Most theories of learning consider inferring a function f from either observations about f or, questions about f. We consider a scenario whereby the learner observes f and asks queries to some set A. If I is a notion of learning then I[A] is the set of concept classes I-learnable by an inductive inference machine with oracle A. A and B are I-equivalent if I[A] = I[B]. The equivalence classes induced are the degrees of inferability. We prove several results about (...) when these degrees are trivial, and when the degrees are omniscient. (shrink)

We investigate dependence of recursively enumerable graphs on the equality relation given by a specific r.e. equivalence relation on ω. In particular we compare r.e. equivalence relations in terms of graphs they permit to represent. This defines partially ordered sets that depend on classes of graphs under consideration. We investigate some algebraic properties of these partially ordered sets. For instance, we show that some of these partial ordered sets possess atoms, minimal and maximal elements. We also fully describe the isomorphism (...) types of some of these partial orders. (shrink)

This paper considers reductions between types of numberings; these reductions preserve the Rogers Semilattice of the numberings reduced and also preserve the number of minimal and positive degrees in their semilattice. It is shown how to use these reductions to simplify some constructions of specific semilattices. Furthermore, it is shown that for the basic types of numberings, one can reduce the left-r.e. numberings to the r.e. numberings and the k-r.e. numberings to the k+1-r.e. numberings; all further reductions are obtained by (...) concatenating these reductions. (shrink)

A generator program for a computable function (by definition) generates an infinite sequence of programs all but finitely many of which compute that function. Machine learning of generator programs for computable functions is studied. To motivate these studies partially, it is shown that, in some cases, interesting global properties for computable functions can be proved from suitable generator programs which cannot be proved from any ordinary programs for them. The power (for variants of various learning criteria from the literature) of (...) learning generator programs is compared with the power of learning ordinary programs. The learning power in these cases is also compared to that of learning limiting programs, i.e., programs allowed finitely many mind changes about their correct outputs. (shrink)

In this modern world, a massive amount of data is processed and broadcasted daily. This includes the use of high energy, massive use of memory space, and increased power use. In a few applications, for example, image processing, signal processing, and possession of data signals, etc., the signals included can be viewed as light in a few spaces. The compressive sensing theory could be an appropriate contender to manage these limitations. “Compressive Sensing theory” preserves extremely helpful while signals are sparse (...) or compressible. It very well may be utilized to recoup light or compressive signals with less estimation than customary strategies. Two issues must be addressed by CS: plan of the estimation framework and advancement of a proficient sparse recovery calculation. The essential intention of this work expects to audit a few ideas and utilizations of compressive sensing and to give an overview of the most significant sparse recovery calculations from every class. The exhibition of acquisition and reconstruction strategies is examined regarding the Compression Ratio, Reconstruction Accuracy, Mean Square Error, and so on. (shrink)

Freivalds defined an acceptable programming system independent criterion for learning programs for functions in which the final programs were required to be both correct and "nearly" minimal size, i.e., within a computable function of being purely minimal size. Kinber showed that this parsimony requirement on final programs limits learning power. However, in scientific inference, parsimony is considered highly desirable. A lim-computablefunction is (by definition) one calculable by a total procedure allowed to change its mind finitely many times about its output. (...) Investigated is the possibility of assuaging somewhat the limitation on learning power resulting from requiring parsimonious final programs by use of criteria which require the final, correct programs to be "not-so-nearly" minimal size, e.g., to be within a lim-computable function of actual minimal size. It is shown that some parsimony in the final program is thereby retained, yet learning power strictly increases. Considered, then, are lim-computable functions as above but for which notations for constructive ordinals are used to bound the number of mind changes allowed regarding the output. This is a variant of an idea introduced by Freivalds and Smith. For this ordinal notation complexity bounded version of lim-computability, the power of the resultant learning criteria form finely graded, infinitely ramifying, infinite hierarchies intermediate between the computable and the lim-computable cases. Some of these hierarchies, for the natural notations determining them, are shown to be optimally tight. (shrink)

We investigate a new paradigm in the context of learning in the limit, namely, learning correction grammars for classes of computably enumerable (c.e.) languages. Knowing a language may feature a representation of it in terms of two grammars. The second grammar is used to make corrections to the first grammar. Such a pair of grammars can be seen as a single description of (or grammar for) the language. We call such grammars correction grammars. Correction grammars capture the observable fact that (...) people do correct their linguistic utterances during their usual linguistic activities. We show that learning correction grammars for classes of c.e. languages in the TxtEx-model (i.e., converging to a single correct correction grammar in the limit) is sometimes more powerful than learning ordinary grammars even in the TxtBe-model (where the learner is allowed to converge to infinitely many syntactically distinct but correct conjectures in the limit). For each n ≥ 0, there is a similar learning advantage, again in learning correction grammars for classes of c.e. languages, but where we compare learning correction grammars that make n + 1 corrections to those that make n corrections. The concept of a correction grammar can be extended into the constructive transfinite, using the idea of counting-down from notations for transfinite constructive ordinals. This transfinite extension can also be conceptualized as being about learning Ershov-descriptions for c.e. languages. For u a notation in Kleene's general system $(O,\, < _o )$ of ordinal notations for constructive ordinals, we introduce the concept of an u-correction grammar, where u is used to bound the number of corrections that the grammar is allowed to make. We prove a general hierarchy result: if u and v are notations for constructive ordinals such that $u\, < _o \,v$ , then there are classes of c.e. languages that can be TxtEx-learned by conjecturing v-correction grammars but not by conjecturing u-correction grammars. Surprisingly, we show that— above "ω-many" corrections—it is not possible to strengthen the hierarchy: TxtEx-learning u-correction grammars of classes of c.e. languages, where u is a notation in O for any ordinal, can be simulated by TxtBe-learning ω-correction grammars, where ω is any notation for the smallest infinite ordinal ω. (shrink)

Limiting identification of r.e. indexes for r.e. languages (from a presentation of elements of the language) and limiting identification of programs for computable functions (from a graph of the function) have served as models for investigating the boundaries of learnability. Recently, a new approach to the study of "intrinsic" complexity of identification in the limit has been proposed. This approach, instead of dealing with the resource requirements of the learning algorithm, uses the notion of reducibility from recursion theory to compare (...) and to capture the intuitive difficulty of learning various classes of concepts. Freivalds, Kinber, and Smith have studied this approach for function identification and Jain and Sharma have studied it for language identification. The present paper explores the structure of these reducibilities in the context of language identification. It is shown that there is an infinite hierarchy of language classes that represent learning problems of increasing difficulty. It is also shown that the language classes in this hierarchy are incomparable, under the reductions introduced, to the collection of pattern languages. Richness of the structure of intrinsic complexity is demonstrated by proving that any finite, acyclic, directed graph can be embedded in the reducibility structure. However, it is also established that this structure is not dense. The question of embedding any infinite, acyclic, directed graph is open. (shrink)

Limiting identification of r.e. indexes for r.e. languages and limiting identification of programs for computable functions have served as models for investigating the boundaries of learnability. Recently, a new approach to the study of "intrinsic" complexity of identification in the limit has been proposed. This approach, instead of dealing with the resource requirements of the learning algorithm, uses the notion of reducibility from recursion theory to compare and to capture the intuitive difficulty of learning various classes of concepts. Freivalds, Kinber, (...) and Smith have studied this approach for function identification and Jain and Sharma have studied it for language identification. The present paper explores the structure of these reducibilities in the context of language identification. It is shown that there is an infinite hierarchy of language classes that represent learning problems of increasing difficulty. It is also shown that the language classes in this hierarchy are incomparable, under the reductions introduced, to the collection of pattern languages. Richness of the structure of intrinsic complexity is demonstrated by proving that any finite, acyclic, directed graph can be embedded in the reducibility structure. However, it is also established that this structure is not dense. The question of embedding any infinite, acyclic, directed graph is open. (shrink)

Identification of programs for computable functions from their graphs and identification of grammars for recursively enumerable languages from positive data are two extensively studied problems in the recursion theoretic framework of inductive inference.In the context of function identification, Freivalds et al. have shown that only those collections of functions, , are identifiable in the limit for which there exists a 1-1 computable numbering ψ and a discrimination function d such that1. for each , the number of indices i such that (...) ψi = ƒ is exactly one and2. for each , there are only finitely many indices i such that ƒ and ψi agree on the first d arguments.A similar characterization for language identification in the limit has turned out to be difficult. A partial answer is provided in this paper. Several new techniques are introduced which have found use in other investigations on language identification. (shrink)

Acceptable programming systems have many nice properties like s-m-n-Theorem, Composition and Kleene Recursion Theorem. Those properties are sometimes called control structures, to emphasize that they yield tools to implement programs in programming systems. It has been studied, among others by Riccardi and Royer, how these control structures influence or even characterize the notion of acceptable programming system. The following is an investigation, how these control structures behave in the more general setting of complete numberings as defined by Mal'cev and Eršov.

Acceptable programming systems have many nice properties like s-m-n-Theorem, Composition and Kleene Recursion Theorem. Those properties are sometimes called control structures, to emphasize that they yield tools to implement programs in programming systems. It has been studied, among others by Riccardi and Royer, how these control structures influence or even characterize the notion of acceptable programming system. The following is an investigation, how these control structures behave in the more general setting of complete numberings as defined by Mal'cev and Eršov.

Hay and, then, Johnson extended the classic Rice and Rice-Shapiro Theorems for computably enumerable sets, to analogs for all the higher levels in the finite Ershov Hierarchy. The present paper extends their work to analogs in the transfinite Ershov Hierarchy. Some of the transfinite cases are done for all transfinite notations in Kleene's important system of notations, equation image. Other cases are done for all transfinite notations in a very natural, proper subsystem equation image of equation image, where equation image (...) has at least one notation for each constructive ordinal. In these latter cases it is open as to what happens for the entire set of transfinite notations in equation image. (shrink)

This paper investigates some delicate tradeoffs between the generality of an algorithmic learning device and the quality of the programs it learns successfully. There are results to the effect that, thanks to small increases in generality of a learning device, the computational complexity of some successfully learned programs is provably unalterably suboptimal. There are also results in which the complexity of successfully learned programs is asymptotically optimal and the learning device is general, but, still thanks to the generality, some of (...) those optimal, learned programs are provably unalterably information deficient—in some cases, deficient as to safe, algorithmic extractability/provability of the fact that they are even approximately optimal. For these results, the safe, algorithmic methods of information extraction will be by proofs in arbitrary, true, computably axiomatizable extensions of Peano Arithmetic. (shrink)

The often heard (and justified) lament that academics do not adequately communicate their ideas to the broader general public has been particularly applicable to those theorists, like scholars of nonviolence, who work on the pressing moral issues facing our world. This work, ultimately the result of co-editor Predgrag Cicovacki’s deep and abiding interest in Jainism, does much to counter such impressions. Comprised of two volumes and forty-six chapters, Nonviolence as A Way of Life brings together insights from a notable international (...) array of fifty-four writers on peace and nonviolence. These writers, who represent 12 countries and 5 continents, have their contributions formally segmented into three parts—history, theory, and practice--even though considerable overlap on these matters is understandably present. The various commentaries are ultimately (albeit loosely) tied together by their discussing issues of nonviolence explicitly under the rubric of the ancient Jain notion of ahimsa. (shrink)

Novel computational representations, such as simulation models of complex systems and video games for scientific discovery, are dramatically changing the way discoveries emerge in science and engineering. The cognitive roles played by such computational representations in discovery are not well understood. We present a theoretical analysis of the cognitive roles such representations play, based on an ethnographic study of the building of computational models in a systems biology laboratory. Specifically, we focus on a case of model-building by an engineer that (...) led to a remarkable discovery in basic bioscience. Accounting for such discoveries requires a distributed cognition analysis, as DC focuses on the roles played by external representations in cognitive processes. However, DC analyses by and large have not examined scientific discovery, and they mostly focus on memory offloading, particularly how the use of existing external representations changes the nature of cognitive tasks. In contrast, we study discovery processes and argue that discoveries emerge from the processes of building the computational representation. The building process integrates manipulations in imagination and in the representation, creating a coupled cognitive system of model and modeler, where the model is incorporated into the modeler's imagination. This account extends DC significantly, and we present some of the theoretical and application implications of this extended account. (shrink)

In the annals of Indian modernity, narratives of tricksters and counterfeiters have a long, popular, and cautionary history. The topographies of deception outlined by colonial and post-colonial police reports established both its history as an aspect of modern industrial life as well as the city as the ‘scene of the crime’. This article explores the meanings that attach to certain contemporary acts of deceiving and faking, and the ways in which they are both produced by being in the city as (...) well as producing certain kinds of relationships. The article focuses on the residents of a Delhi slum and their various acts of producing fake identity cards and a variety of other documents. It offers a discussion about simulation and dissimulation, feigning and duplicity, and passing and pretending as significant contexts for gaining security of livelihood and residence in the city as well as constituting specific senses of community. Faking and counterfeiting, the article suggests, are arenas where the state both constitutes itself and contributes to the making of imagined non-state sensibilities of community. (shrink)

This research explores the influence of religiosity on consumer perception of, and response toward, sexual appeals. The first study (survey, national sample; n = 423) examines the relationship between religiosity and consumer response toward sexual appeals using causal modeling. Study 1 finds that high intrinsic religiosity consumers exhibit more adverse ethical judgments toward the company’s use of sexual appeals and these judgments, in turn, result in inferior attitudes and purchase intent toward the advertised brand. To confirm and expand on these (...) findings, the second study (experiment, young adult sample; n = 216) examines the influence of intrinsic religiosity on consumer response toward both sexual and nonsexual appeals. The results show that sexual appeals elicit inferior (superior) ethical judgments, attitudes, and purchase intent among consumers high (low) in intrinsic religiosity. In contrast, nonsexual appeals elicit (un)favorable responses from consumers who are (low) high in intrinsic religiosity. (shrink)

The well-established techniques of the professional storyteller not only have the potential to model complex “truth” but also to dig deeply into that complexity, thereby perhaps getting closer to that truth. This applies not only to fiction, but also to medicine and even science. Compelling storytelling ability may have conferred an evolutionary survival advantage and, if so, is likely represented in the neural circuitry of the human brain. Functional imaging will likely point to a neuroanatomical basis for compelling storytelling ability; (...) this will presumably reflect underlying cellular and molecular mechanisms. (shrink)

Recent experiments show video games have a range of positive cognitive effects, such as improvement in attention, spatial cognition and mental rotation, and also overcoming of cognitive disabilities such as fear of flying. Further, game environments are now being used to generate scientific discoveries, and bring about novel phenomenological effects, such as out-of-body experiences. These advances provide interesting interaction design possibilities for video games. However, since the cognitive mechanisms underlying these experimental effects are unknown, it is difficult to systematically derive (...) novel systems and interaction designs based on these results. We review the emerging cognitive mechanism known as common coding, and outline how this mechanism could provide an integrated account of the cognitive effects of video games. We then illustrate, using two ongoing projects, how novel video game interaction designs could be derived by extending common coding theory. (shrink)

Modified rules for the accumulation and discharge of international sovereign debt can codify the moral and legal basis for existing ad hoc deviations and present a justifiable framework within which international lending and borrowing can take place.

I present a case study of scientific discovery, where building two functional and behavioral approximations of neurons, one physical and the other computational, led to conceptual and implementation breakthroughs in a neural engineering laboratory. Such building of external systems that mimic target phenomena, and the use of these external systems to generate novel concepts and control structures, is a standard strategy in the new engineering sciences. I develop a model of the cognitive mechanism that connects such built external systems with (...) internal models, and I examine how new discoveries, and consensus on discoveries, could arise from this external‐internal coupling and the building process. The model is based on the emerging framework of common coding, which proposes a shared representation in the brain between the execution, perception, and imagination of movement. (shrink)

We outline three challenges involved in designing external representations that promote sustainable use of natural resources. First, the task environment of sustainable resource-use is highly unstructured, and involves many uncoordinated and asynchronous actions. Following from this complex nature of the task environment, more task constraints and task interactions are involved in designing representations promoting sustainability, compared to representations that seek to make tasks easier in structured task environments, such as aircraft cockpits and control rooms. Second, external representations promoting sustainable resource-use (...) need to motivate people to make decisions that sustain resources, and persist with this behavior, even though alternate behaviors are easier and commonplace. Third, external representations promoting sustainability also need to lower the cognitive load involved in sustainability decisions. This three-tiered function (meeting complex task constraints, providing motivation, lowering cognitive load) makes such representations challenging to design. However, some early prototype designs promoting sustainable resource-use have appeared recently, primarily addressing electricity use. Analyzing these digital prototypes, we outline three design principles they share, and show how these seek to address the complexities of the sustainability problem-space (complexity of task environments, goals, and representations). We then argue that at least two further cognitive scaffolds are required for effectively promoting sustainable resource use (action scripts, deconstruction). We close with some of the limitations of this approach to promoting sustainability, and outline future work. (shrink)

We outline three challenges involved in designing external representations that promote sustainable use of natural resources. First, the task environment of sustainable resource-use is highly unstructured, and involves many uncoordinated and asynchronous actions. Following from this complex nature of the task environment, more task constraints and task interactions are involved in designing representations promoting sustainability, compared to representations that seek to make tasks easier in structured task environments, such as aircraft cockpits and control rooms. Second, external representations promoting sustainable resource-use (...) need to motivate people to make decisions that sustain resources, and persist with this behavior, even though alternate behaviors are easier and commonplace. Third, external representations promoting sustainability also need to lower the cognitive load involved in sustainability decisions. This three-tiered function makes such representations challenging to design. However, some early prototype designs promoting sustainable resource-use have appeared recently, primarily addressing electricity use. Analyzing these digital prototypes, we outline three design principles they share, and show how these seek to address the complexities of the sustainability problem-space. We then argue that at least two further cognitive scaffolds are required for effectively promoting sustainable resource use. We close with some of the limitations of this approach to promoting sustainability, and outline future work. (shrink)

. Management scholars and practitioners often believe that individuals and organizations benefit by trusting their work contacts. (Husted, 1998; Sonnenberg, 1994) Trust is generally viewed as “good” and imperative to a modern functioning economy (Blau, 1964; Hosmer, 1995; Zucker, 1986) Consequently, scholars and practitioners have given scant attention to the “downside” of trust, despite the fact that trust involves taking risk under conditions of uncertainty (Rousseau et al., 1998) Recent corporate scandals show that people suffer when they misplace trust in (...) untrustworthy organizations and individuals. This paper develops a model of the causes and consequences of “over-trust,” which we define as a state where a trustor’s trust exceeds that which is warranted given the conditions. The antecedents of overtrust related to characteristics of the trustee, the trustor, and situational characteristics. We examine the role played by self-monitoring and perceived power base of the trustee as two key trustee characteristics. Among trustor characteristics, we examine the role (played by trustor’s core evaluation, core values). based on cultural affiliation), prior experiences with trustees, and use of habitual thinking behavior. Under characteristics of the situation, we examine the role played by uncertainty inherent in the situation, perceived threat from the context, degree of task interdependence, and organizational systems and routines. Next, we examine three consequences of over-trust – leniency in judging the trustee, delay in perceiving exploitation, and increased risk-taking. We conclude our paper by developing a set of guidelines that organizational members may employ to avoid over-trust. (shrink)

ABSTRACT:Globally, family firms are the dominant organizational form. Family involvement in business and unique family dynamics impacts organizational strategy and performance. However, family control of business has rarely been adopted as a discriminating variable in the organizations and the natural environment (ONE) research field. Drawing on the theory of planned behavior we develop a conceptual framework of the drivers of proactive environmental strategy (PES) in family firms. We argue that family involvement in business influences the attitudes, subjective norms, and perceived (...) behavioral control of a firm’s dominant coalition. Together these factors determine the extent of the dominant coalition’s intentions to undertake PES. Further, family firms with lower levels of relationship conflict within the controlling family will be more successful in translating the dominant coalition’s intentions to allocate resources for the pursuit of PES. Research implications of the theory are discussed. (shrink)

International monetary arrangements currently appear to have consequences that are incompatible with a global egalitarian conception of distributive justice. How can we create alternatives?

ABSTRACT:Globally, family firms are the dominant organizational form. Family involvement in business and unique family dynamics impacts organizational strategy and performance. However, family control of business has rarely been adopted as a discriminating variable in the organizations and the natural environment (ONE) research field. Drawing on the theory of planned behavior we develop a conceptual framework of the drivers of proactive environmental strategy (PES) in family firms. We argue that family involvement in business influences the attitudes, subjective norms, and perceived (...) behavioral control of a firm’s dominant coalition. Together these factors determine the extent of the dominant coalition’s intentions to undertake PES. Further, family firms with lower levels of relationship conflict within the controlling family will be more successful in translating the dominant coalition’s intentions to allocate resources for the pursuit of PES. Research implications of the theory are discussed. (shrink)

There is an increasing need for norms to be embedded in technology as the widespread deployment of applications such as autonomous driving, warfare and big data analysis for crime fighting and counter-terrorism becomes ever closer. Current approaches to norms in multi-agent systems tend either to simply make prohibited actions unavailable, or to provide a set of rules which the agent is obliged to follow, either as part of its design or to avoid sanctions and punishments. In this paper we argue (...) for the position that agents should be equipped with the ability to reason about a system’s norms, by reasoning about the social and moral values that norms are designed to serve; that is, perform the sort of moral reasoning we expect of humans. In particular we highlight the need for such reasoning when circumstances are such that the rules should arguably be broken, so that the reasoning can guide agents in deciding whether to comply with the norms and, if violation is desirable, how best to violate them. One approach to enabling this is to make use of an argumentation scheme based on values and designed for practical reasoning: arguments for and against actions are generated using this scheme and agents choose between actions based on their preferences over these values. Moral reasoning then requires that agents have an acceptable set of values and an acceptable ordering on their values. We first discuss how this approach can be used to think about and justify norms in general, and then discuss how this reasoning can be used to think about when norms should be violated, and the form this violation should take. We illustrate how value based reasoning can be used to decide when and how to violate a norm using a road traffic example. We also briefly consider what makes an ordering on values acceptable, and how such an ordering might be determined. (shrink)

This article contains an abstract of Dr. Sanjay Patnaik’s dissertation as well as a commentary essay on the research process in the appendix. In his dissertation, Dr. Patnaik examines the importance of the non-market environment for firm strategy and performance within the context of newly introduced regulations for greenhouse gases in Europe. The dissertation abstract contains a description of each dissertation chapter, including research questions, methodologies, and results. The commentary essay describes the author’s perspective on conducting research as an (...) emerging scholar. (shrink)