This paper addresses a common challenge with computational cognitive models: identifying parameter values that are both theoretically plausible and generate predictions that match well with empirical data. While computational models can offer deep explanations of cognition, they are computationally complex and often out of reach of traditional parameter fitting methods. Weak methodology may lead to premature rejection of valid models or to acceptance of models that might otherwise be falsified. Mathematically robust fitting methods are, therefore, essential to the progress of (...) computational modeling in cognitive science. In this article, we investigate the capability and role of modern fitting methods—including Bayesian optimization and approximate Bayesian computation—and contrast them to some more commonly used methods: grid search and Nelder–Mead optimization. Our investigation consists of a reanalysis of the fitting of two previous computational models: an Adaptive Control of Thought—Rational model of skill acquisition and a computational rationality model of visual search. The results contrast the efficiency and informativeness of the methods. A key advantage of the Bayesian methods is the ability to estimate the uncertainty of fitted parameter values. We conclude that approximate Bayesian computation is (a) efficient, (b) informative, and (c) offers a path to reproducible results. (shrink)

In many areas of scientific inquiry, the phenomena under investigation are viewed as functions on the real numbers. Since observational precision is limited, it makes sense to view these phenomena as bounded functions on the rationals. One may translate the basic notions of recursion theory into this framework by first interpreting a partial recursive function as a function on Q. The standard notions of inductive inference carry over as well, with no change in the theory. When considering the class (...) of computable functions on Q, there are a number of natural ways in which to define the distance between two functions. We utilize standard metrics to explore notions of approximate inference — our inference machines will attempt to guess values which converge to the correct answer in these metrics. We show that the new inference notions, NV∞, EX∞, and BC∞, infer more classes of functions than their standard counterparts, NV, EX, and BC. Furthermore, we give precise inclusions between the new inference notions and those in the standard inference hierarchy. We also explore weaker notions of approximate inference, leading to inference hierarchies analogous to the EXn and BCn hierarchies. Oracle inductive inference is also considered, and we give sufficient conditions under which approximate inference from a generic oracle G is equivalent to approximate inference with only finitely many queries to G. (shrink)

Scientists and Bayesian statisticians often study hypotheses that they know to be false. This creates an interpretive problem because the Bayesian probability of a hypothesis is supposed to represent the probability that the hypothesis is true. I investigate whether Bayesianism can accommodate the idea that false hypotheses are sometimes approximately true or that some hypotheses or models can be closer to the truth than others. I argue that the idea that some hypotheses are approximately true in an absolute sense is (...) hard to square with Bayesianism, but that the notion that some hypotheses are comparatively closer to the truth than others can be made compatible with Bayesianism, and that this provides an adequate and potentially useful solution to the interpretive problem. Finally, I compare my ``verisimilitude'' solution to the interpretive problem with a ``counterfactual'' solution recently proposed by Jan Sprenger. (shrink)

We investigate the logical and conceptual connections between abductive reasoning construed as a process of belief change, on the one hand, and truth approximation, construed as increasing (estimated) verisimilitude, on the other. We introduce the notion of ‘(verisimilitude-guided) abductive belief change’ and discuss under what conditions abductively changing our theories or beliefs does lead them closer to the truth, and hence tracks truth approximation conceived as the main aim of inquiry. The consequences of our analysis for some recent discussions concerning (...) belief revision aiming at truth approximation and inference to the best explanation are also highlighted. (shrink)

The standard theory for belief revision provides an elegant and powerful framework for reasoning about how a rational agent should change its beliefs when confronted with new information. However, the agents considered are extremely idealized. Some recent models attempt to tackle the problem of plausible belief revision by adding structure to the belief bases and using nonstandard inference operations. One of the key ideas is that not all of an agent's beliefs are relevant for an operation of belief change.In (...) this paper we incorporate the insights pertaining to local change and relevance sensitivity with the use of approximate inference relations. These approximate inference relations offer us partial solutions at any stage of the revision process. The quality of the approximations improves as we allow for more and more resources to be used. We are provided with upper and lower bounds to what would be obtained with the use of classical inference. (shrink)

mentation for languages such as Chinese. Almost no NLP task is truly standalone. The end-to-end performance of natural Most current systems for higher-level, aggre-.

The technical results presented here on continuity and approximate implication are obviously incomplete. In particular, a syntactic characterization of approximate implication is highly desirable. Nevertheless, I believe the results above do show that the theory has considerable promise for application to the areas mentioned at the top of the paper.Formulation and defense of realist interpretations of science, for example, require approximate truth because we hardly ever have evidence that a particular scientific theory corresponds perfectly with a portion (...) of the real world. Realists need to assert, then, that evidence for a theory is evidence for its approximate truth, not its truth (see [3] and [18]). Approximate truth is, however, a vague notion, and specification of quantity terms and of a sense of approximation are needed to make precise applications of it. Suitability of both vocabulary and sense of approximation depend on the subject matter, and their selection is a partly empirical matter that raises complex issues. In light of the number of common inferences which are not continuous, realists also need to be concerned about indiscriminate use of deductive logic to derive consequences from approximately true theories. These issues will be considered further in a future paper.Approximate truth also has potential application in areas of artificial intelligence that require inference from inaccurate data. In the ‘qualitative’ physical theories of de Kleer and Brown [6], for example, ‘qualitative’ values are derived by partitioning the real numbers into regions. Inferences leading from inside to outside a region must be identified and avoided, and approximate implication and continuity may prove useful in doing this. More generally, growing use of predicate logic as a programming language invites application of the theory of approximate truth as a symbolic substitute for numerical evaluation of computation errors. This too will be the subject of a future paper. (shrink)

Viewing the brain as an organ of approximate Bayesian inference can help us understand how it represents the self. We suggest that inferred representations of the self have a normative function: to predict and optimise the likely outcomes of social interactions. Technically, we cast this predict-and-optimise as maximising the chance of favourable outcomes through active inference. Here the utility of outcomes can be conceptualised as prior beliefs about final states. Actions based on interpersonal representations can therefore be (...) understood as minimising surprise – under the prior belief that one will end up in states with high utility. Interpersonal representations thus serve to render interactions more predictable, while the affective valence of interpersonal inference renders self-perception evaluative. Distortions of self-representation contribute to major psychiatric disorders such as depression, personality disorder and paranoia. The approach we review may therefore operationalise the study of interpersonal representations in pathological states. (shrink)

An influential suggestion about the relationship between Bayesianism and inference to the best explanation holds that IBE functions as a heuristic to approximate Bayesian reasoning. While this view promises to unify Bayesianism and IBE in a very attractive manner, important elements of the view have not yet been spelled out in detail. I present and argue for a heuristic conception of IBE on which IBE serves primarily to locate the most probable available explanatory hypothesis to serve as a (...) working hypothesis in an agent’s further investigations. Along the way, I criticize what I consider to be an overly ambitious conception of the heuristic role of IBE, according to which IBE serves as a guide to absolute probability values. My own conception, by contrast, requires only that IBE can function as a guide to the comparative probability values of available hypotheses. This is shown to be a much more realistic role for IBE given the nature and limitations of the explanatory considerations with which IBE operates. (shrink)

The term fuzzy logic is used in this paper to describe an imprecise logical system, FL, in which the truth-values are fuzzy subsets of the unit interval with linguistic labels such as true, false, not true, very true, quite true, not very true and not very false, etc. The truth-value set, , of FL is assumed to be generated by a context-free grammar, with a semantic rule providing a means of computing the meaning of each linguistic truth-value in as a (...) fuzzy subset of [0, 1].Since is not closed under the operations of negation, conjunction, disjunction and implication, the result of an operation on truth-values in requires, in general, a linguistic approximation by a truth-value in . As a consequence, the truth tables and the rules of inference in fuzzy logic are (i) inexact and (ii) dependent on the meaning associated with the primary truth-value true as well as the modifiers very, quite, more or less, etc. (shrink)

An interesting consequence of the structuralist theory of truth approximation, as developed in my From Instrumentalism to Constructive Realism , henceforth ICR, concerns so-called ‘inference to the best explanation’ . It will be argued that this popular rule among scientific realists can better be replaced by, various kinds of, ‘inference to the best theory’.

An interesting consequence of the structuralist theory of truth approximation, as developed in my From Instrumentalism to Constructive Realism, henceforth ICR, concerns so-called ‘inference to the best explanation’. It will be argued that this popular rule among scientific realists can better be replaced by, various kinds of, ‘inference to the best theory’.

It has long been recognized that the concept of inconsistency is a central part of commonsense reasoning. In this issue, a number of authors have explored the idea of reasoning with maximal consistent subsets of an inconsistent stratified knowledge base. This paradigm, often called “coherent-based reasoning", has resulted in some interesting proposals for para-consistent reasoning, non-monotonic reasoning, and argumentation systems. Unfortunately, coherent-based reasoning is computationally very expensive. This paper harnesses the approach of approximate entailment by Schaerf and Cadoli [SCH (...) 95] to develop the concept of “approximate coherent-based reasoning". To this end, we begin to present a multi-modal propositional logic that incorporates two dual families of modalities: □S and?S defined for each subset S of the set of atomic propositions. The resource parameter S indicates what atoms are taken into account when evaluating formulas. Next, we define resource-bounded consolidation operations that limit and control the generation of maximal consistent subsets of a stratified knowledge base. Then, we present counterparts to existential, universal, and argumentative inference that are prominent in coherence-based approaches. By virtue of modalities □S and?S, these inferences are approximated from below and from above, in an incremental fashion. Based on these features, we show that an anytime view of coherent-based reasoning is tenable. (shrink)

This paper draws on the resources of computational neuroscience (an account of active inference under the free energy principle) to address Bas van Fraassen's bad lot objection to the inference to the best explanation (IBE). The general assumption of this paper is that IBE is a finessed form of active inferences that self-organising systems perform to maximise the chance of their survival. Under this assumption, the paper aims to establish the following points: first, the capacity to learn to (...) perform explanatory inferences comes with evolutionary privileges; second, adaptive actions guide beliefs and beliefs are action-oriented; and third, IBE is not inconsistent with (approximate) Bayesianism but plays a heuristic role to it. (shrink)

This monograph presents new ideas in nomic truth approximation. It features original and revised papers from a philosopher of science who has studied the concept for more than 35 years. Over the course of time, the author's initial ideas evolved. He discovered a way to generalize his first theory of nomic truth approximation, viz. by dropping an unnecessarily strong assumption. In particular, he first believed to have to assume that theories were maximally specific in the sense that they did not (...) only exclude certain conceptual possibilities, but also that all non-excluded possibilities were in fact claimed to be nomically possible. Now, he argues that the exclusion claim alone, or for that matter the inclusion claim alone, is sufficient to motivate the formal definition of being closer to the nomic truth. The papers collected here detail this generalized view of nomic truthlikeness or verisimilitude. Besides this, the book presents, in adapted form, the relation with several other topics, such as, domain revision, aesthetic progress, abduction, inference to the best explanation, pragmatic aspects, probabilistic methods, belief revision and epistemological positions, notably constructive realism. Overall, the volume presents profound insight into nomic truth approximation. This idea seeks to determine how one theory can be closer to, or more similar to, the truth about what is nomically, e.g. physically, chemically, biologically, possible than another theory. As a result, it represents the ultimate goal of theory oriented empirical science. Theo Kuipers is the author of Studies in Inductive Probability and Rational Expectation, From Instrumentalism to Constructive Realism and Structures in Science. He is the volume-editor of the Handbook on General Philosophy of Science. In 2005 there appeared two volumes of Essays in Debate with Theo Kuipers, entitled Confirmation, Empirical Progress, and Truth Approximation and Cognitive Structures in Scientific Inquiry. (shrink)

Scientific Realists argue that it would be a miracle if scientific theories were getting more predictive without getting closer to the truth; so they must be getting closer to the truth. Van Fraassen, Laudan et al. argue that owing to the underdetermination of theory by data (UDT) for all we know, it is a miracle, a fluke. So we should not believe in even the approximate truth of theories. I argue that there is a test for who is right: (...) suppose we are at the limit of inquiry. Suppose that we then have all the logically possible theories that are adequate to all the actual data. If they all resembled in their theoretical claims, since one of them must be true, all of them would then resemble it, whichever it is. We would thus be justified in saying they all approximated the truth in the degree to which they co-resembled. If they don't all co-resemble, the SRs are wrong; more predictive theories are not necessarily closer to the theoretical truth. Prior to the limit, if, in spite of our best efforts to the contrary, all the theories we can make adequate to current data tend to co-resemble, we have inductive warrant for thinking more predictive theories are closer to the truth. If they don't resemble, we have inductive warrant for thinking that more predictive theories are not necessarily closer to the truth. (shrink)

There is wide support in logic, philosophy, and psychology for the hypothesis that the probability of the indicative conditional of natural language, P(if A then B), is the conditional probability of B given A, P(B|A). We identify a conditional which is such that P(if A then B)=P(B|A) with de Finetti's conditional event, B|A. An objection to making this identification in the past was that it appeared unclear how to form compounds and iterations of conditional events. In this paper, we illustrate (...) how to overcome this objection with a probabilistic analysis, based on coherence, of these compounds and iterations. We interpret the compounds and iterations as conditional random quantities which, given some logical dependencies, may reduce to conditional events. We show how the inference to B|A from A and B can be extended to compounds and iterations of both conditional events and biconditional events. Moreover, we determine the respective uncertainty propagation rules. Finally, we make some comments on extending our analysis to counterfactuals. (shrink)

Algorithms for approximate Bayesian inference, such as those based on sampling (i.e., Monte Carlo methods), provide a natural source of models of how people may deal with uncertainty with limited cognitive resources. Here, we consider the idea that individual differences in working memory capacity (WMC) may be usefully modeled in terms of the number of samples, or “particles,” available to perform inference. To test this idea, we focus on two recent experiments that report positive associations between WMC (...) and two distinct aspects of categorization performance: the ability to learn novel categories, and the ability to switch between different categorization strategies (“knowledge restructuring”). In favor of the idea of modeling WMC as a number of particles, we show that a single model can reproduce both experimental results by varying the number of particles—increasing the number of particles leads to both faster category learning and improved strategy‐switching. Furthermore, when we fit the model to individual participants, we found a positive association between WMC and best‐fit number of particles for strategy switching. However, no association between WMC and best‐fit number of particles was found for category learning. These results are discussed in the context of the general challenge of disentangling the contributions of different potential sources of behavioral variability. (shrink)

Most standard results on structure identification in first order theories depend upon the correctness and completeness (in the limit) of the data, which are provided to the learner. These assumption are essential for the reliability of inductive methods and for their limiting success (convergence to the truth). The paper investigates inductive inference from (possibly) incorrect and incomplete data. It is shown that such methods can be reliable not in the sense of truth approximation, but in the sense that the (...) methods converge to "empirically adequate" theories, i.e. theories, which are consistent with all data (past and future) and complete with respect to a given complexity class of L-sentences. Adequate theories of bounded complexity can be inferred uniformly and effectively by polynomial-time learning algorithms. Adequate theories of unbounded complexity can be inferred pointwise by less efficient methods. (shrink)

. Prediction of crop yield is significant in order to accurately meet market requirements and proper administration of agricultural activities directed towards enhancement in yield. Several parameters such as weather, pests, biophysical and physio morphological features merit their consideration while determining the yield. However, these parameters are uncertain in their nature, thus making the determined amount of yield to be approximate. It is exactly here that the fuzzy logic comes into play. This paper elaborates an attempt to develop fuzzy (...) inference systems for crop yield prediction. Physio morphological features of Sorghum were considered. A huge database of physio morphological features such as days of 50 percent flowering, dead heart percentage, plant height, panicle length, panicle weight and number of primaries and the corresponding yield were considered for the development of the model. In order to find out the sensitivity of parameters, one-to-one, two-to-one and three-to-one combinations of input and output were considered. The results have clearly shown that panicle length contributes for the yield as the lone parameter with almost one-to-one matching between predicted yield and actual value while panicle length and panicle weight in combination seemed to play a decisive role in contributing for the yield with the prediction accuracy reflected by very low RMS value. (shrink)

ABSTRACT The term fuzzy logic has two different meanings -broad and narrow. In Zadeh's opinion, fuzzy logic is an extension of many- valued logic but having a different agenda—as generalized modus ponens, max-min inference, linguistic quantifiers etc. The question we address in this paper is whether there is something in Zadeh's specific agenda which cannot be grasped by “classiceli”, “traditional” mathematical logic. We show that much of fuzzy logic can be understood as classical deduction in a many-sorted many-valued Pavelka- (...) Lukasiewicz style rational quantification logic. This means that, besides the linguistic or approximation aspects, the logical aspect is present too and can be made explicit. (shrink)

We are often justified in acting on the basis of evidential confirmation. I argue that such evidence supports belief in non-quantificational generic generalizations, rather than universally quantified generalizations. I show how this account supports, rather than undermines, a Bayesian account of confirmation. Induction from confirming instances of a generalization to belief in the corresponding generic is part of a reasoning instinct that is typically (but not always) correct, and allows us to approximate the predictions that formal epistemology would make.

In this article, we consider estimation of the parameters of a generalized Pareto distribution and some lifetime indices such as those relating to reliability and hazard rate functions when the failure data are progressive first-failure censored. Both classical and Bayesian techniques are obtained. In the Bayesian framework, the point estimations of unknown parameters under both symmetric and asymmetric loss functions are discussed, after having been estimated using the conjugate gamma and discrete priors for the shape and scale parameters, respectively. In (...) addition, both exact and approximate confidence intervals as well as the exact confidence region for the estimators are constructed. A practical example using a simulated data set is analyzed. Finally, the performance of Bayes estimates is compared with that of maximum likelihood estimates through a Monte Carlo simulation study. (shrink)

Approximately one in six top economic research papers draws an explicitly causal conclusion. But what do economists mean when they conclude that A 'causes' B? Does 'cause' say that we can influence B by intervening on A, or is it only a label for the correlation of variables? Do quantitative analyses of observational data followed by such causal inferences constitute sufficient grounds for guiding economic policymaking? The Philosophy of Causality in Economics addresses these questions by analyzing the meaning of causal (...) claims made by economists and the philosophical presuppositions underlying the research methods used. The book considers five key causal approaches: the regularity approach, probabilistic theories, counterfactual theories, mechanisms, and interventions and manipulability. Each chapter opens with a summary of literature on the relevant approach and discusses its reception amongst economists. The text details case studies, and goes on to examine papers which have adopted the approach in order to highlight the methods of causal inference used in contemporary economics. It analyses the meaning of the causal claim put forward, and finally reconstructs the philosophical presuppositions accepted implicitly by economists. The strengths and limitations of each method of causal inference are also considered in the context of using the results as evidence for policymaking. This book is essential reading to those interested in literature on the philosophy of economics, as well as the philosophy of causality and economic methodology in general. (shrink)

The method of strong inference, wherein multiple hypotheses are constructed and a crucial experiment is carried out, is said to have special status in science because it guarantees falsifying results. However, the proposition that strong inference is in any way superior to the method of constructing and testing a single hypothesis is contradicted both by close rational analysis and by the empirical evidence. An experiment is reviewed in which subjects who conduct strong tests are much less likely to (...) discover or approximate the truth than subjects who conduct simple tests of a false hypothesis. It is concluded that a potential to falsify is necessary for a test to have corroborative value; however, arguments as to the general superiority of one type of potentially falsifying test over another have no logical basis. Any claim as to a general superiority of strong tests over simple tests would require access to information about the probability of each strategy to produce various relationships between the truth and whatever explanations are most accessible, and such information is not knowable, even in principle. (shrink)

S There is a long tradition of representing causal relationships by directed acyclic graphs (Wright, 1934 ). Spirtes ( 1994), Spirtes et al. ( 1993) and Pearl & Verma ( 1991) describe procedures for inferring the presence or absence of causal arrows in the graph even if there might be unobserved confounding variables, and/or an unknown time order, and that under weak conditions, for certain combinations of directed acyclic graphs and probability distributions, are asymptotically, in sample size, consistent. These results (...) are surprising since they seem to contradict the standard statistical wisdom that consistent estimators of causal effects do not exist for nonrandomised studies if there are potentially unobserved confounding variables. We resolve the apparent incompatibility of these views by closely examining the asymptotic properties of these causal inference procedures. We show that the asymptotically consistent procedures are ‘pointwise consistent’, but ‘uniformly consistent’ tests do not exist. Thus, no finite sample size can ever be guaranteed to approximate the asymptotic results. We also show the nonexistence of valid, consistent confidence intervals for causal effects and the nonexistence of uniformly consistent point estimators. Our results make no assumption about the form of the tests or estimators. In particular, the tests could be classical independence tests, they could be Bayes tests or they could be tests based on scoring methods such as  or . The implications of our results for observational studies are controversial and are discussed briefly in the last section of the paper. The results hinge on the following fact: it is possible to find, for each sample size n, distributions P and Q such that P and Q are empirically indistinguishable and yet P and Q correspond to different causal effects. (shrink)

A common type of inductive problem is to predict the nature of an unobserved finite sample of a given population on the basis of an observed finite sample of the same population. More precisely, given a class of events A, we examine a sample Sn having n members, of which mi belong to the class Bi. On the basis of our knowledge that mi/n of Sn have been Bi, we attempt to predict the ratio of members of Bi to members (...) of A in a sample Sr containing r unobserved members of A. This type of inference has been called “predictive inference” by Carnap. It is not necessary to argue that all inductive problems reduce to this form; we merely observe that such problems frequently arise, and that they have practical and theoretical importance. In The Short Run I suggested that this kind of problem could be handled by first determining the long run probability P of Bi, relative to A of Bi, to A in the observed sample Sn) and then predicting that the relative frequency of Bi within the unobserved sample Sr will approximate P sufficiently for practical purposes. The foregoing procedure requires a rule of each of two types: a rule for the ascertainment of the values of long run probabilities, and a rule for the application of knowledge of long run probabilities to predictions in the short run. The Short Run was not concerned with the nature and justification of rules of the first type, but rather sought to justify a rule of the second type on the assumption that we already possess knowledge of long run probabilities. (shrink)

We present a system for deciding whether a given sentence can be inferred from text. Each sentence is represented as a directed graph (extracted from a dependency parser) in which the nodes represent words or phrases, and the links represent syntactic and semantic relationships. We develop a learned graph matching model to approximate entailment by the amount of the sentence’s semantic content which is contained in the text. We present results on the Recognizing Textual Entailment dataset (Dagan et al., (...) 2005), and show that our approach outperforms Bag- Of-Words and TF-IDF models. (shrink)

We prove that the problem of determining the minimum propositional proof length is NP- hard to approximate within a factor of 2 log 1 - o(1) n . These results are very robust in that they hold for almost all natural proof systems, including: Frege systems, extended Frege systems, resolution, Horn resolution, the polynomial calculus, the sequent calculus, the cut-free sequent calculus, as well as the polynomial calculus. Our hardness of approximation results usually apply to proof length measured either (...) by number of symbols or by number of inferences, for tree-like or dag-like proofs. We introduce the Monotone Minimum (Circuit) Satisfying Assignment problem and reduce it to the problems of approximation of the length of proofs. (shrink)

The epistemology of the historical sciences has been debated recently. Cleland argued that the effects of the past overdetermine it. Turner argued that the past is underdetermined by its effects because of the decay of information from the past. I argue that the extent of over- and underdetermination cannot be approximated by philosophical inquiry. It is an empirical question that each historical science attempts to answer. Philosophers should examine how paradigmatic cases of historical science handled underdetermination or utilized overdetermination. I (...) analyze such a paradigmatic case, Darwin’s phylogenetic inferences. Darwin proceeded in three consecutive stages. The initial inference that there was some common cause of homologies was usually overdetermined. The final inference of the character traits of ancestor species was usually underdetermined. The second stage inference of the causal net that connected the species that share some common cause was inbetween. A comparison with Comparative Historical Linguistics demonstrates similar three stages of inference that move from the over- to the underdetermined. (shrink)

The free energy principle (FEP) portends to provide a unifying principle for the biological and cognitive sciences. It states that for a system to maintain non-equilibrium steady-state with its environment it must minimise its (information-theoretic) free energy. Under the FEP, to minimise free energy is equivalent to engaging in approximate Bayesian inference. According to the FEP, therefore, inference is at the explanatory base of biology and cognition. In this paper, we discuss a specific challenge to this inferential (...) formulation of adaptive self-organisation. We call it the universal ethology challenge: it states that the FEP cannot unify biology and cognition, for life itself (or adaptive self-organisation) does not require inferential routines to select adaptive solutions to environmental pressures (as mandated by the FEP). We show that it is possible to overcome the universal ethology challenge by providing a cautious and exploratory treatment of inference under the FEP. We conclude that there are good reasons for thinking that the FEP can unify biology and cognition under the notion of approximate Bayesian inference, even if further challenges must be addressed to properly draw such a conclusion. (shrink)

In this article, a new adaptive fuzzy wavelet neural network model is proposed for nonlinear function approximation problems. The AFWNN model is based on the traditional Takagi-Sugeno-Kang fuzzy system. Specifically, this model replaces the membership functions of fuzzy rules with wavelet basis functions, which are known to have time and frequency localization properties, i.e., they can approximate patterns both in the time and frequency domains. The structure of the AFWNN model is derived from that of the adaptive neuro-fuzzy (...) class='Hi'>inference system. However, the AFWNN improves over the ANFIS by replacing Gaussian functions in the hidden layer with wavelet basis functions. The AFWNN model is trained using a gradient-based optimization algorithm. The AFWNN is then tested on three function approximation problems of time series prediction. For certain types of nonlinear time series, for instance fractal processes, the AFWNN is found to be substantially more accurate than alternative methods. (shrink)

This paper argues against a particular version of the inference from the success of a scientific theory to the claim that the theory must be approximately true to some extent. The kind of success at issue is comparative, where one theory is more empirically successful than its rival if that theory predicts phenomena that are inexplicable or anomalous according to its rival. A theory that exhibits this kind of comparative success can be seen as thereby achieving empirical progress over (...) its rival. David Harker has developed a form of selective scientific realism based on the idea that this kind of success is evidence for the approximate truth of the parts of theories responsible for such success. Counterexamples to Harker’s position are cases in which a theory is more successful than its rival in virtue of containing parts that are not even approximately true. In order to identify some counterexamples to Harker’s position, this paper considers four historical cases that Greg Frost-Arnold has recently used to motivate a novel historical challenge to realism called the Problem of Misleading Evidence. This paper argues that these four cases are counterexamples to Harker’s position, and that they provide a strong reason to doubt his position and the kind of success-to-truth inference that he defends. (shrink)

This paper is a sequel to an earlier result of the authors that in making inferences from certain probabilistic knowledge bases the maximum entropy inference process, ME, is the only inference process respecting “common sense.” This result was criticized on the grounds that the probabilistic knowledge bases considered are unnatural and that ignorance of dependence should not be identified with statistical independence. We argue against these criticisms and also against the more general criticism that ME is representation dependent. (...) In a final section, however, we provide a criticism of our own of ME, and of inference processes in general, namely that they fail to satisfy compactness. (shrink)

The main aim of this paper is to revisit the curve fitting problem using the reliability of inductive inference as a primary criterion for the ‘fittest' curve. Viewed from this perspective, it is argued that a crucial concern with the current framework for addressing the curve fitting problem is, on the one hand, the undue influence of the mathematical approximation perspective, and on the other, the insufficient attention paid to the statistical modeling aspects of the problem. Using goodness-of-fit as (...) the primary criterion for ‘best', the mathematical approximation perspective undermines the reliability of inference objective by giving rise to selection rules which pay insufficient attention to ‘accounting for the regularities in the data'. A more appropriate framework is offered by the error-statistical approach, where (i) statistical adequacy provides the criterion for assessing when a curve captures the regularities in the data adequately, and (ii) the relevant error probabilities can be used to assess the reliability of inductive inference. Broadly speaking, the fittest curve (statistically adequate) is not determined by the smallness if its residuals, tempered by simplicity or other pragmatic criteria, but by the nonsystematic (e.g. white noise) nature of its residuals. The advocated error-statistical arguments are illustrated by comparing the Kepler and Ptolemaic models on empirical grounds. ‡I am grateful to Deborah Mayo and Clark Glymour for many valuable suggestions and comments on an earlier draft of the paper; estimating the Ptolemaic model was the result of Glymour's prompting and encouragement. †To contact the author, please write to: Department of Economics, Virginia Tech 3019 Pamplin Hall (0316), Blacksburg, VA 24061; e-mail: [email protected]. (shrink)

The exegesis of sacred rites in the Talmud is subject to a restriction on the iteration and composition of inference rules. In order to determine the scope and limits of that restriction, the sages of the Talmud deploy those very same inference rules. We present the remarkable features of this early use of self-reference to navigate logical constraints and uncover the hidden complexity behind the sages? arguments. Appendix 11 contains a translation of the relevant sugya. 1Hebrew and Aramaic (...) transliteration approximates traditional Sephardic pronunciation, which is closer to academic standard transliteration than the various Ashkenazic pronunciations, yet is legible. Specific references follow the convention of folio (number), side (a or b), number of lines from the top or (if negative) bottom of the page. (shrink)

Gigerenzer and his collaborators have shown that the Take the Best heuristic (TTB) approximates optimal decision behavior for many inference problems. We studied the effect of incomplete cue knowledge on the quality of this approximation. Bayesian algorithms clearly outperformed TTB in case of partial cue knowledge, especially when the validity of the recognition cue is assumed to be low.

Re-Engineering Philosophy for Limited Beings is about new approaches to many of the big topics in philosophy of science today, but with a very different take. To begin with, we are urged to reject the received Cartesian-Laplacean myths: Descartes’ certainty and Laplace’s computational omniscience. Instead, Wimsatt re-engineers a philosophy for human beings with all their cognitive limitations. His approaches find their starting point in the actual practices of scientists themselves, which he strongly identifies with engineering practices as the source of (...) researchers’ solutions for dealing with a complex world. He aims to construct an understanding of scientific methodology around the central role of reduction. But he dismisses eliminative reductionism in favor of a heuristic-based realist view. Wimsatt’s world is a complex one, and this means that science needs to do away with all the absolute and simple answers, because they do not reflect the world we are living in. A complex world requires the mindset and tinkering of an engineer to uncover its reality. The appropriate response must be heuristics all the way down as we constantly seek out reliable inferences on often shifting ground. To this end, we aim for models and theories that are robust, just as engineers aim to build robust machines. And although errors occur and approaches are fallible, they allow us to continually adapt the heuristics applied and sharpen our perceptions so as to develop more refined tools for investigating and understanding the world. (shrink)

In this paper, we study natural language constructions which were first examined by Barwise: The richer the country, the more powerful some of its officials. Guided by Barwise’s observations, we suggest that conceivable interpretations of such constructions express the existence of various similarities between partial orders such as homomorphism or embedding. Semantically, we interpret the constructions as polyadic generalized quantifiers restricted to finite models. We extend the results obtained by Barwise by showing that similarity quantifiers are not expressible in elementary (...) logic over finite models. We also investigate whether the proposed readings are sound from the cognitive perspective. We prove that almost all similarity quantifiers are intractable. This leads us to first-order variants, which only approximate the strong readings, but are cognitively more plausible. Driven by the question of ambiguity, we recall Barwise’s argumentation in favour of strong readings, enriching it with some arguments of our own. Given that Barwise-like sentences are indeed ambiguous, we use a generalized Strong Meaning Hypothesis to derive predictions for their verification. Finally, we propose a hypothesis according to which conflicting pressures of communication and cognition might give rise to an ambiguous construction, provided that different semantic variants of the construction withstand different pressures involved in its usage. (shrink)

This article describes the use of continuous vector space models for reasoning with a formal knowledge base. The practical significance of these models is that they support fast, approximate but robust inference and hypothesis generation, which is complementary to the slow, exact, but sometimes brittle behaviour of more traditional deduction engines such as theorem provers.The article explains the way logical connectives can be used in semantic vector models, and summarizes the development of Predication-based Semantic Indexing, which involves the (...) use of Vector Symbolic Architectures to represent the concepts and relationships from a knowledge base of subject-predicate-object triples. Experiments show that the use of continuous models for formal reasoning is not only possible, but already demonstrably effective for some recognized informatics tasks, and showing promise in other traditional problem areas. Examples described in this article include: predicting new uses for existing drugs in biomedical informatics; removing unwanted meanings from search results in information retrieval and concept navigation; type inference from attributes; comparing words based on their orthography; and representing tabular data, including modelling numerical values.The algorithms and techniques described in this article are all publicly released and freely available in the Semantic Vectors open-source software package.1. (shrink)

Predictive processing (PP) is now a prominent theoretical framework in the philosophy of mind and cognitive science. This review focuses on PP research with a relatively philosophical focus, taking stock of the framework and discussing new directions. The review contains an introduction that describes the full PP toolbox; an exploration of areas where PP has advanced understanding of perceptual and cognitive phenomena; a discussion of PP's impact on foundational issues in cognitive science; and a consideration of the philosophy of science (...) of PP. The overall picture is that PP is a fruitful framework, with exciting new directions awaiting exploration. (shrink)

To become more broadly applicable, positions on AI ethics require perspectives from non-Western regions and cultures such as China and Japan. In this paper, we propose that the addition of the concept of harmony to the discussion on ethical AI would be highly beneficial due to its centrality in East Asian cultures and its applicability to the challenge of designing AI for social good. We first present a synopsis of different definitions of harmony in multiple contexts, such as music and (...) society, which reveals that the concept is, at its core, about well-balanced relationships and appropriate actions which give rise to order, balance, and aesthetically pleasing phenomena. The mediator for these well-balanced relationships isTaktwhich is an ability to act thoughtfully and sensibly according to the specific situation and to put things into proportion and order. We propose that the central challenge of building harmonizing AI is to make intelligent systems tactful and also to design and use them tactfully. For an AI system to become tactful, it needs to be able to have an advanced sensitivity to the specific contexts which it is in and their social and ethical implications and have the capability of approximately inferring the emotional and cognitive states of people with whom it is interacting. (shrink)

Most current statistical natural language processing models use only local features so as to permit dynamic programming in inference, but this makes them unable to fully account for the long distance structure that is prevalent in language use. We show how to solve this dilemma with Gibbs sam- pling, a simple Monte Carlo method used to perform approximate inference in factored probabilistic models. By using simulated annealing in place of Viterbi decoding in sequence models such as HMMs, (...) CMMs, and CRFs, it is possible to incorporate non-local structure while preserving tractable inference. We use this technique to augment an existing CRF-based information extraction system with long-distance dependency models, enforcing label consistency and extraction template consistency constraints. This technique results in an error reduction of up to 9% over state-of-the-art systems on two established information extraction tasks. (shrink)

An interdisciplinary account of phenomenal unity, investigating how experiential wholes can be characterized and how such characterizations can be analyzed computationally. How can we account for phenomenal unity? That is, how can we characterize and explain our experience of objects and groups of objects, bodily experiences, successions of events, and the attentional structure of consciousness as wholes? In this book, Wanja Wiese develops an interdisciplinary account of phenomenal unity, investigating how experiential wholes can be characterized and how such characterization can (...) be analyzed conceptually as well as computationally. Wiese first addresses how the unity of consciousness can be characterized phenomenologically, discussing what it is like to experience wholes and what is the experiential contribution of phenomenal unity. Considering the associated conceptual and empirical issues, he draws connections to phenomenological accounts and research on Gestalt theory. The results show how the attentional structure of experience, the experience of temporal flow, and different types of experiential wholes contribute to our sense of phenomenal unity. Moreover, characterizing phenomenal unity in terms of the existence of a single global phenomenal state is neither necessary nor sufficient to adequately address the problem of phenomenal unity. Wiese then suggests that the concepts and ideas of predictive processing can be used to analyze phenomenal unity computationally. The result is both a conceptual framework and an interdisciplinary account: the regularity account of phenomenal unity. According to this account, experienced wholes correspond to a hierarchy of connecting regularities. The brain tracks these regularities by hierarchical prediction error minimization, which approximates hierarchical Bayesian inference. (shrink)

In many learning or inference tasks human behavior approximates that of a Bayesian ideal observer, suggesting that, at some level, cognition can be described as Bayesian inference. However, a number of findings have highlighted an intriguing mismatch between human behavior and standard assumptions about optimality: People often appear to make decisions based on just one or a few samples from the appropriate posterior probability distribution, rather than using the full distribution. Although sampling-based approximations are a common way to (...) implement Bayesian inference, the very limited numbers of samples often used by humans seem insufficient to approximate the required probability distributions very accurately. Here, we consider this discrepancy in the broader framework of statistical decision theory, and ask: If people are making decisions based on samples—but as samples are costly—how many samples should people use to optimize their total expected or worst-case reward over a large number of decisions? We find that under reasonable assumptions about the time costs of sampling, making many quick but locally suboptimal decisions based on very few samples may be the globally optimal strategy over long periods. These results help to reconcile a large body of work showing sampling-based or probability matching behavior with the hypothesis that human cognition can be understood in Bayesian terms, and they suggest promising future directions for studies of resource-constrained cognition. (shrink)