In [7], open questions are raised regarding the computational strengths of so-called ∞-α -Turing machines, a family of models of computation resembling the infinite-time Turing machine model of [2], except with α -length tape . Let TαTα denote the machine model of tape length α . Define that TαTα is computationally stronger than TβTβ precisely when TαTα can compute all TβTβ-computable functions ƒ: min2→min2 plus more. The following results are found: Tω1≻TωTω1≻Tω. There are countable ordinals α such that Tα≻TωTα≻Tω, (...) the smallest of which is precisely γ , the supremum of ordinals clockable by TωTω. In fact, there is a hierarchy of countable TαTαs of increasing strength corresponding to the transfinite Turing-jump operator ▼. There is a countable ordinal μ such that neither Tμ⪰Tω1Tμ⪰Tω1 nor Tμ⪯Tω1Tμ⪯Tω1—that is, the models TμTμ and Tω1Tω1 are computation-strength incommensurable . A similar fact holds for any larger uncountable device replacing Tω1Tω1. Further observations are made about countable TαTα. (shrink)

In [8], the third author defined a reducibility$\le _w^{\rm{*}}$that lets us compare the computing power of structures of any cardinality. In [6], the first two authors showed that the ordered field of reals${\cal R}$lies strictly above certain related structures. In the present paper, we show that$\left \equiv _w^{\rm{*}}{\cal R}$. More generally, for the weak-looking structure${\cal R}$ℚconsisting of the real numbers with just the ordering and constants naming the rationals, allo-minimal expansions of${\cal R}$ℚare equivalent to${\cal R}$. Using this, we show that (...) for any analytic functionf,$\left \equiv _w^{\rm{*}}{\cal R}$. $is noto-minimal.). (shrink)

We present a new manifestation of Gödel’s second incompleteness theorem and discuss its foundational significance, in particular with respect to Hilbert’s program. Specifically, we consider a proper extension of Peano arithmetic ( $\mathbf {PA}$ ) by a mathematically meaningful axiom scheme that consists of $\Sigma ^0_2$ -sentences. These sentences assert that each computably enumerable ( $\Sigma ^0_1$ -definable without parameters) property of finite binary trees has a finite basis. Since this fact entails the existence of polynomial time algorithms, it is (...) relevant for computer science. On a technical level, our axiom scheme is a variant of an independence result due to Harvey Friedman. At the same time, the meta-mathematical properties of our axiom scheme distinguish it from most known independence results: Due to its logical complexity, our axiom scheme does not add computational strength. The only known method to establish its independence relies on Gödel’s second incompleteness theorem. In contrast, Gödel’s theorem is not needed for typical examples of $\Pi ^0_2$ -independence (such as the Paris–Harrington principle), since computational strength provides an extensional invariant on the level of $\Pi ^0_2$ -sentences. (shrink)

The effects of lexical context on phonological processing are pervasive and there have been indications that such effects may be modulated by attention. However, attentional modulation in speech processing is neither well documented nor well understood. Experiment 1 demonstrated attentional modulation of lexical facilitation of speech sound recognition when task and critical stimuli were identical across attention conditions. We propose modulation of lexical activation as a neurophysiologically plausible computational mechanism that can account for this type of modulation. Contrary to (...) the claims of critics, this mechanism can account for attentional modulation without violating the principle of interactive processing. Simulations of the interactive TRACE model extended to include two different ways of modulating lexical activation showed that each can account for attentional modulation of lexical feedback effects. Experiment 2 tested conflicting predictions from the two implementations and provided evidence that is consistent with bias input as the mechanism of attentional control of lexical activation. (shrink)

There are theoretical limitations to what can be implemented by a computer program. In this paper we are concerned with a limitation on the strength of computer implemented deduction. We use a version of the Curry paradox to arrive at this limitation.

This paper provides a unifying axiomatic account of the interpretation of recursive types that incorporates both domain-theoretic and realizability models as concrete instances. Our approach is to view such models as full subcategories of categorical models of intuitionistic set theory. It is shown that the existence of solutions to recursive domain equations depends upon the strength of the set theory. We observe that the internal set theory of an elementary topos is not strong enough to guarantee their existence. In (...) contrast, as our first main result, we establish that solutions to recursive domain equations do exist when the category of sets is a model of full intuitionistic Zermelo–Fraenkel set theory. We then apply this result to obtain a denotational interpretation of FPC, a recursively typed lambda-calculus with call-by-value operational semantics. By exploiting the intuitionistic logic of the ambient model of intuitionistic set theory, we analyse the relationship between operational and denotational semantics. We first prove an “internal” computational adequacy theorem: the model always believes that the operational and denotational notions of termination agree. This allows us to identify, as our second main result, a necessary and sufficient condition for genuine “external” computational adequacy to hold, i.e. for the operational and denotational notions of termination to coincide in the real world. The condition is formulated as a simple property of the internal logic, related to the logical notion of 1-consistency. We provide useful sufficient conditions for establishing that the logical property holds in practice. Finally, we outline how the methods of the paper may be applied to concrete models of FPC. In doing so, we obtain computational adequacy results for an extensive range of realizability and domain-theoretic models. (shrink)

Over the past few years numerous proposals have appeared that attempt to characterize consciousness in terms of what could be called its computational correlates: Principles of information processing with which to characterize the differences between conscious and unconscious processing. Proposed computational correlates include architectural specialization (such as the involvement of specific regions of the brain in conscious processing), properties of representations (such as their stability in time or their strength), and properties of specific processes (such as resonance, (...) synchrony, interactivity, or information integration). In exactly the same way as one can engage in a search for the neural correlates of consciousness, one can thus search for the computational correlates of consciousness. The most direct way of doing is to contrast models of conscious versus unconscious information processing. In this paper, I review these developments and illustrate how computational modeling of specific cognitive processes can be useful in exploring and in formulating putative computational principles through which to capture the differences between conscious and unconscious cognition. What can be gained from such approaches to the problem of consciousness is an understanding of the function it plays in information processing and of the mechanisms that subtend it. Here, I suggest that the central function of consciousness is to make it possible for cognitive agents to exert ?exible, adaptive control over behavior. From this perspective, consciousness is best characterized as involving (1) a graded continuum de?ned over quality of representation, such that availability to consciousness and to cognitive control correlates with properties of representation, and (2) the implication of systems of meta-representations. (shrink)

We study the proof-theoretic strength and effective content of the infinite form of Ramsey's theorem for pairs. Let RT n k denote Ramsey's theorem for k-colorings of n-element sets, and let RT $^n_{ denote (∀ k)RT n k . Our main result on computability is: For any n ≥ 2 and any computable (recursive) k-coloring of the n-element sets of natural numbers, there is an infinite homogeneous set X with X'' ≤ T 0 (n) . Let IΣ n and (...) BΣ n denote the Σ n induction and bounding schemes, respectively. Adapting the case n = 2 of the above result (where X is low 2 ) to models of arithmetic enables us to show that RCA 0 + IΣ 2 + RT 2 2 is conservative over RCA 0 + IΣ 2 for Π 1 1 statements and that $RCA_0 + I\Sigma_3 + RT^2_{ , is Π 1 1 -conservative over RCA 0 + IΣ 3 . It follows that RCA 0 + RT 2 2 does not imply BΣ 3 . In contrast, J. Hirst showed that $RCA_0 + RT^2_{ does imply BΣ 3 , and we include a proof of a slightly strengthened version of this result. It follows that $RT^2_{ is strictly stronger than RT 2 2 over RCA 0. (shrink)

We investigate the connections between computability theory and Nonstandard Analysis. In particular, we investigate the two following topics and show that they are intimately related. A basic property of Cantor space$2^ $ is Heine–Borel compactness: for any open covering of $2^ $, there is a finite subcovering. A natural question is: How hard is it to compute such a finite subcovering? We make this precise by analysing the complexity of so-called fan functionals that given any $G:2^ \to $, output a (...) finite sequence $\langle f_0, \ldots,f_n \rangle $ in $2^ $ such that the neighbourhoods defined from $\overline {f_i } G\left$ for $i \le n$ form a covering of $2^ $. A basic property of Cantor space in Nonstandard Analysis is Abraham Robinson’s nonstandard compactness, i.e., that every binary sequence is “infinitely close” to a standard binary sequence. We analyse the strength of this nonstandard compactness property of Cantor space, compared to the other axioms of Nonstandard Analysis and usual mathematics.Our study of yields exotic objects in computability theory, while leads to surprising results in Reverse Mathematics. We stress that and are highly intertwined, i.e., our study is holistic in nature in that results in computability theory yield results in Nonstandard Analysis and vice versa. (shrink)

Kierstead showed that every computable marriage problem has a computable matching under the assumption of computable expanding Hall condition and computable local finiteness for boys and girls. The strength of the marriage theorem reaches or if computable expanding Hall condition or computable local finiteness for girls is weakened. In contrast, the provability of the marriage theorem is maintained in even if local finiteness for boys is completely removed. Using these conditions, we classify the strength of variants of marriage (...) theorems in the context of reverse mathematics. Furthermore, we introduce another condition that also makes the marriage theorem provable in, and investigate the sequential and Weihrauch strength of marriage theorems under that condition. (shrink)

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.

This article reviews the strengths and limitations of five major paradigms of medical computer-assisted decision making (CADM): (1) clinical algorithms, (2) statistical analysis of collections of patient data, (3) mathematical models of physical processes, (4) decision analysis, and (5) symbolic reasoning or artificial intelligence (Al). No one technique is best for all applications, and there is recent promising work which combines two or more established techniques. We emphasize both the inherent power of symbolic reasoning and the promise of artificial intelligence (...) and the other techniques to complement each other. Keywords: Diagnosis, Computer Assisted Decision Making, Artificial Intelligence * Current address: Intelligenetics, 124 University Avenue, Palo Alto, CA. 94301, U.S.A. ** Dr. Shortliffe is a Henry J. Kaiser Family Foundation Faculty Scholar in General Internal Medicine and recipient of research career development award LM0048 from the National Library of Medicine. CiteULike Connotea Del.icio.us What's this? (shrink)

The aim of this paper is to propose a formal approach to reasoning about desires, understood as logical propositions which we would be pleased to make true, also acknowledging the fact that desire is a matter of degree. It is first shown that, at the static level, desires should satisfy certain principles that differ from those to which beliefs obey. In this sense, from a static perspective, the logic of desires is different from the logic of beliefs. While the accumulation (...) of beliefs tend to reduce the remaining possible worlds they point at, the accumulation of desires tends to increase the set of states of affairs tentatively considered as satisfactory. Indeed beliefs are expected to be closed under conjunctions, while, in the positive view of desires developed here, one can argue that endorsing \ as a desire means to desire \ and to desire \. However, desiring \ and \ at the same time is not usually regarded as rational, since it does not make much sense to desire one thing and its contrary at the same time. Thus when a new desire is added to the set of desires of an agent, a revision process may be necessary. Just as belief revision relies on an epistemic entrenchment relation, desire revision is based on a hedonic entrenchment relation satisfying other properties, due to the different natures of belief and desire. While epistemic entrenchment relations are known to be qualitative necessity relations, hedonic relations obeying a set of reasonable postulates correspond to another set-function in possibility theory, called guaranteed possibility, that drive well-behaved desire revision operations. Then the general framework of possibilistic logic provides a syntactic setting for encoding desire change. The paper also insists that desires should be carefully distinguished from goals. (shrink)

This article reviews the strengths and limitations of five major paradigms of medical computer-assisted decision making (CADM): (1) clinical algorithms, (2) statistical analysis of collections of patient data, (3) mathematical models of physical processes, (4) decision analysis, and (5) symbolic reasoning or artificial intelligence (Al). No one technique is best for all applications, and there is recent promising work which combines two or more established techniques. We emphasize both the inherent power of symbolic reasoning and the promise of artificial intelligence (...) and the other techniques to complement each other. (shrink)

At the heart of the uniqueness debate is the possibility that the computer revolution may demand more in the way of ethical analysis than our traditional (that is, modern) ethical edification has prepared us for. In short, it may present new and unique problems and therefore demand new and unique solutions. In this article I argue that the solution is in fact an old and not‐so‐unique one: casuistry. Appealing to Jonsen and Toulmin's analysis of casuistry (1988), I argue that a (...) casuistic methodology is a more accurate description of the moral reasoning used by contemporary computer ethicists than are other accounts. In addition, I argue that the strengths that enabled casuistry to deal successfully with radical social, economic, and religious changes in the sixteenth and seventeenth centuries render casuistry well suited to the task of dealing with radically new situations like those found in twentieth‐ and twenty‐first‐century computer technology. Before concluding, I briefly explore Pascal's fatal critique of casuistry and its relevance for contemporary computer ethics. (shrink)

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

This thesis is devoted to the exploration of the complexity of some mathematical problems using the framework of computable analysis and descriptive set theory. We will especially focus on Weihrauch reducibility as a means to compare the uniform computational strength of problems. After a short introduction of the relevant background notions, we investigate the uniform computational content of problems arising from theorems that lie at the higher levels of the reverse mathematics hierarchy.We first analyze the strength (...) of the open and clopen Ramsey theorems. Since there is not a canonical way to phrase these theorems as multi-valued functions, we identify eight different multi-valued functions and study their degree from the point of view of Weihrauch, strong Weihrauch, and arithmetic Weihrauch reducibility.We then discuss some new operators on multi-valued functions and study their algebraic properties and the relations with other previously studied operators on problems. In particular, we study the first-order part and the deterministic part of a problem f, capturing the Weihrauch degree of the strongest multi-valued problem that is reducible to f and that, respectively, has codomain $\mathbb {N}$ or is single-valued.These notions proved to be extremely useful when exploring the Weihrauch degree of the problem $\mathsf {DS}$ of computing descending sequences in ill-founded linear orders. They allow us to show that $\mathsf {DS}$, and the Weihrauch equivalent problem $\mathsf {BS}$ of finding bad sequences through non-well quasi-orders, while being very “hard” to solve, are rather weak in terms of uniform computational strength. We then generalize $\mathsf {DS}$ and $\mathsf {BS}$ by considering $\boldsymbol {\Gamma }$ -presented orders, where $\boldsymbol {\Gamma }$ is a Borel pointclass or $\boldsymbol {\Delta }^1_1$, $\boldsymbol {\Sigma }^1_1$, $\boldsymbol {\Pi }^1_1$. We study the obtained $\mathsf {DS}$ -hierarchy and $\mathsf {BS}$ -hierarchy of problems in comparison with the Baire hierarchy and show that they do not collapse at any finite level.Finally, we work in the context of geometric measure theory and we focus on the characterization, from the point of view of descriptive set theory, of some conditions involving the notions of Hausdorff/Fourier dimension and Salem sets. We first work in the hyperspace $\mathbf {K}$ of compact subsets of $[0,1]$ and show that the closed Salem sets form a $\boldsymbol {\Pi }^0_3$ -complete family. This is done by characterizing the complexity of the family of sets having sufficiently large Hausdorff or Fourier dimension. We also show that the complexity does not change if we increase the dimension of the ambient space and work in $\mathbf {K}$. We also generalize the results by relaxing the compactness of the ambient space and show that the closed Salem sets are still $\boldsymbol {\Pi }^0_3$ -complete when we endow $\mathbf {F}$ with the Fell topology. A similar result holds also for the Vietoris topology.We conclude by analyzing the same notions from the point of view of effective descriptive set theory and Type-2 Theory of Effectivity, and show that the complexities remain the same also in the lightface case. In particular, we show that the family of all the closed Salem sets is $\Pi ^0_3$ -complete. We furthermore characterize the Weihrauch degree of the functions computing Hausdorff and Fourier dimension of closed sets.prepared by Manlio Valenti.E-mail:[email protected]. (shrink)

At the heart of the uniqueness debate is the possibility that the computer revolution may demand more in the way of ethical analysis than our traditional (that is, modern) ethical edification has prepared us for. In short, it may present new and unique problems and therefore demand new and unique solutions. In this article I argue that the solution is in fact an old and not‐so‐unique one: casuistry. Appealing to Jonsen and Toulmin's analysis of casuistry (1988), I argue that a (...) casuistic methodology is a more accurate description of the moral reasoning used by contemporary computer ethicists than are other accounts. In addition, I argue that the strengths that enabled casuistry to deal successfully with radical social, economic, and religious changes in the sixteenth and seventeenth centuries render casuistry well suited to the task of dealing with radically new situations like those found in twentieth‐ and twenty‐first‐century computer technology. Before concluding, I briefly explore Pascal's fatal critique of casuistry and its relevance for contemporary computer ethics. (shrink)

We present a novel argumentation-based method for finding and analyzing communities in social media on the Web, where a community is regarded as a set of supported opinions that might be in conflict. Based on their stance, we identify argumentative coalitions to define them; then, we apply a similarity-based evaluation method over the set of arguments in the coalition to determine the level of cohesion inherent to each community, classifying them appropriately. Introducing conflict points and attacks between coalitions based on (...) argumentative (dis)similarities to model the interaction between communities leads to considering a meta-argumentation framework where the set of coalitions plays the role of the set of arguments and where the attack relation between the coalitions is assigned a particular strength which is inherited from the arguments belonging to the coalition. Various semantics are introduced to consider attacks’ strength to particularize the effect of the new perspective. Finally, we analyze a case study where all the elements of the formal construction of the formalism are exercised. (shrink)

The connections between mathematical logic and combinatorics have a rich history. This paper focuses on one aspect of this relationship: understanding the strength, measured using the tools of computability theory and reverse mathematics, of various partition theorems. To set the stage, recall two of the most fundamental combinatorial principles, König's Lemma and Ramsey's Theorem. We denote the set of natural numbers by ω and the set of finite sequences of natural numbers by ω<ω. We also identify each n ∈ (...) ω with its set of predecessors, so n = {0, 1, 2, …, n − 1}. (shrink)

Computers have far to go to match human strengths, and our estimates will depend on analogy and extrapolation. Fortunately, these are grounded in the first bit of the journey, now behind us. Thirty years of computer vision reveals that 1 MIPS can extract simple features from real-time imagery--tracking a white line or a white spot on a mottled background. 10 MIPS can follow complex gray-scale patches--as smart bombs, cruise missiles and early self-driving vans attest. 100 MIPS can follow moderately unpredictable (...) features like roads--as recent long NAVLAB trips demonstrate. 1,000 MIPS will be adequate for coarse-grained three-dimensional spatial awareness--illustrated by several mid-resolution stereoscopic vision programs, including my own. 10,000 MIPS can find three-dimensional objects in clutter--suggested by several "bin-picking" and high-resolution stereo-vision demonstrations, which accomplish the task in an hour or so at 10 MIPS. The data fades there--research careers are too short, and computer memories too small, for significantly more elaborate experiments. (shrink)

We study the computability-theoretic complexity and proof-theoretic strength of the following statements: (1) "If X is a well-ordering, then so is ε X ", and (2) "If X is a well-ordering, then so is φ(α, X)", where α is a fixed computable ordinal and φ represents the two-placed Veblen function. For the former statement, we show that ω iterations of the Turing jump are necessary in the proof and that the statement is equivalent to ${\mathrm{A}\mathrm{C}\mathrm{A}}_{0}^{+}$ over RCA₀. To prove (...) the latter statement we need to use ω α iterations of the Turing jump, and we show that the statement is equivalent to ${\mathrm{\Pi }}_{{\mathrm{\omega }}^{\mathrm{\alpha }}}^{0}{-\mathrm{C}\mathrm{A}}_{0}$ . Our proofs are purely computability-theoretic. We also give a new proof of a result of Friedman: the statement "if x is a well-ordering, then so is φ(x, 0)" is equivalent to ATR₀ over RCA₀. (shrink)

The Grätzer-Schmidt theorem of lattice theory states that each algebraic lattice is isomorphic to the congruence lattice of an algebra. We study the reverse mathematics of this theorem. We also show thatthe set of indices of computable lattices that are complete is Π11\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Pi ^1_1$$\end{document}-complete;the set of indices of computable lattices that are algebraic is Π11\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Pi ^1_1$$\end{document}-complete;the set of compact elements of a computable (...) lattice is Π11\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Pi ^{1}_{1}$$\end{document} and can be Π11\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Pi ^1_1$$\end{document}-complete; andthe set of compact elements of a distributive computable lattice is Π30\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Pi ^{0}_{3}$$\end{document}, and there is an algebraic distributive computable lattice such that the set of its compact elements is Π30\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Pi ^0_3$$\end{document}-complete. (shrink)

Normative positions are sometimes illustrated in diagrams, in particular in didactic contexts. Traditional examples are the Aristotelian polygons of opposition for deontic modalities (squares, triangles, hexagons, etc.), and the Hohfeldian squares for obligative and potestative concepts. Relying on previous work, we show that Hohfeld’s framework can be used as a basis for developing several Aristotelian polygons and more complex diagrams. Then, we illustrate how logical theories of increasing strength can be built based on these diagrams, and how those theories (...) enable us to determine in a computably efficient way whether a set of normative positions can be derived from another set of normative positions. (shrink)

We prove that the statement “there is aksuch that for everyfthere is ak-bounded diagonally nonrecursive function relative tof” does not imply weak König’s lemma over${\rm{RC}}{{\rm{A}}_0} + {\rm{B\Sigma }}_2^0$. This answers a question posed by Simpson. A recursion-theoretic consequence is that the classic fact that everyk-bounded diagonally nonrecursive function computes a 2-bounded diagonally nonrecursive function may fail in the absence of${\rm{I\Sigma }}_2^0$.

In recent years, the gastronomy industry has increased the demand for rigorous and reliable tools to evaluate culinary creativity; but conceptually, creativity is difficult to define and even more difficult to measure. In this paper, we propose an AI-based method for assessing culinary product creativity by using the renowned high cuisine restaurant elBulli as a case study to understand the proliferation and scale of an entity’s creativity and innovation. To achieve so, we trained a Random Forest Classifier to assess the (...) level of creativity within the restaurant’s recipes. The application of this model to elBulli’s recipes allowed us to answer the following questions: how can creativity in a culinary product be characterized? Is there a single trait that is the key to culinary creativity? Is the creative culinary product a truly original outcome? Our key findings are (1) although ingredients and preparation techniques prove to be suitable attributes to characterize creativity in a recipe, none of them nor an elite subset clearly identifies creative cuisine, (2) new products are not radically novel with respect to previous creations, (3) creativity is more related to new uses and combinations of existing ingredients and techniques rather than to new ingredients or techniques. We believe that our method can find practical applications in supporting and guiding the creation of culinary products, identifying their strengths and weaknesses, and helping restaurants maintain a sustainable competitive advantage. (shrink)

The more recent computer developments cause us to take a new look at human intelligence. The prevailing occidental view of human intelligence represents a very one-sided, logocentric approach, so that it is becoming more urgent to look for a more complete view. In this way, specific strengths of so-called human information processing are becoming particularly evident in a new way. To provide a general substantiation for this view, some elements of a phenomenological model for a dialectical coherence of human expressions (...) of life are briefly outlined. The starting point is the everyday experience of constantly being confronted with contradictory situations. A model of polar, or dualistic, dialectic is proposed, which attempts to systematically establish the contradictions and contingencies of human life in theoretical structures. It is assumed that formal logic fails to work — strictly speaking — when applied to real situations of human interaction. Instead, definite negations are supposed to be involved. In this way, four polarities, pairs of concepts which are mutually dependent on each other and negate each other definitely, are presented: process and structure, the individual and general (societal), acting and imagining, subject-subject-relation and subject-object-relation (love and work). The latter gives rise to the dialectic of emotion and cognition, which plays a decisive role in a comparison of human and computer-“intelligence”.To cope with the specific human strengths, which are expressed through these polarities, self-learning computers would have to be able to act and to love like human beings and to grow up in a society like people. Furthermore, the learning process would have to implement the process-structure-dialectic with its aspects of finality. In spite of the recent breath-taking achievements of computers, one can not imagine how computers would ever achieve this. Computers are, however, thought of, by virtue of their complexity, being qualitatively different from machines. But human abilities still represent a new level of complexity: the level of dialectic. (shrink)

Argumentation has been an important topic in knowledge representation, reasoning and multi-agent systems during the last twenty years. In this paper, we propose a new abstract framework where arguments are associated with a strength, namely a quantitative information which is used to determine whether an attack between arguments succeeds or not. Our Strength-based Argumentation Framework combines ideas of Preference-based and Weighted Argumentation Frameworks in an original way, which permits to define acceptability semantics sensitive to the existence of accruals (...) between arguments. The question of accruals arises in situations where several arguments defending the same position against another argument are unable to individually defeat this argument, but could do it collectively if they combine their strengths. We investigate some of the theoretical and computational properties of our new framework and semantics, and present a reasoning algorithm that is based on a translation of the problem into pseudo-boolean constraint satisfaction. This paper proposes an intuitive framework which allows strength compensations in an argumentation context where attacks may not succeed, completed by an approach which detects accruals throughout the reasoning process without requiring the elicitation of all compensatory combinations of arguments as an input. (shrink)

‘It is much more difficult than is often admitted to make a strong case for the ownership of computer software.’ This closely argued study of the strengths and weaknesses of the case for intellectual property rights and against software piracy is based on material contained in the author’s joint work with Douglas Adeney, Computer and Information Ethics, Greenwood Press, an imprint of Greenwood Publishing Group, INC., Westport, CT, forthcoming May, 1997. The author is a member of the School of Information (...) Studies at Charles Sturt University, PO Box 588, Wagga Wagga, NSW 2650 Australia; tel 61 69 33 2372; fax 61 69 33 2733; email [email protected] wishes to acknowledge the contribution to this paper of Douglas Adeney of the University of Melbourne. (shrink)

According to pancomputationalism, all physical systems – atoms, rocks, hurricanes, and toasters – perform computations. Pancomputationalism seems to be increasingly popular among some philosophers and physicists. In this paper, we interpret pancomputationalism in terms of computational descriptions of varying strength—computational interpretations of physical microstates and dynamics that vary in their restrictiveness. We distinguish several types of pancomputationalism and identify essential features of the computational descriptions required to support them. By tying various pancomputationalist theses directly to notions (...) of what counts as computation in a physical system, we clarify the meaning, strength, and plausibility of pancomputationalist claims. We show that the force of these claims is diminished when weaknesses in their supporting computational descriptions are laid bare. Specifically, once computation is meaningfully distinguished from ordinary dynamics, the most sensational pancomputationalist claims are unwarranted, whereas the more modest claims offer little more than recognition of causal similarities between physical processes and the most primitive computing processes. (shrink)

The relatively recent increase in prominence of computer simulations in scientific inquiry gives us more reasons than ever before for asserting that mathematics is a wonderful tool. In fact, a practical knowledge of scientific computation has become essential for scientists working in all disciplines involving mathematics. Despite their incontestable success, it must be emphasized that the numerical methods subtending simulations provide at best approximate solutions and that they can also return very misleading results. Accordingly, epistemological sobriety demands that we clarify (...) the circumstances under which simulations can be relied upon. With this in mind, this paper articulates a general perspective to better understand and compare the strengths and weaknesses of various error-analysis methods. (shrink)

This paper presents a soundness and completeness proof for propositional intuitionistic calculus with respect to the semantics of computability logic. The latter interprets formulas as interactive computational problems, formalized as games between a machine and its environment. Intuitionistic implication is understood as algorithmic reduction in the weakest possible — and hence most natural — sense, disjunction and conjunction as deterministic-choice combinations of problems , and “absurd” as a computational problem of universal strength.

Most axiomatizations of set theory that have been treated metamathematically have been based either entirely on classical logic or entirely on intuitionistic logic. But a natural conception of the settheoretic universe is as an indefinite (or “potential”) totality, to which intuitionistic logic is more appropriately applied, while each set is taken to be a definite (or “completed”) totality, for which classical logic is appropriate; so on that view, set theory should be axiomatized on some correspondingly mixed basis. Similarly, in the (...) case of predicative analysis, the natural numbers are considered to form a definite totality, while the universe of sets (or functions) of natural numbers are viewed as an indefinite totality, so that, again, a mixed semi-constructive logic should be the appropriate one to treat the two together. Various such semiconstructive systems of analysis and set theory are formulated here and their proof-theoretic strength is characterized. Interestingly, though the logic is weakened, one can in compensation strengthen certain principles in a way that could be advantageous for mathematical applications. (shrink)

Causal queries about singular cases, which inquire whether specific events were causally connected, are prevalent in daily life and important in professional disciplines such as the law, medicine, or engineering. Because causal links cannot be directly observed, singular causation judgments require an assessment of whether a co‐occurrence of two events c and e was causal or simply coincidental. How can this decision be made? Building on previous work by Cheng and Novick (2005) and Stephan and Waldmann (2018), we propose a (...) computational model that combines information about the causal strengths of the potential causes with information about their temporal relations to derive answers to singular causation queries. The relative causal strengths of the potential cause factors are relevant because weak causes are more likely to fail to generate effects than strong causes. But even a strong cause factor does not necessarily need to be causal in a singular case because it could have been preempted by an alternative cause. We here show how information about causal strength and about two different temporal parameters, the potential causes' onset times and their causal latencies, can be formalized and integrated into a computational account of singular causation. Four experiments are presented in which we tested the validity of the model. The results showed that people integrate the different types of information as predicted by the new model. (shrink)

We study the complexity of (finitely-valued and transfinitely-valued) Euclidean functions for computable Euclidean domains. We examine both the complexity of the minimal Euclidean function and any Euclidean function. Additionally, we draw some conclusions about the proof-theoretical strength of minimal Euclidean functions in terms of reverse mathematics.

Forensic evidence often involves an evaluation of whether two impressions were made by the same source, such as whether a fingerprint from a crime scene has detail in agreement with an impression taken from a suspect. Human experts currently outperform computer-based comparison systems, but the strength of the evidence exemplified by the observed detail in agreement must be evaluated against the possibility that some other individual may have created the crime scene impression. Therefore, the strongest evidence comes from features (...) in agreement that are also not shared with other impressions from other individuals. We characterize the nature of human expertise by applying two extant metrics to the images used in a fingerprint recognition task and use eye gaze data from experts to both tune and validate the models. The Attention via Information Maximization model quantifies the rarity of regions in the fingerprints to determine diagnosticity for purposes of excluding alternative sources. The CoVar model captures relationships between low-level features, mimicking properties of the early visual system. Both models produced classification and generalization performance in the 75%–80% range when classifying where experts tend to look. A validation study using regions identified by the AIM model as diagnostic demonstrates that human experts perform better when given regions of high diagnosticity. The computational nature of the metrics may help guard against wrongful convictions, as well as provide a quantitative measure of the strength of evidence in casework. (shrink)

The paper investigates inaccessible set axioms and their consistency strength in constructive set theory. In ZFC inaccessible sets are of the form Vκ where κ is a strongly inaccessible cardinal and Vκ denotes the κth level of the von Neumann hierarchy. Inaccessible sets figure prominently in category theory as Grothendieck universes and are related to universes in type theory. The objective of this paper is to show that the consistency strength of inaccessible set axioms heavily depend on the (...) context in which they are embedded. The context here will be the theory CZF− of constructive Zermelo–Fraenkel set theory but without -Induction . Let INAC be the statement that for every set there is an inaccessible set containing it. CZF−+INAC is a mathematically rich theory in which one can easily formalize Bishop style constructive mathematics and a great deal of category theory. CZF−+INAC also has a realizability interpretation in type theory which gives its theorems a direct computational meaning. The main result presented here is that the proof theoretic ordinal of CZF−+INAC is a small ordinal known as the Feferman–Schütte ordinal Γ0. (shrink)

There has been increasing use of argument-based approaches in the development of safety-critical systems. Within this approach, a safety case plays a key role in the system development life cycle. The key components in a safety case are safety arguments, which are designated to demonstrate that the system is acceptably safe. Inappropriate reasoning in safety arguments could undermine a system's safety claims which in turn contribute to safety-related failures of the system. The review of safety arguments is therefore a crucial (...) step in the development of safety-critical systems. Reviews are conducted using dialogues where elements of the argument and their relations are proposed and scrutinised. This paper investigates an approach of conducting argument review using dialectical models. After studying five established dialectical models with varying strengths and drawbacks, a new dialectical model specially designed to support persuasion and information-seeking dialogues has been proposed to suit the requir... (shrink)

‘It is much more difficult than is often admitted to make a strong case for the ownership of computer software.’ This closely argued study of the strengths and weaknesses of the case for intellectual property rights and against software piracy is based on material contained in the author’s joint work with Douglas Adeney, Computer and Information Ethics, Greenwood Press, an imprint of Greenwood Publishing Group, INC., Westport, CT, forthcoming May, 1997. The author is a member of the School of Information (...) Studies at Charles Sturt University, PO Box 588, Wagga Wagga, NSW 2650 Australia; tel 61 69 33 2372; fax 61 69 33 2733; email [email protected] wishes to acknowledge the contribution to this paper of Douglas Adeney of the University of Melbourne. (shrink)

In trying to control various aspects concerning utterance production in multi-party human–computer dialogue, argumentative considerations play an important part, particularly in choosing appropriate lexical units so that we fine-tune the degree of persuasion that each utterance has. A preliminary step in this endeavor is the ability to place an ordering relation between semantic forms (that are due to be realized as utterances, by the machine), concerning their persuasion strength, with respect to certain (explicit or implicit) conclusions. Thus, in this (...) article, we propose a mechanism for assessing utterances, in terms of their argumentative force. The framework designed conflates insights from Asher and Lascarides’ SDRT (“Segmented Discourse Representation Theory”), and from Anscombre and Ducrot’s AT (“Argumentation Theory”). These mechanisms are included in a language generation component of a multi-party dialogue system for book reservation applications (i.e., a “virtual librarian”), and thus evaluated via typical human–machine conversations. (shrink)

This article addresses the use of computer-assisted career guidance systems in career interventions. Major CACGS developed in the past decades were based on the trait-factor or person-environment fit approaches in their conceptualization and design. The strengths and limitations of these CACGS in addressing the career development needs of individuals are discussed. The Career Construction Theory is a promising paradigm to guide the development of new generations of CACGS. The narrative tradition, career adaptability model, and life-design interventions of CCT offer rich (...) conceptual and practical applications that could expand the scope and breadth of career exploration and identity construction through using CACGS. A digital system developed in Hong Kong called Infinity is a case-in-point of a CACGS where users could learn about career planning, engage in self and career construction through using the quantitative and qualitative assessment applications and gamified tools, take career planning actions over time, and communicate with their social supportive systems. Initial findings suggested that users of the system reported lesser decision-making difficulties, higher levels of decision clarity, and better understanding of what is career planning than non-users. Users from high academic achievement schools reported higher levels of career adaptability than their counterparts in schools of similar academic background. Users from low achievement schools reported higher intention to pursue government-supported universities than non-users from schools of similar background. Research and practice implications in schools and organizational settings are discussed. (shrink)

Different approaches analyze the strength of a natural language argument in different ways. This paper contrasts the dialectical, structural, probabilistic (or Bayesian), computational, and empirical approaches by exemplarily applying them to a single argumentative text (Epicureans on Squandering Life; Aikin & Talisse, 2019). Rather than pitching these approaches against one another, our main goal is to show the room for fruitful interaction. Our focus is on a dialectical analysis of the squandering argument as an argumentative response that voids (...) an interlocutor’s right to assertion. This analysis addresses the pragmatic dimensions of arguing and implies an argument structure that is consistent with empirical evidence of perceived argument strength. Results show that the squandering argument can be evaluated as a (non-fallacious) ad hominem argument, which however is not necessarily stronger than possible arguments attacking it. (shrink)

A commonly held background assumption about the sciences is that they connect along borders characterized by ontological or explanatory relationships, usually given in the order of mathematics, physics, chemistry, biology, psychology, and the social sciences. Interdisciplinary work, in this picture, arises in the connecting regions of adjacent disciplines. Philosophical research into interdisciplinary model transfer has increasingly complicated this picture by highlighting additional connections orthogonal to it. But most of these works have been done through case studies, which due to their (...) strong focus struggle to provide foundations for claims about large-scale relations between multiple scientific disciplines. As a supplement, in this contribution, we propose to philosophers of science the use of modern science mapping techniques to trace connections between modeling techniques in large literature samples. We explain in detail how these techniques work, and apply them to a large, contemporary, and multidisciplinary data set (n=383.961 articles). Through the comparison of textual to mathematical representations, we suggest formulaic structures that are particularly common among different disciplines and produce first results indicating the general strength and commonality of such relationships. (shrink)

The threshold view says that a person forms an outright belief P if and only if her credence for P reaches a certain threshold. Using computer simulations, I compare different versions of the threshold view to understand how they perform under time pressure in decision problems. The results illuminate the strengths and weaknesses of the various cognitive strategies in different decision contexts. A threshold view that performs well across diverse contexts is likely to be a cognitively flexible and context-dependent fusion (...) of several of the existing theories. The results of the simulations also cast doubts on the possibility of a threshold view that is both simple enough to streamline our reasoning while also allowing us to form good action-guiding beliefs. (shrink)

The theme of this volume is the multi-faceted 'computational turn' that is occurring through the interaction of the disciplines of philosophy and computing. In computer and information sciences, there are significant conceptual and methodological questions that require reflection and analysis. Moreover, digital, information and communication technologies have had tremendous impact on society, which raises further philosophical questions. This book tries to facilitate the task to continuously work to ensure that its diversity of perspectives and methods proves a source of (...) strength and collaboration rather than a source of instability and disintegration. The first three contributions explore the phenomenon of virtual worlds. The next four focus on robots and artificial agents. Then a group of chapters discusses the relation between human mentality and information processing in computers and the final section covers a broad range of issues at the interface of computers and society. (shrink)

The most ambitious simulation approach to computer-aided diagnosis is probably that of CADUCEUS. A review of its strategies may be expected to reveal some, at least, of the strengths and weaknesses of this approach, as well as to turn up problems of interest to the philosopher of science concerned with the logical structures implicit in the process of diagnostic judgment. CiteULike Connotea Del.icio.us What's this?

Electroencephalogram based Brain–Computer Interfaces enable stroke and motor neuron disease patients to communicate and control devices. Mindfulness meditation has been claimed to enhance metacognitive regulation. The current study explores whether mindfulness meditation training can thus improve the performance of BCI users. To eliminate the possibility of expectation of improvement influencing the results, we introduced a music training condition. A norming study found that both meditation and music interventions elicited clear expectations for improvement on the BCI task, with the strength (...) of expectation being closely matched. In the main 12 week intervention study, seventy-six healthy volunteers were randomly assigned to three groups: a meditation training group; a music training group; and a no treatment control group. The mindfulness meditation training group obtained a significantly higher BCI accuracy compared to both the music training and no-treatment control groups after the intervention, indicating effects of meditation above and beyond expectancy effects. (shrink)