddable below every non-zero computably enumerable degree.

The particular design of any technology may have profound social implications. Computing technologies are deeply intermeshed with the activities of daily life, playing an ever more central role in how we work, learn, communicate, socialize, and participate in government. Despite the many ways they have improved life, they cannot be regarded as unambiguously beneficial or even value-neutral. Recent experience shows they can lead to unintended but harmful consequences. Some technologies are thought to threaten democracy through the spread of propaganda on (...) online social networks, or to threaten privacy through the aggregation of datasets that include increasingly personal information, or to threaten justice when machine learning is used in such high-stakes, decision-making contexts as loan application reviews, employment procedures, or parole hearings. It is insufficient to ethically assess technology after it has produced negative social impacts, as has happened, for example, with facial recognition software that discriminates against people of color and with self-driving cars that are unable to cope with pedestrians who jay-walk. Developers of new technologies should aim to identify potential harmful consequences early in the design process and take steps to eliminate or mitigate them. This task is not easy. Designers will often have to negotiate among competing values—for instance, between efficiency and accessibility for a diverse user population, or between maximizing benefits and avoiding harm. There is no simple recipe for identifying and solving ethical problems. -/- Computer science education can help meet these challenges by making ethical reasoning about computing technologies a central element in the curriculum. Students can learn to think not only about what technology they could create, but also whether they should create that technology. Learning to reason this way requires courses unlike those currently standard in computer science curricula. A range of university courses on topics in areas of computing, ethics, society and public policy are emerging to meet this need. Some cover computer science broadly, while others focus on specific problems like privacy and security; typically, these classes exist as stand-alone courses in the computer science curriculum. Others have integrated ethics into the teaching of introductory courses on programming, artificial intelligence, and human-computer interaction. (shrink)

We present a necessary and sufficient condition for the embeddability of a finite principally decomposable lattice into the computably enumerable degrees preserving greatest element.

We focus on a particular class of computably enumerable degrees, the array noncomputable degrees defined by Downey, Jockusch, and Stob, to answer questions related to lattice embeddings and definability in the partial ordering of c. e. degrees under Turing reducibility. We demonstrate that the latticeM5 cannot be embedded into the c. e. degrees below every array noncomputable degree, or even below every nonlow array noncomputable degree. As Downey and Shore have proved that M5 can be embedded below every nonlow2 degree, (...) our result is the best possible in terms of array noncomputable degrees and jump classes. Further, this result shows that the array noncomputable degrees are definably different from the nonlow2 degrees. We note also that there are embeddings of M5 in which all five degrees are array noncomputable, and in which the bottom degree is the computable degree 0 but the other four are array noncomputable. (shrink)

We show that any partial order with a Σ3 enumeration can be effectively embedded into any partial order obtained by imposing a strong reducibility such as ≤tt on the c. e. sets. As a consequence, we obtain that the partial orders that result from imposing a strong reducibility on the sets in a level of the Ershov hiearchy below ω + 1 are co-embeddable.

This paper pertains to research works aiming at linking ethics and automated reasoning in autonomous machines. It focuses on a formal approach that is intended to be the basis of an artificial agent’s reasoning that could be considered by a human observer as an ethical reasoning. The approach includes some formal tools to describe a situation and models of ethical principles that are designed to automatically compute a judgement on possible decisions that can be made in a given situation and (...) explain why a given decision is ethically acceptable or not. It is illustrated on three ethical frameworks—utilitarian ethics, deontological ethics and the Doctrine of Double effect whose formal models are tested on ethical dilemmas so as to examine how they respond to those dilemmas and to highlight the issues at stake when a formal approach to ethical concepts is considered. The whole approach is instantiated on the drone dilemma, a thought experiment we have designed; this allows the discrepancies that exist between the judgements of the various ethical frameworks to be shown. The final discussion allows us to highlight the different sources of subjectivity of the approach, despite the fact that concepts are expressed in a more rigorous way than in natural language: indeed, the formal approach enables subjectivity to be identified and located more precisely. (shrink)

Partial combinatory algebras (pcas) are algebraic structures that serve as generalized models of computation. In this article, we study embeddings of pcas. In particular, we systematize the embeddings between relativizations of Kleene’s models, of van Oosten’s sequential computation model, and of Scott’s graph model, showing that an embedding between two relativized models exists if and only if there exists a particular reduction between the oracles. We obtain a similar result for the lambda calculus, showing in particular that it cannot (...) be embedded in Kleene’s first model. (shrink)

This essay provides a critique of mainstream computer ethics and argues for the importance of a complementary approach called disclosive computer ethics, which is concerned with the moral deciphering of embedded values and norms in computer systems, applications and practices. Also, four key values are proposed as starting points for disclosive studies in computer ethics: justice, autonomy, democracy and privacy. Finally, it is argued that research in disclosive computer ethics should be multi-level and interdisciplinary, distinguishing between a disclosure level, a (...) theoretical level, and an an application level. (shrink)

This article explores some of the roles of computer simulation in measurement. A model-based view of measurement is adopted and three types of measurement—direct, derived, and complex—are distinguished. It is argued that while computer simulations on their own are not measurement processes, in principle they can be embedded in direct, derived, and complex measurement practices in such a way that simulation results constitute measurement outcomes. Atmospheric data assimilation is then considered as a case study. This practice, which involves combining information (...) from conventional observations and simulation-based forecasts, is characterized as a complex measuring practice that is still under development. The case study reveals challenges that are likely to resurface in other measuring practices that embed computer simulation. It is also noted that some practices that embed simulation are difficult to classify; they suggest a fuzzy boundary between measurement and non-measurement. 1 Introduction2 A Contemporary View of Measurement3 Three Types of Measurement4 Can Computer Simulations Measure Real-World Target Systems?5 Case Study: Atmospheric Data Assimilation5.1 Why data assimilation?5.2 A complex measuring practice under development5.3 Epistemic iteration6 The Boundaries of Measurement7 Epistemology, Not Terminology. (shrink)

Downey and Lempp 1215–1240) have shown that the contiguous computably enumerable degrees, i.e. the c.e. Turing degrees containing only one c.e. weak truth-table degree, can be characterized by a local distributivity property. Here we extend their result by showing that a c.e. degree a is noncontiguous if and only if there is an embedding of the nonmodular 5-element lattice N5 into the c.e. degrees which maps the top to the degree a. In particular, this shows that local nondistributivity coincides (...) with local nonmodularity in the computably enumerable degrees. (shrink)

One of the most lasting contributions of Marr's posthumous book is his articulation of the different “levels of analysis” that are needed to understand vision. Although a variety of work has examined how these different levels are related, there is comparatively little examination of the assumptions on which his proposed levels rest, or the plausibility of the approach Marr articulated given those assumptions. Marr placed particular significance on computational level theory, which specifies the “goal” of a computation, its appropriateness for (...) solving a particular problem, and the logic by which it can be carried out. The structure of computational level theory is inherently teleological: What the brain does is described in terms of its purpose. I argue that computational level theory, and the reverse-engineering approach it inspires, requires understanding the historical trajectory that gave rise to functional capacities that can be meaningfully attributed with some sense of purpose or goal, that is, a reconstruction of the fitness function on which natural selection acted in shaping our visual abilities. I argue that this reconstruction is required to distinguish abilities shaped by natural selection—“natural tasks” —from evolutionary “by-products”, rather than merely demonstrating that computational goals can be embedded in a Bayesian model that renders a particular behavior or process rational. (shrink)

To measure non-cognitive facets of competence, we developed and tested a new method that we refer to as Embedded Experience Sampling (EES). Domain-specific problem-solving competence is a multi-faceted construct that is not limited to cognitive facets such as domain knowledge or problem-solving strategies but also comprises non-cognitive facets in the sense of domain-specific emotional and motivational dispositions such as interest and self-concept. However, in empirical studies non-cognitive facets are usually either neglected or measured by generalized self-report questionnaires that are detached (...) from the performance assessment. To enable an integrated measurement, we developed the EES method to collect data on non-cognitive facets during scenario-based low-stakes assessments. Test-takers are requested to stop at certain times and spontaneously answer short items (EES items) regarding their actual experience of the problem situation. These EES items are embedded in an EES event that resembles typical social interactions with non-player characters. To evaluate the feasibility and validity of the method, we implemented EES in a series of three studies in the context of commercial vocational education and training (VET): A feasibility study with 77 trainees, a pilot study with 20 trainees, and the main study with 780 trainees who worked on three complex problem scenarios in a computer-based office simulation. In the present paper, we investigate how test-takers perceived the EES events, and whether social desirability biased their answers, and investigate the internal structure of the data and the relationship between EES data and data from several other sources. Interview data and survey data indicated no biases due to social desirability and no additional burden for the test-takers due to the EES events. A correlation analysis following the multitrait-multimethod approach as well as the calibration of a multidimensional model based on Item Response Theory (IRT) also supported the construct validity. Furthermore, EES data shows substantial correlations with test motivation but almost zero correlations with data from generalized retrospective self-report questionnaires on non-cognitive facets. Altogether, EES offers an alternative approach to measuring non-cognitive facets of competence under certain conditions. For instance, EES is also based on self-reporting and thus might not be suitable for high-stakes testing. (shrink)

From Curriculum Vitae parsing to web search and recommendation systems, Word2Vec and other word embedding techniques have an increasing presence in everyday interactions in human society. Biases, such as gender bias, have been thoroughly researched and evidenced to be present in word embeddings. Most of the research focuses on discovering and mitigating gender bias within the frames of the vector space itself. Nevertheless, whose bias is reflected in word embeddings has not yet been investigated. Besides discovering and mitigating gender (...) bias, it is also important to examine whether a feminine or a masculine-centric view is represented in the biases of word embeddings. This way, we will not only gain more insight into the origins of the before mentioned biases, but also present a novel approach to investigating biases in Natural Language Processing systems. Based on previous research in the social sciences and gender studies, we hypothesize that masculine-centric, otherwise known as androcentric, biases are dominant in word embeddings. To test this hypothesis we used the largest English word association test data set publicly available. We compare the distance of the responses of male and female participants to cue words in a word embedding vector space. We found that the word embedding is biased towards a masculine-centric viewpoint, predominantly reflecting the worldviews of the male participants in the word association test data set. Therefore, by conducting this research, we aimed to unravel another layer of bias to be considered when examining fairness in algorithms. (shrink)

1 INTIMACY Among Descartes's most and consequential achievements has been his of the mental as an independent ontological domain. By taking the mind as a substance, with cognitions as its modes, he accorded them a status as self-standing and determinate on their own, without essential regard to other entities. Only with this metaphysical conception in place, could the idea of solipsism-the idea of an intact ego existing with nothing else in the universe-so much as make sense. And behind that engine (...) have trailed the sorry boxcars of hyperbolic doubt. the mind-body problem, the problem of the external world, the problem of other minds, and so on. -/- Although the assumptions have been under fire, off and on. at least since Hegel-including with renewed intensity in recent years … the Cartesian separation that is still so pervasive as to be almost invisible. In particular, inter-relationist accounts retain a principled distinction between the mental and the corporeal-a distinction that is reflected in contrasts like semantics versus syntax, the space of reasons versus the space of causes, or the intentional versus the physical. (Notice that each of these contrasts can be heard either as higher versus lower’ level" or as inner versus outer 'sphere‘.) The contrary of this separation-or battery of separations-is not inter-relationist holism but something that I would like to call the intimacy of the mind's embodiment and embeddedness in the world. The term 'intimacy' is meant to suggest more than just necessary interrelation or interdependence but a kind of commingling or integralness of mind, body,and world-that is, to undermine their very distinctness. The challenge is as much to spell out what this could mean as to make a case for it. Indeed, no sooner does such a possibility seem intelligible at all, than ways bring out its plausibility and significance turn up everywhere. -/- There is little original in what follows. The strategy will be to bring some well known principles of systems analysis to bear on the mind- body-world 'system' in a way that refocuses questions of division and unity, and then to canvas a selection of investigations and proposals - some fairly recent, others not-in the light of this new focus. The hope is that these superficially disparate ideas, none of them new, will seem to converge around the theme of intimacy in a way that illuminates and supports them all. Sorting and and aligning issues in this manner has sometimes been discussed under titles like 'embedded computation’ and 'situated cognition'. (shrink)

We characterize the class of c.e. degrees that bound a critical triple as those degrees that compute a function that has no ω-c.e. approximation.

Building on previous works which argued that scalar implicatures can be computed in embedded positions, this paper proposes a constraint on exhaustification which restricts the conditions under which an exhaustivity operator can be licensed. We show that this economy condition allows us to derive a number of generalizations, such as, in particular, the ‘Implicature Focus Generalization’: scalar implicatures can be embedded under a downward-entailing operator only if the scalar term bears pitch accent. Our economy condition also derives specific predictions regarding (...) the licensing of so-called Hurford disjunctions. (shrink)

Context: At present, we lack a common understanding of both the process of cognition in living organisms and the construction of knowledge in embodied, embedded cognizing agents in general, including future artifactual cognitive agents under development, such as cognitive robots and softbots. Purpose: This paper aims to show how the info-computational approach (IC) can reinforce constructivist ideas about the nature of cognition and knowledge and, conversely, how constructivist insights (such as that the process of cognition is the process of life) (...) can inspire new models of computing. Method: The info-computational constructive framework is presented for the modeling of cognitive processes in cognizing agents. Parallels are drawn with other constructivist approaches to cognition and knowledge generation. We describe how cognition as a process of life itself functions based on info-computation and how the process of knowledge generation proceeds through interactions with the environment and among agents. Results: Cognition and knowledge generation in a cognizing agent is understood as interaction with the world (potential information), which by processes of natural computation becomes actual information. That actual information after integration becomes knowledge for the agent. Heinz von Foerster is identified as a precursor of natural computing, in particular bio computing. Implications: IC provides a framework for unified study of cognition in living organisms (from the simplest ones, such as bacteria, to the most complex ones) as well as in artifactual cognitive systems. Constructivist content: It supports the constructivist view that knowledge is actively constructed by cognizing agents and shared in a process of social cognition. IC argues that this process can be modeled as info-computation. (shrink)

We present a straightforward embedding of modal nonmonotonic logics into default logic.

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

While the notion of the mind as information-processor--a kind of computational system--is widely accepted, many scientists and philosophers have assumed that this account of cognition shows that the mind's operations are characterizable independent of their relationship to the external world. Existential Cognition challenges the internalist view of mind, arguing that intelligence, thought, and action cannot be understood in isolation, but only in interaction with the outside world. Arguing that the mind is essentially embedded in the external world, Ron McClamrock provides (...) a schema that allows cognitive scientists to address such long-standing problems in artificial intelligence as the "frame" problem and the issue of "bounded" rationality. Extending this schema to cover progress in other studies of behavior, including language, vision, and action, McClamrock reinterprets the importance of the organism/environment distinction. McClamrock also considers the broader philosophical question of the place of mind in the world, particularly with regard to questions of intentionality, subjectivity, and phenomenology. With implications for philosophy, cognitive and computer science, AI, and psychology, this book synthesizes state-of-the-art work in philosophy and cognitive science on how the mind interacts with the world to produce thoughts, ideas, and actions. (shrink)

Hahn’s embedding theorem asserts that linearly ordered abelian groups embed in some lexicographic product of real groups. Hahn’s theorem is generalized to a class of residuated semigroups in this paper, namely, to odd involutive commutative residuated chains which possess only finitely many idempotent elements. To this end, the partial lexicographic product construction is introduced to construct new odd involutive commutative residuated lattices from a pair of odd involutive commutative residuated lattices, and a representation theorem for odd involutive commutative residuated (...) chains which possess only finitely many idempotent elements, by means of linearly ordered abelian groups and the partial lexicographic product construction is presented. (shrink)

We construct a faithful interpretation of ukasiewicz's logic in product logic (both propositional and predicate). Using known facts it follows that the product predicate logic is not recursively axiomatizable.We prove a completeness theorem for product logic extended by a unary connective of Baaz [1]. We show that Gödel's logic is a sublogic of this extended product logic.

We examine topological pairs (\Delta, \Sigma) which have computable type: if X is a computable topological space and f:\Delta \rightarrow X a topological embedding such that f(\Delta) and f(\Sigma) are semicomputable sets in X, then f(\Delta) is a computable set in X. It it known that (D, W) has computable type, where D is the Warsaw disc and W is the Warsaw circle. In this paper we identify a class of topological pairs which are similar (...) to (D, W) and have computable type: we prove that (\Delta, \Sigma) has computable type if \Delta can somehow be approximated by a 2-cell whose boundary circle approximates \Sigma. Moreover, we examine higher-dimensional analogues of such pairs. (shrink)