This isnotabout the symbolic manipulation of functions so popular these days. Rather it is about the more abstract, but infinitely less practical, problem of the primitive. Simply stated:Given a derivativef: ℝ → ℝ, how can we recover its primitive?The roots of this problem go back to the beginnings of calculus and it is even sometimes called “Newton's problem”. Historically, it has played a major role in the development of the theory of the integral. For example, it was Lebesgue's primary motivation (...) behind his theory of measure and integration. Indeed, the Lebesgue integral solves the primitive problem for the important special case whenfis bounded. Yet, as Lebesgue noted with apparent regret, there are very simple derivatives = 0,F=x2sinforx≠ 0) which cannot be inverted using his integral.The general problem of the primitive was finally solved in 1912 by A. Denjoy. But his integration process was more complicated than that of Lebesgue. Denjoy's basic idea was to first calculate the definite integralf dxover as many intervals as possible, using Lebesgue integration. Then, he showed that by using these results, the definite integral could be found over even more intervals, either by using the standard improper integral technique of Cauchy, or an extension technique developed by Lebesgue. (shrink)

A number of recent attempts to bridge Husserlian phenomenology of time consciousness and contemporary tools and results from cognitive science or computational neuroscience are described and critiqued. An alternate proposal is outlined that lacks the weaknesses of existing accounts.

Computer simulations are involved in numerous branches of modern science, and science would not be the same without them. Yet the question of how they can explain real-world processes remains an issue of considerable debate. In this context, a range of authors have highlighted the inferences back to the world that computer simulations allow us to draw. I will first characterize the precise relation between computer and target of a simulation that allows us to draw such inferences. I then argue (...) that in a range of scientifically interesting cases they are particular abductions and defend this claim by appeal to two case studies. (shrink)

Recently, a version of realism has been offered to address the simplification strategies used in computational neuroscience (Chirimuuta, 2023; 2024). According to this view, computational models provide us with knowledge about the brain, but they should not be taken literally in any sense, even rejecting the idea that the brain performs computations (computationalism). I acknowledge the need for considerations regarding simplification strategies in neuroscience and how they contribute to our interpretations of computational models; however, I argue that whether we should (...) accept or reject computationalism about the brain is a separate issue that can be addressed independently by a philosophical theory of physical computation. This takes seriously the idea that the brain performs computations while also taking an analogical stance toward computational models in neuroscience. I call this version of realism “Analogical Computational Realism.” Analogical Computational Realism is a realist view in virtue of being committed to computationalism while taking certain computational models to pick out real patterns (Dennett, 1991; Potochnik, 2017) that provide a how-possibly explanation without also thinking that the model is literally implemented in the brain. (shrink)

In light of the growing use of tablets for news reading and mobile news consumption behaviors, this study examined whether an innovative way of structuring news on the tablet that mimics mobile news behaviors reinforced attention for, and learning from, news. Specifically, it was theorized that the chronological and associative structuring of news articles into so-called developing news stories would lead to more attention for news, and better recall and comprehension of news, than the linear print newspaper structure that newspaper (...) publishers continue to copy from print to tablet. A multiple-day experiment was set up using the eye-tracking method to measure and control for attention. The results show that the developing news structure increased comprehension of news substantively, independently of attention effects; no effects were found on attention and factual recall. (shrink)

This paper takes up a recent challenge to mechanistic approaches to computational implementation, the view that computational implementation is best explicated within a mechanistic framework. The challenge, what has been labelled “the abstraction problem”, claims that one of MAC’s central pillars – medium independence – is deeply confused when applied to the question of computational implementation. The concern is that while it makes sense to say that computational processes are abstract (i.e. medium-independent), it makes considerably less sense to say that (...) they are also concrete processes of a mechanism. After outlining the problem and its effect on MAC, I examine a recent response from Kuokkanen and Rusanen [2018. “Making Too Many Enemies: Hutto and Myin’s Attack on Computationalism.” Philosophical Explorations 21 (2): 282–294. doi:10.1080/13869795.2018.1477980]. I argue that Kuokkanen and Rusanen’s response comes up short insofar as it makes problematic trade-offs among various desiderata we have for a theory of implementation. This leads to a general dilemma for MAC: either give up being an objective theory of implementation or concede the abstraction problem and so reintroduce triviality concerns. In response, I argue that conceiving of computations as abstracta rather than illata provides a way to avoid the proposed dilemma and articulate a notion of medium independence that addresses the abstraction problem. (shrink)

Concerning the question about consciousness, Georges Rey argues that it does not exist from the success of computational theory of human mind. Everything that such a theory requires can be fulfilled by machines which do not have consciousness. So, according to theoretical parsimony, we do not have to attribute consciousness even to human beings. I wish to offer reasons why we should not doubt the existence of consciousness by showing that computational explanations can be explanations of just one part of (...) an aspect of the human mind. Consciousness is also an explanandum rather than an explanans, and the possible reference of “what it is like” expression. Epistemic situation regarding possible accesses to consciousness is also considered. (shrink)

This article uses a 36-million word corpus of news reporting on Hurricane Katrina in the United States to explore how computer-based methods can help researchers to investigate the construction of newsworthiness. It makes use of Bednarek and Caple’s discursive approach to the analysis of news values, and is both exploratory and evaluative in nature. One aim is to test and evaluate the integration of corpus techniques in applying discursive news values analysis. We employ and evaluate corpus techniques that have not (...) been tested previously in relation to the large-scale analysis of news values. These techniques include tagged lemma frequencies, collocation, key part-of-speech tags and key semantic tags. A secondary aim is to gain insights into how a specific happening – Hurricane Katrina – was linguistically constructed as newsworthy in major American news media outlets, thus also making a contribution to ecolinguistics. (shrink)

It is often claimed that scientists can obtain new knowledge about nature by running computer simulations. How is this possible? I answer this question by arguing that computer simulations are arguments. This view parallels Norton’s argument view about thought experiments. I show that computer simulations can be reconstructed as arguments that fully capture the epistemic power of the simulations. Assuming the extended mind hypothesis, I furthermore argue that running the computer simulation is to execute the reconstructing argument. I discuss some (...) objections and reject the view that computer simulations produce knowledge because they are experiments. I conclude by comparing thought experiments and computer simulations, assuming that both are arguments. (shrink)

Tense operators in effect algebras play a key role for the representation of the dynamics of formally described physical systems. For this, it is important to know how to construct them on a given effect algebra \( E\) and how to compute all possible pairs of tense operators on \( E\) . However, we firstly need to derive a time frame which enables these constructions and computations. Hence, we usually apply a suitable set of states of the effect algebra (...) \( E\) in question. To approximate physical reality in quantum mechanics, we use only the so-called Jauch–Piron states on \( E\) in our paper. To realize our constructions, we are restricted on lattice effect algebras only. (shrink)

Scientists of many disciplines use theoretical models to explain and predict the dynamics of the world. They often have to rely on digital computer simulations to draw predictions fromthe model. But to deliver phenomenologically adequate results, simulations deviate from the assumptions of the theoretical model. Therefore the role of simulations in scientific explanation demands itself an explanation. This paper analyzes the relation between real-world system, theoretical model, and simulation. It is argued that simulations do not explain processes in the real (...) world directly. The way in which simulations help explaining real-world processes is conceived as indirect, mediated by the theoretical model. Simulacra are characterized further, and turn out to be a priori measurable. This gives a clue to a better understanding of the epistemic role of computer simulations in scientific research. (shrink)

Hi everybody! It's a great pleasure for me to be back here at the new, improved Santa Fe Institute in this spectacular location. I guess this is my fourth visit and it's always very stimulating, so I'm always very happy to visit you guys. I'd like to tell you what I've been up to lately. First of all, let me say what algorithmic information theory is good for, before telling you about the new version of it I've got.

To have a fully integrated understanding of neurobiological systems, we must address two fundamental questions: 1. What do brains do (what is their function)? and 2. How do brains do whatever it is that they do (how is that function implemented)? I begin by arguing that these questions are necessarily inter-related. Thus, addressing one without consideration of an answer to the other, as is often done, is a mistake. I then describe what I take to be the best available approach (...) to addressing both questions. Specifically, to address 2, I adopt the Neural Engineering Framework (NEF) of Eliasmith & Anderson [Neural engineering: Computation representation and dynamics in neurobiological systems. Cambridge, MA: MIT Press, 2003] which identifies implementational principles for neural models. To address 1, I suggest that adopting statistical modeling methods for perception and action will be functionally sufficient for capturing biological behavior. I show how these two answers will be mutually constraining, since the process of model selection for the statistical method in this approach can be informed by known anatomical and physiological properties of the brain, captured by the NEF. Similarly, the application of the NEF must be informed by functional hypotheses, captured by the statistical modeling approach. (shrink)

Computable general equilibrium models are widely used by governmental organizations and academic institutions to analyze the economy-wide effects of events such as climate change, tax policies and immigration. This book provides a practical, how-to guide to CGE models suitable for use at the undergraduate college level. Its introductory level distinguishes it from other available books and articles on CGE models. The book provides intuitive and graphical explanations of the economic theory that underlies a CGE model and includes many examples and (...) hands-on modeling exercises. It may be used in courses on economics principles, microeconomics, macroeconomics, public finance, environmental economics and international trade and finance, because it shows students the role of theory in a realistic model of an economy. The book is also suitable for courses on general equilibrium models and research methods and for professionals interested in learning how to use CGE models. (shrink)

Unlike behaviorism, cognitive psychology relies on mental concepts to explain behavior. Yet mental processes are not directly observable and multiple explanations are possible, which poses a challenge for finding a useful framework. In this article, I distinguish three new frameworks for explanations that emerged after the cognitive revolution. The first is called tools‐to‐theories: Psychologists' new tools for data analysis, such as computers and statistics, are turned into theories of mind. The second proposes as‐if theories: Expected utility theory and Bayesian statistics (...) are turned into theories of mind, describing an optimal solution of a problem but not its psychological process. The third studies the adaptive toolbox (formal models of heuristics) that describes mental processes in situations of uncertainty where an optimal solution is unknown. Depending on which framework researchers choose, they will model behavior in either situations of risk or of uncertainty, and construct models of cognitive processes or not. The frameworks also determine what questions are asked and what kind of data are generated. What all three frameworks have in common, however, is a clear preference for formal models rather than explanations by general dichotomies or mere verbal concepts. The frameworks have considerable potential to inform each other and to generate points of integration. (shrink)

Contemporary ICTs such as speaking machines and computer games tend to create illusions. Is this ethically problematic? Is it deception? And what kind of “reality” do we presuppose when we talk about illusion in this context? Inspired by work on similarities between ICT design and the art of magic and illusion, responding to literature on deception in robot ethics and related fields, and briefly considering the issue in the context of the history of machines, this paper discusses these questions through (...) the lens of stage magic and illusionism, with the aim of reframing the very question of deception. It investigates if we can take a more positive or at least morally neutral view of magic, illusion, and performance, while still being able to understand and criticize the relevant phenomena, and if we can describe and evaluate these phenomena without recourse to the term “deception” at all. This leads the paper into a discussion about metaphysics and into taking a relational and narrative turn. Replying to Tognazzini, the paper identifies and analyses two metaphysical positions: a narrative and performative non-dualist position is articulated in response to what is taken to be a dualist, in particular Platonic, approach to “deception” phenomena. The latter is critically discussed and replaced by a performative and relational approach which avoids a distant “view from nowhere” metaphysics and brings us back to the phenomena and experience in the performance relation. The paper also reflects on the ethical and political implications of the two positions: for the responsibility of ICT designers and users, which are seen as co-responsible magicians or co-performers, and for the responsibility of those who influence the social structures that shape who has power to deceive or to let others perform. (shrink)

The use of computer simulation for building theoretical models in social science is introduced. It is proposed that agent-based models have potential as a “third way” of carrying out social science, in addition to argumentation and formalisation. With computer simulations, in contrast to other methods, it is possible to formalise complex theories about processes, carry out experiments and observe the occurrence of emergence. Some suggestions are offered about techniques for building agent-based models and for debugging them. A scheme for structuring (...) a simulation program into agents, the environment and other parts for modifying and observing the agents is described. The article concludes with some references to modelling tools helpful for building computer simulations. (shrink)

Yang returns to the problem of referential ambiguity, addressed in the opening paper by Gleitman and Trueswell. Using a computational approach, he argues that “big data” approaches to resolving referential ambiguity are destined to fail, because of the inevitable computational explosion needed to keep track of contextual associations present when a word is uttered. Yang tests several computational models, two of which depend on one‐trial learning, as described in Gleitman and Trueswell’s paper. He concludes that such models outperform cross‐situational learning (...) models, thereby formalizing, reinforcing, and advancing the conclusions offered by Gleitman and Trueswell. (shrink)

Miscommunication phenomena such as repair in dialogue are important indicators of the quality of communication. Automatic detection is therefore a key step toward tools that can characterize communication quality and thus help in applications from call center management to mental health monitoring. However, most existing computational linguistic approaches to these phenomena are unsuitable for general use in this way, and particularly for analyzing human–human dialogue: Although models of other-repair are common in human-computer dialogue systems, they tend to focus on specific (...) phenomena, missing the range of repair and repair initiation forms used by humans; and while self-repair models for speech recognition and understanding are advanced, they tend to focus on removal of “disfluent” material important for full understanding of the discourse contribution, and/or rely on domain-specific knowledge. We explain the requirements for more satisfactory models, including incrementality of processing and robustness to sparsity. We then describe models for self- and other-repair detection that meet these requirements and investigate how they perform on datasets from a range of dialogue genres and domains, with promising results. (shrink)

The GOOGLE and XPRIZE $5,000,000 for the practical and socially useful utilization of the quantum computer is the starting point for ontomathematical reflections for what it can really serve. Its “output by measurement” is opposed to the conjecture for a coherent ray able alternatively to deliver the ultimate result of any quantum calculation immediately as a Dirac -function therefore accomplishing the transition of the sequence of increasingly narrow probability density distributions to their limit. The GOOGLE and XPRIZE problem’s solution needs (...) the initial understanding that the result of any quantum calculation is a wave function, or respectively, a probability (density or not) distribution unlike the Turing machine one, and only a “calculating ray” is able to transform the former into the later without any “curving” disturbances. Thus, the unique capability of the quantum computer due to its inherent quantum parallelism can be conserved for all Gödel unresolvable problems, only on the fast “NP” track of which the quantum computer “Achilles” is able practically to overrun the Turing machine “Tortoise” since the latter can “sprint” only by any “P” calculating speed even on it and unlike “Achilles” himself able for “NP” velocities as well. The way for any material body to “calculate” the certain trajectory of least action also resolves the “traveling salesman problem” in fact, therefore illustrating furthermore what the “NP” output of a quantum computer by a “calculating ray” should mean. Another example is the problem of the number of all prime numbers less than “N”, which is suggested to visualize once again the quantum computer capability to resolve problems by a “NP” speed and thus qualitatively to overrun any competing Turing machine. The technically implemented idea of laser is now reinterpreted to “radiate a wave function” in order to explain the “calculating ray” option for a quantum computer “NP” output. The generalization of an entanglement “trigger ray” described by any non-Hermitian operator (unlike a laser) is suggested as well as those “sci-fi” horizons which it reveals. One of them is meant for elucidating the practical meaning of the “Yang-Mills existence and mass gap problem”, one more of the CMI “Millennium Problems” after that of “P vs NP”. -/- . (shrink)

We discuss robotic art, emotion in robotic art, and compassion in the philosophy of art. We discuss a particular animated artwork, survivor, the walking chair, symbolising survivors of landmine blasts, learning to use crutches, and maimed emotionally as well as physically. Its control incorporates mutual relations between very rudimentary representations of distinct emotions. This artwork is intended for sensitising viewers to the horror experienced by those who survive, and those who don’t. We can only give a small sample, here, of (...) the reactions of viewers on various occasions when survivor was exhibited. Regardless of how much which pertains to human mental functions the tool embodies or doesn’t, it is the effect on the human perceivers which matters most to us, and enables us to understand something more about human cognition. Arguably this project is instructive in respect of the ethical-social implications of the synthetic method, i.e. the construction of inorganic systems in order to understand autonomous intentional action; in this project, the latter pertains to the humans involved. (shrink)

The identification and analysis of the spatiotemporal dynamic traffic patterns in citywide road networks constitute a crucial process for complex traffic management and control. However, city-scale and synchronal traffic data pose challenges for such kind of quantification, especially during peak hours. Traditional studies rely on data from road-based detectors or multiple communication systems, which are limited in not only access but also coverage. To avoid these limitations, we introduce real-time, traffic condition digital maps as our input. The digital maps keep (...) spatiotemporal urban traffic information in nature and are open to access. Their pixel colors represent traffic conditions on corresponding road segments. We propose a stacked convolutional autoencoder-based method to extract a low-dimension feature vector for each input. We compute and analyze the distances between vectors. The statistical results show different traffic patterns during given periods. With the actual data of Chongqing city, we compare the feature extraction performance between our proposed method and histogram. The result shows our proposed method can extract spatiotemporal features better. For the same data set, there is little difference in the number distribution of red pixels found in the statistics result of the histogram, while differences do exist in the results of our proposed method. We find the most fluctuated morning is on Friday; the most fluctuated evening is on Tuesday; and the most stable evening is on Wednesday. The distance captured by our method can represent the evolution of different traffic conditions during the morning and evening peak hours. Our proposed method provides managers with assistance to sense the dynamics of citywide traffic conditions in quantity. (shrink)

Interactions between humans and machines that include artificial intelligence are increasingly common in nearly all areas of life. Meanwhile, AI-products are increasingly endowed with emotional characteristics. That is, they are designed and trained to elicit emotions in humans, to recognize human emotions and, sometimes, to simulate emotions (EAI). The introduction of such systems in our lives is met with some criticism. There is a rather strong intuition that there is something wrong about getting attached to a machine, about having certain (...) emotions towards it, and about getting involved in a kind of affective relationship with it. In this paper, I want to tackle these worries by focusing on the last aspect: in what sense could it be problematic or even wrong to establish an emotional relationship with EAI-systems? I want to show that the justifications for the widespread intuition concerning the problems are not as strong as they seem at first sight. To do so, I discuss three arguments: the argument from self-deception, the argument from lack of mutuality, and the argument from moral negligence. (shrink)

This artists’ text examines the relationship between photographic images and Massively Multiplayer Online (MMO) environments. We note that such scripted image worlds necessitate a fundamental reconsideration of the capacities of image, its formation, reproduction, storage and circulation. As an archaeologist would document an excavation, extending conventional methods through 3D visualization technology to work in new ways with the archaeological record, we chose to document a world built and razed digitally by a now dormant group of anonymous gamers called the Yung (...) Cum Bois (YCBs). We turn to some definitions of griefer as a subcultural phenomenon within online culture to attempt to contextualize our involvement some more, thinking through the forms of image-gathering that grief play has generated, such as scripted object attacks where image-objects spawn and self-replicate, continually spurting out copies of themselves, lagging the region, slowing down frame rates, consuming land resources. Here we witness images blockading network logistics. This was active fieldwork. We got involved. We applied visualization technology learnt from archaeological computing research to the avatars, temporary structures and abandoned ruins of an online world, Second Life (SL). We patched together a kind of virtual photogrammetry, enabling the monumentalization of avatars, objects and scenarios, recompiling these into new configurations and uploading them freely to be reused, detourned and weaponized by our virtual friends. We situate this endeavour within a cobbled history of imaging technology, the networked self and its pathologies, riffling through our own image dump. Here. (shrink)

A related note on why European (and other) research plans will fail because of the lack of a suitable lower level education system Unjamming the education pipeline: Thoughts on educational prerequisites for an ambitious European research initiative.

The article investigates a system of polymorphically typed combinatory logic which is equivalent to Gödel’s T. A notion of (strong) reduction is defined over terms of this system and it is proved that the class of well-formed terms is closed under both bracket abstraction and reduction. The main new result is that the number of contractions needed to reduce a term to normal form is computed by an ε 0-recursive function. The ordinal assignments used to obtain this result are also (...) used to prove that the system under consideration is indeed equivalent to Gödel’s T. It is hoped that the methods used here can be extended so as to obtain similar results for stronger systems of polymorphically typed combinatory terms. An interesting corollary of such results is that they yield ordinally informative proofs of normalizability for sub-systems of second-order intuitionist logic, in natural deduction style. (shrink)

This paper presents a formalization of informal logic using the Carneades Argumentation System, a formal, computational model of argument that consists of a formal model of argument graphs and audiences. Conflicts between pro and con arguments are resolved using proof standards, such as preponderance of the evidence. Carneades also formalizes argumentation schemes. Schemes can be used to check whether a given argument instantiates the types of argument deemed normatively appropriate for the type of dialogue.

What is required to be an interdisciplinary theory in cognitive science is for it to span more than one traditional domain. Generally speaking, as I discuss ...

Simulation and Similarity is a novel and comprehensive account of, in first place, models and modeling. The author’s writing is exceptionally clear and intelligible. Simulation is referred to in the book only once, where it is defined as a kind of numerical analysis involving “computing the behavior of the model using a particular set of initial conditions” (82). Modeling, which is defined as “the indirect study of real-world systems via the construction and analysis of models” (4), appears to be the (...) primary focus of this book. This emphasis seems legitimate because the modeling practice precedes any simulation and is the key to its understanding as well.Chapter 2 “Three kinds of models” presents an account of the following kinds of models: concrete models (San Francisco Bay model being an example), mathematical models (Lottka–Volterra model of predation as an example), and computational models (illustrated by Schelling’s segregation model). First model example is a hydraulic one; the .. (shrink)

Computer simulations and experiments share many important features. One way of explaining the similarities is to say that computer simulations just are experiments. This claim is quite popular in the literature. The aim of this paper is to argue against the claim and to develop an alternative explanation of why computer simulations resemble experiments. To this purpose, experiment is characterized in terms of an intervention on a system and of the observation of the reaction. Thus, if computer simulations are experiments, (...) either the computer hardware or the target system must be intervened on and observed. I argue against the first option using the non-observation argument, among others. The second option is excluded by e.g. the over-control argument, which stresses epistemological differences between experiments and simulations. To account for the similarities between experiments and computer simulations, I propose to say that computer simulations can model possible experiments and do in fact often do so. (shrink)

We propose a framework for including information‐processing bounds in rational analyses. It is an application of bounded optimality (Russell & Subramanian, 1995) to the challenges of developing theories of mechanism and behavior. The framework is based on the idea that behaviors are generated by cognitive mechanisms that are adapted to the structure of not only the environment but also the mind and brain itself. We call the framework computational rationality to emphasize the incorporation of computational mechanism into the definition of (...) rational action. Theories are specified as optimal program problems, defined by an adaptation environment, a bounded machine, and a utility function. Such theories yield different classes of explanation, depending on the extent to which they emphasize adaptation to bounds, and adaptation to some ecology that differs from the immediate local environment. We illustrate this variation with examples from three domains: visual attention in a linguistic task, manual response ordering, and reasoning. We explore the relation of this framework to existing “levels” approaches to explanation, and to other optimality‐based modeling approaches. (shrink)

Almost all computational models of the mind and brain ignore details about neurotransmitters, hormones, and other molecules. The neglect of neurochemistry in cognitive science would be appropriate if the computational properties of brains relevant to explaining mental functioning were in fact electrical rather than chemical. But there is considerable evidence that chemical complexity really does matter to brain computation, including the role of proteins in intracellular computation, the operations of synapses and neurotransmitters, and the effects of neuromodulators such as hormones. (...) Neurochemical computation has implications for understanding emotions, cognition, and artificial intelligence. (shrink)

Just as theory of representation is deficient if it can’t explain how misrepresentation is possible, a theory of computation is deficient if it can’t explain how miscomputation is possible. Nonetheless, philosophers have generally ignored miscomputation. My primary goal in this paper is to clarify both what miscomputation is and how to adequately explain it. Miscomputation is a special kind of malfunction: a system miscomputes when it computes in a way that it shouldn’t. To explain miscomputation, you must provide accounts of (...) computational behavior, computational norms, and how computational behavior can deviate from computational norms. A secondary goal of this paper is to defend an (quasi-)individualist, mechanistic theory of miscomputation. Computational behavior is narrowly individuated. Computational norms are widely individuated. A system miscomputes when its behavior manifests a narrow computational structure that the widely individuated norms say that it should not have. (shrink)

Many mathematics students have trouble the first time they take a course, such as linear algebra, abstract algebra, introductory analysis, or discrete mathematics, in which they are asked to prove various theorems. This textbook will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it (...) is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed "scratchwork" sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. Numerous exercises give students the opportunity to construct their own proofs. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians. (shrink)

In this paper, we investigate the rules that should underlie a computer program that is capable of revising its beliefs or opinions. Such a program maintains a model of its environment, which is updated to reflect perceived changes in the environment. This model is stored in a knowledge base, and the program draws logical inferences from the information in the knowledge base. All the inferences drawn are added to the knowledge base. Among the propositions in the knowledge base, there are (...) some in which the program believes, and there may be others in which the program does not believe. Inputs from the outside world or reasoning carried out by the program may lead to the detection of contradictions, in which case the program has to revise its beliefs in order to get rid of the contradiction and to accommodate the new information. (shrink)

I argue that of the four kinds of quantitative description relevant for understanding brain function, a control theoretic approach is most appealing. This argument proceeds by comparing computational, dynamical, statistical and control theoretic approaches, and identifying criteria for a good description of brain function. These criteria include providing useful decompositions, simple state mappings, and the ability to account for variability. The criteria are justified by their importance in providing unified accounts of multi-level mechanisms that support intervention. Evaluation of the four (...) kinds of description with respect to these criteria supports the claim that control theoretic characterizations of brain function are the kind of quantitative description we ought to provide.Keywords: Neural computation; Control theory; Neural representation; Cognitive architecture; Cognitive models; Theoretical neuroscience. (shrink)

Computability theorists have introduced multiple hierarchies to measure the complexity of sets of natural numbers. The Kleene Hierarchy classifies sets according to the first-order complexity of their defining formulas. The Ershov Hierarchy classifies limit computable sets with respect to the number of mistakes that are needed to approximate them. Biacino and Gerla extended the Kleene Hierarchy to the realm of fuzzy sets, whose membership functions range in a complete lattice. In this paper, we combine the Ershov Hierarchy and fuzzy set (...) theory, by introducing and investigating the Fuzzy Ershov Hierarchy. (shrink)

The distinction between open and closed class items represents a fundamental bifurcation in the mental lexicon. It proved useful to express certain basic generalisations in linguistics and in the study of language acquisition and language pathology. The distinction is too rough tough: it must be refined by paying attention to the computational properties of the two classes and their division of labor in the generation of complex expressions. It will be shown how the distinction is expressed within current linguistic models (...) of the principles and parameters / minimalist type. (shrink)