The main objective of the paper is to propose a frequentist interpretation of probability in the context of model-based induction, anchored on the Strong Law of Large Numbers (SLLN) and justifiable on empirical grounds. It is argued that the prevailing views in philosophy of science concerning induction and the frequentist interpretation of probability are unduly influenced by enumerative induction, and the von Mises rendering, both of which are at odds with frequentist model-based (...) class='Hi'>induction that dominates current practice. The differences between the two perspectives are brought out with a view to defend the model-based frequentist interpretation of probability against certain well-known charges, including [i] the circularity of its definition, [ii] its inability to assign ‘single event’ probabilities, and [iii] its reliance on ‘random samples’. It is argued that charges [i]–[ii] stem from misidentifying the frequentist ‘long-run’ with the von Mises collective. In contrast, the defining characteristic of the long-run metaphor associated with model-based induction is neither its temporal nor its physical dimension, but its repeatability (in principle); an attribute that renders it operational in practice. It is also argued that the notion of a statistical model can easily accommodate non-IID samples, rendering charge [iii] simply misinformed. (shrink)

Category-based induction is an inferential mechanism that uses knowledge of conceptual relations in order to estimate how likely is for a property to be projected from one category to another. During the last decades, psychologists have identified several features of this mechanism, and they have proposed different formal models of it. In this article; we propose a new mathematical model for category-based induction based on distances on conceptual spaces. We show how this model (...) can predict most of the properties of this kind of reasoning while providing a solid theoretical foundation for it. We also show that it subsumes some of the previous models proposed in the literature and that it generates new predictions. (shrink)

This paper argues that the linguistic approach to analyzing induction, according to which induction is a type of inference or argument composed of statements or propositions, is unsuitable to account for scientific reasoning. Consequently, a novel approach to induction in model-based science is suggested. First, in order to show their adherence to the linguistic treatment of induction, two strategies are reviewed: (i) Carnap and Reichenbach’s attempts to justify induction and (ii) Norton’s recent material (...) theory of induction. Second, three reasons are provided to support the claim that the linguistic treatment of induction is insufficient in accounting for model-based reasoning in science. Finally, a framework focused on models—rather than statements or propositions—is suggested to address induction in science. William Whewell’s theory of induction is briefly outlined as an example of a non-propositional treatment of induction that is consistent with model-based scientific practice. (shrink)

This paper presents a computational model of the way humans inductively identify and aggregate concepts from the low-level stimuli they are exposed to. Based on the idea that humans tend to select the simplest structures, it implements a dynamic hierarchical chunking mechanism in which the decision whether to create a new chunk is based on an information-theoretic criterion, the Minimum Description Length (MDL) principle. We present theoretical justifications for this approach together with results of an experiment in (...) which participants, exposed to meaningless symbols, have been implicitly encouraged to create high-level concepts by grouping them. Results show that the designed model, called hereafter MDLChunker, makes precise quantitative predictions both on the kind of chunks created by the participants and also on the moment at which these creations occur. They suggest that the simplicity principle used to design MDLChunker is particularly efficient to model chunking mechanisms. The main interest of this model over existing ones is that it does not require any adjustable parameter. (shrink)

Automated Software Testing (AST) using Model Checking is in this article epistemologically analysed in order to argue in favour of a model-based reasoning paradigm in computer science. Preliminarily, it is shown how both deductive and inductive reasoning are insufficient to determine whether a given piece of software is correct with respect to specified behavioural properties. Models algorithmically checked in Model Checking to select executions to be observed in Software Testing are acknowledged as analogical models which establish (...) isomorphic relations with the target system’s data set. Analogical models developed in AST are presented as abductive models providing hypothetical explanations to observed executions. The model assumption—algorithmic check—software testing process is understood as the abduction—deduction—induction process defining the selective abduction and turned to isolate a set of model-based hypotheses concerning the target system behaviours. A manipulative abduction process is finally recognized in the practice of adapting, abstracting and refining models that do not provide successful predictions. (shrink)

According to usage‐based approaches to language acquisition, linguistic knowledge is represented in the form of constructions—form‐meaning pairings—at multiple levels of abstraction and complexity. The emergence of syntactic knowledge is assumed to be a result of the gradual abstraction of lexically specific and item‐based linguistic knowledge. In this article, we explore how the gradual emergence of a network consisting of constructions at varying degrees of complexity can be modeled computationally. Linguistic knowledge is learned by observing natural language utterances in (...) an ambiguous context. To determine meanings of constructions starting from ambiguous contexts, we rely on the principle of cross‐situational learning. While this mechanism has been implemented in several computational models, these models typically focus on learning mappings between words and referents. In contrast, in our model, we show how cross‐situational learning can be applied consistently to learn correspondences between form and meaning beyond such simple correspondences. (shrink)

I begin with a typology of reasoning and cross it with types of processes. I demonstrate that the thrust of Plato’s Republic is theory-building. This involves the critical and dialectic processes which are paradigms of Platonic methodology. Book I displays abductive analogical reasoning joined by an induction that is embedded in a deduction; hence there is a deduction–induction–abduction chain. In Book VI, Plato constructs a visual model of the divided line, which also displays model-based and (...) abductive hypothesis generation that is essential to theory building. Book VII provides an abductive metaphor model of the allegory of the cave. Both models depict degrees of reality and the ascendency of knowledge. The multimodal model-based allegory has far reaching applications from criminal justice to information systems. I conclude by capturing the narrative of the Republic as a critical and dialectic process of theory building using deductive–inductive–abductive chains, an abductive visual model and an abductive metaphor model. Hence, the Republic is simultaneously a masterpiece of deductive reasoning and a marvel of complex model-based abduction, involving visual models, analogies and metaphors. (shrink)

In this paper we address the classical but still pending question regarding Thought Experiments: how can an imagined scenario bring new information or insight about the actual world? Our claim is that this general problem actually embraces two distinct questions: how can the creation of a just imagined scenario become functional to either a scientific or a philosophical research? and how can Thought Experiments hold a strong inferential power if their structures “do not seem to translate easily into standard forms (...) of deduction or induction”? :534–541, 1999). We contend that, in order to answer both questions, we should consider the relation between the creation of the imagined scenario and the inferential power of Thought Experiments. Specifically, we will analyze Thought Experiments from an eco-cognitive point of view as goal-oriented objects, explaining their inferential power considering their generation as the result of abductive cognition and the construction of an imagined scenario as a process of scientific modeling. This will lead us to consider the creation of a Thought Experiment as a case of sophisticated model-based abduction. (shrink)

Computational models of meaning trained on naturally occurring text successfully model human performance on tasks involving simple similarity measures, but they characterize meaning in terms of undifferentiated bags of words or topical dimensions. This has led some to question their psychological plausibility (Murphy, 2002;Schunn, 1999). We present here a fully automatic method for extracting a structured and comprehensive set of concept descriptions directly from an English part‐of‐speech‐tagged corpus. Concepts are characterized by weighted properties, enriched with concept–property types that approximate (...) classical relations such as hypernymy and function. Our model outperforms comparable algorithms in cognitive tasks pertaining not only to concept‐internal structures (discovering properties of concepts, grouping properties by property type) but also to inter‐concept relations (clustering into superordinates), suggesting the empirical validity of the property‐based approach. (shrink)

Under what conditions does machine learning (ML) model opacity inhibit the possibility of explaining and understanding phenomena? In this article, I argue that nonepistemic values give shape to the ML opacity problem even if we keep researcher interests fixed. Treating ML models as an instance of doing model-based science to explain and understand phenomena reveals that there is (i) an external opacity problem, where the presence of inductive risk imposes higher standards on externally validating models, and (ii) (...) an internal opacity problem, where greater inductive risk demands a higher level of transparency regarding the inferences the model makes. (shrink)

Les modèles basés sur des agents en interactions, constituent des systèmes sociaux complexes, qui peuvent être simulés par informatiques. Ils se répandent dans les sciences économiques et sociales - comme dans la plupart des sciences des systèmes complexes. Des énigmes épistémologiques (ré)apparaissent. On a souvent opposé modèles et investigations empiriques : d’un côté, on considère les sciences empiriques fondées sur une observation méthodique (enquêtes, expériences) tandis que de l’autre, on conçoit les approches théoriques et la modélisation comme s’appuyant sur une (...) approche conceptuelle ou hypothético-déductive. la simulation a de son coté souvent été comparée à une forme d’expérience ou à une méthode intermédiaire entre la théorie et l’expérience. Tesfatsion a parlé de « laboratoire computationnel » comme d’une manière d’étudier « les comportements des systèmes complexes au moyen d’expériences sous contrôle qu’on peut répéter (réplicable)» et Axelrod a proclamé que la simulation serait « une troisième manière de pratiquer la science dans les sciences sociales », entre l’induction et la déduction. Nous introduisons de nouveaux concepts épistémologiques afin de montrer dans quelle mesure les auteurs ont raison lorsqu'ils se concentrent sur une signification empirique, instrumentale ou conceptuelle de leur modèle ou simulation. La première partie du chapitre discute plus particulièrement de l'épistémologie des modèles économiques à partir des travaux d’Hausman, Guala, Mäki, Sugden, Schelling etc. pour expliquer les divergences entre modèles et simulations. En distinguant entre modèles et simulations, comme entre entre types de modèles, types de simulations informatiques et types d'empiricité obtenue par une simulation, la seconde partie donne la possibilité de comprendre plus précisément - et ensuite de justifier - la diversité des positions épistémologiques présentées dans la première partie. En utilisant les notion de sous-symbolisation (due à Smolensky) et, de hiérarchie dénotationnelle (due à Goodman), une attention particulière est accordée à la multiplicité des pouvoirs dénotationnels des symboles en jeu dans les modèles complexes et les simulations informatiques. Selon cette grille d'analyse, on peut déterminer, dans chaque cas particulier son statut épistémique et la crédibilité qui peut y être associée. -/- Ce chapitre est une traduction (par Gilles Campagnolo) réviséee et augmentée par les auteurs de : Agent-Based Models and Simulations in Economics and Social Sciences: From Conceptual Exploration to Distinct Ways of Experimenting, Journal of Artificial Societies and Social Simulation 13 (1) 5 DOI: 10.18564/jasss.1532. (shrink)

Computational models of meaning trained on naturally occurring text successfully model human performance on tasks involving simple similarity measures, but they characterize meaning in terms of undifferentiated bags of words or topical dimensions. This has led some to question their psychological plausibility (Murphy, 2002;Schunn, 1999). We present here a fully automatic method for extracting a structured and comprehensive set of concept descriptions directly from an English part‐of‐speech‐tagged corpus. Concepts are characterized by weighted properties, enriched with concept–property types that approximate (...) classical relations such as hypernymy and function. Our model outperforms comparable algorithms in cognitive tasks pertaining not only to concept‐internal structures (discovering properties of concepts, grouping properties by property type) but also to inter‐concept relations (clustering into superordinates), suggesting the empirical validity of the property‐based approach. (shrink)

By action model, we understand any logic-based representation of effects and executability preconditions of individual actions within a certain domain. In the context of artificial intelligence, such models are necessary for planning and goal-oriented automated behaviour. Currently, action models are commonly hand-written by domain experts in advance. However, since this process is often difficult, time-consuming, and error-prone, it makes sense to let agents learn the effects and conditions of actions from their own observations. Even though the research in (...) the area of action learning, as a certain kind of inductive reasoning, is relatively young, there already exist several distinctive action learning methods. We will try to identify the collection of the most important properties of these methods, or challenges that they are trying to overcome, and briefly outline their impact on practical applications. (shrink)

A productive way to think about imagistic mental models of physical systems is as though they were sources of quasi‐empirical evidence. People depict or imagine events at those points in time when they would experiment with the world if possible. Moreover, just as they would do when observing the world, people induce patterns of behavior from the results depicted in their imaginations. These resulting patterns of behavior can then be cast into symbolic rules to simplify thinking about future problems and (...) to reveal higher order relationships. Using simple gear problems, three experiments explored the occasions of use for, and the inductive transitions between, depictive models and number‐based rules. The first two experiments used the convergent evidence of problem‐solving latencies, hand motions, referential language and error data to document the initial use of a model, the induction of rules from the modeling results, and the fallback to a model when a rule fails. The third experiment explored the intermediate representations that facilitate the induction of rules from depictive models. The strengths and weaknesses of depictive modeling and more analytic systems of reasoning are delineated to motivate the reasons for these transitions. (shrink)

This work emerged from funded research examining collaboration among stake-holder organizations present at three U.S. nuclear weapons complex sites. The authors examine issues such as how and why stakeholder groups form collaborative alliances when dealing with the target organization, what leaders of stakeholder organizations actually think about when collaborating to deal with the target organization, and what outcomes result from the collaboration process. Drawing on stakeholder theory and research in interorganizational collaboration, the authors used an inductive, interview-based methodology to (...) build a model of collaboration among nonprofit stakeholder groups. The model contributes to the descriptive stream of stakeholder theory and, in turn, has implications for the instrumental stream. The model also offers implications for future researchers, leaders of stakeholder alliances, and leaders of target organizations. (shrink)

This paper is an effort to realize and explore the connections that exist between nonmonotonic logic and confirmation theory. We pick up one of the most wide-spread nonmonotonic formalisms – default logic – and analyze to what extent and under what adjustments it could work as a logic of induction in the philosophical sense. By making use of this analysis, we extend default logic so as to make it able to minimally perform the task of a logic of (...) class='Hi'>induction, having as a result a system which we believe has interesting properties from the standpoint of theory of confirmation. It is for instance able to represent chains of inductive rules as well as to reason paraconsistently on the conclusions obtained from them. We then use this logic to represent some traditional ideas concerning confirmation theory, in particular the ones proposed by Carl Hempel in his classical paper "Studies in the Logic of Confirmation" of 1945 and the ones incorporated in the so-called abductive and hy-pothetico-deductive models. (shrink)

The implementation of an artificial neural network for predicting induction heating region locations is proposed in this research. Steel plate deformations during the induction heating process are produced using an analytical solution derived from electromagnetic and plate theory. The plate transform following vertical displacements in each divided area was used as input of neural following desired shape of the steel plate and the specified heating areas for induction treatment as output parameters to predict and evaluate the (...) class='Hi'>model. A dataset used 90% for training and remaining 10% for testing to implement on the efficient models when changing hidden layer and its neurons relatively. The trial and error for analyzing and predicting heating-affected regions with the ANNs model reached the high average accuracy and lowest mean square error at 98.08% and 0.00913, respectively. Consequently, the feasibility test indicates that the developed approach may be well utilized to identify the heating positions by grid area in order to achieve the desired plate deformation. Moreover, the analysis of vertical displacement during induction heating and its response behaviour of steel plate based on thermo-mechanical are also addressed. (shrink)

This paper presents a novel approach to the unsupervised learning of syntactic analyses of natural language text. Most previous work has focused on maximizing likelihood according to generative PCFG models. In contrast, we employ a simpler probabilistic model over trees based directly on constituent identity and linear context, and use an EM-like iterative procedure to induce structure. This method produces much higher quality analyses, giving the best published results on the ATIS dataset.

This paper presents a novel approach to the unsupervised learning of syntactic analyses of natural language text. Most previous work has focused on maximizing likelihood according to generative PCFG models. In contrast, we employ a simpler probabilistic model over trees based directly on constituent identity and linear context, and use an EM-like iterative procedure to induce structure. This method produces much higher quality analyses, giving the best published results on the ATIS dataset.

The present study examined the effects of semantic structure on simple inductive judgments about category members. For a particular category, subjects were told that one of the species had a given property and were asked to estimate the proportion of instances in the other species that possessed the property. The results indicated that category structure—in particular, the typicality of the species—influenced subjects' judgments. These results were interpreted by models based on the following assumption: When little is known about the (...) underlying distribution of a property, subjects assume that the distribution mirrors that of better-known properties. For this reason, if subjects learn that an unknown property is possessed by a typical species, they are more likely to generalize than if the same fact had been learned about an atypical species. (shrink)

The Emergic Cognitive Model (ECM) is a unified computational model of visual filling-in based on the Emergic Network architecture. The Emergic Network was designed to help realize systems undergoing continuous change. In this thesis, eight different filling-in phenomena are demonstrated under a regime of continuous eye movement (and under static eye conditions as well). -/- ECM indirectly demonstrates the power of unification inherent with Emergic Networks when cognition is decomposed according to finer-grained functions supporting change. These can (...) interact to raise additional emergent behaviours via cognitive re-use, hence the Emergic prefix throughout. Nevertheless, the model is robust and parameter free. Differential re-use occurs in the nature of model interaction with a particular testing paradigm. -/- ECM has a novel decomposition due to the requirements of handling motion and of supporting unified modelling via finer functional grains. The breadth of phenomenal behaviour covered is largely to lend credence to our novel decomposition. -/- The Emergic Network architecture is a hybrid between classical connectionism and classical computationalism that facilitates the construction of unified cognitive models. It helps cutting up of functionalism into finer-grains distributed over space (by harnessing massive recurrence) and over time (by harnessing continuous change), yet simplifies by using standard computer code to focus on the interaction of information flows. Thus while the structure of the network looks neurocentric, the dynamics are best understood in flowcentric terms. Surprisingly, dynamic system analysis (as usually understood) is not involved. An Emergic Network is engineered much like straightforward software or hardware systems that deal with continuously varying inputs. Ultimately, this thesis addresses the problem of reduction and induction over complex systems, and the Emergic Network architecture is merely a tool to assist in this epistemic endeavour. -/- ECM is strictly a sensory model and apart from perception, yet it is informed by phenomenology. It addresses the attribution problem of how much of a phenomenon is best explained at a sensory level of analysis, rather than at a perceptual one. As the causal information flows are stable under eye movement, we hypothesize that they are the locus of consciousness, howsoever it is ultimately realized. (shrink)

The fault prediction and abductive fault diagnosis of three-phase induction motors are of great importance for improving their working safety, reliability, and economy; however, it is difficult to succeed in solving these issues. This paper proposes a fault analysis method of motors based on modified fuzzy reasoning spiking neural P systems with real numbers for fault prediction and abductive fault diagnosis. To achieve this goal, fault fuzzy production rules of three-phase induction motors are first proposed. Then, the (...) rMFRSNPS is presented to model the rules, which provides an intuitive way for modelling the motors. Moreover, to realize the parallel data computing and information reasoning in the fault prediction and diagnosis process, three reasoning algorithms for the rMFRSNPS are proposed: the pulse value reasoning algorithm, the forward fault prediction reasoning algorithm, and the backward abductive fault diagnosis reasoning algorithm. Finally, some case studies are given, in order to verify the feasibility and effectiveness of the proposed method. (shrink)

In this article, 41 models of covariation detection from 2 × 2 contingency tables were evaluated against past data in the literature and against data from new experiments. A new model was also included based on a limiting case of the normative phi‐coefficient under an extreme rarity assumption, which has been shown to be an important factor in covariation detection (McKenzie & Mikkelsen, 2007) and data selection (Hattori, 2002; Oaksford & Chater, 1994, 2003). The results were supportive of (...) the new model. To investigate its explanatory adequacy, a rational analysis using two computer simulations was conducted. These simulations revealed the environmental conditions and the memory restrictions under which the new model best approximates the normative model of covariation detection in these tasks. They thus demonstrated the adaptive rationality of the new model. (shrink)

The inductive category formation framework, an influential set of theories of learning in psychology and artificial intelligence, is deeply flawed. In this framework a set of necessary and sufficient features is taken to define a category. Such definitions are not functionally justified, are not used by people, and are not inducible by a learning system. Inductive theories depend on having access to all and only relevant features, which is not only impossible but begs a key question in learning. The crucial (...) roles of other cognitive processes (such as explanation and credit assignment) are ignored or oversimplified. Learning necessarily involves pragmatic considerations that can only be handled by complex cognitive processes.We provide an alternative framework for learning according to which category definitions must be based on category function. The learning system invokes other cognitive processes to accomplish difficult tasks, makes inferences, analyses and decides among potential features, and specifies how and when categories are to be generated and modified. We also examine the methodological underpinnings of the two approaches and compare their motivations. (shrink)

Coherence and correspondence are classical contenders as theories of truth. In this paper we examine them instead as interacting factors in the dynamics of belief across epistemic networks. We construct an agent-based model of network contact in which agents are characterized not in terms of single beliefs but in terms of internal belief suites. Individuals update elements of their belief suites on input from other agents in order both to maximize internal belief coherence and to incorporate ‘trickled in’ (...) elements of truth as correspondence. Results, though often intuitive, prove more complex than in simpler models (Hegselmann & Krause 2002, 2006; Grim, Singer, Reade & Fisher 2015). The optimistic finding is that pressures toward internal coherence can exploit and expand on small elements of truth as correspondence is introduced into epistemic networks. Less optimistic results show that pressures for coherence can also work directly against the incorporation of truth, particularly when coherence is established first and new data is introduced later. (shrink)

There are two important traditions in the philosophy of induction. According to one tradition, which has dominated for the last couple of centuries, inductive arguments are warranted by rules. Bayesianism is the most popular view within this tradition. Rules of induction provide functional accounts of inductive support, but no rule is universal; hence, no rule is by itself an accurate model of inductive support. According to another tradition, inductive arguments are not warranted by rules but by matters (...) of fact. Norton’s material theory of induction (MTI) is an influential view within this tradition. Norton’s MTI fails to provide an account of inductive support, but it provides a good account of inductive warrant that can help us define the domain of validity of each rule of induction. Despite their limitations, both approaches to induction are illuminating important aspects of how relations of inductive support work. In this article I present a hybrid theory of induction (HTI), in which I acknowledge and articulate the role of both rules and matters of fact in our understanding of inductive support. According to the HTI, rules of induction accurately describe relations of inductive support when they are warranted, and a rule of induction is warranted if the right facts about the matter of the induction obtain. Crucially, the HTI allows us to address the main challenges that each tradition faces while retaining their strengths, thus obtaining a functional and accurate account of inductive support. The HTI also provides a useful general framework to examine and understand induction, to make sense of how different rules of induction can coexist and to tackle some problems in epistemology. Moreover, the HTI allows us to clarify and resolve some current debates on induction, like the apparent divide between Norton and rule-based theorists. (shrink)

Within analytic philosophy, induction has been seen as a problem concerning inferences that have been analysed as relations between sentences. In this article, we argue that induction does not primarily concern relations between sentences, but between properties and categories. We outline a new approach to induction that is based on two theses. The first thesis is epistemological. We submit that there is not only knowledge-how and knowledge-that, but also knowledge-what. Knowledge-what concerns relations between properties and categories (...) and we argue that it cannot be reduced to knowledge-that. We support the partition of knowledge by mapping it onto the long-term memory systems: procedural, semantic and episodic memory. The second thesis is that the role of inductive reasoning is to generate knowledge-what. We use conceptual spaces to model knowledge-what and the relations between properties and categories involved in induction. (shrink)

Within analytic philosophy, induction has been seen as a problem concerning inferences that have been analysed as relations between sentences. In this article, we argue that induction does not primarily concern relations between sentences, but between properties and categories. We outline a new approach to induction that is based on two theses. The first thesis is epistemological. We submit that there is not only knowledge-how and knowledge-that, but also knowledge-what. Knowledge-what concerns relations between properties and categories (...) and we argue that it cannot be reduced to knowledge-that. We support the partition of knowledge by mapping it onto the long-term memory systems: procedural, semantic and episodic memory. The second thesis is that the role of inductive reasoning is to generate knowledge-what. We use conceptual spaces to model knowledge-what and the relations between properties and categories involved in induction. (shrink)

This chapter presents a typology of the different kinds of inductive inferences we can draw from our evidence, based on the explanatory relationship between evidence and conclusion. Drawing on the literature on graphical models of explanation, I divide inductive inferences into (a) downwards inferences, which proceed from cause to effect, (b) upwards inferences, which proceed from effect to cause, and (c) sideways inferences, which proceed first from effect to cause and then from that cause to an additional effect. I (...) further distinguish between direct and indirect forms of downwards and upwards inferences. I then show how we can subsume canonical forms of inductive inference mentioned in the literature, such as inference to the best explanation, enumerative induction, and analogical inference, under this typology. Along the way, I explore connections with probability and confirmation, epistemic defeat, the relation between abduction and enumerative induction, the compatibility of IBE and Bayesianism, and theories of epistemic justification. (shrink)

As our epistemic ambitions grow, the common and scientific endeavours are becoming increasingly dependent on Machine Learning (ML). The field rests on a single experimental paradigm, which consists of splitting the available data into a training and testing set and using the latter to measure how well the trained ML model generalises to unseen samples. If the model reaches acceptable accuracy, an a posteriori contract comes into effect between humans and the model, supposedly allowing its deployment to (...) target environments. Yet the latter part of the contract depends on human inductive predictions or generalisations, which infer a uniformity between the trained ML model and the targets. The paper asks how we justify the contract between human and machine learning. It is argued that the justification becomes a pressing issue when we use ML to reach ‘elsewheres’ in space and time or deploy ML models in non-benign environments. The paper argues that the only viable version of the contract can be based on optimality (instead of on reliability which cannot be justified without circularity) and aligns this position with Schurz’s optimality justification. It is shown that when dealing with inaccessible/unstable ground-truths (‘elsewheres’ and non-benign targets), the optimality justification undergoes a slight change, which should reflect critically on our epistemic ambitions. Therefore, the study of ML robustness should involve not only heuristics that lead to acceptable accuracies on testing sets. The justification of human inductive predictions or generalisations about the uniformity between ML models and targets should be included as well. Without it, the assumptions about inductive risk minimisation in ML are not addressed in full. (shrink)

While rules and exemplars are usually viewed as opposites, this paper argues that they form end points of the same distribution. By representing both rules and exemplars as (partial) trees, we can take into account the fluid middle ground between the two extremes. This insight is the starting point for a new theory of language learning that is based on the following idea: If a language learner does not know which phrase‐structure trees should be assigned to initial sentences, s/he (...) allows (implicitly) for all possible trees and lets linguistic experience decide which is the “best” tree for each sentence. The best tree is obtained by maximizing “structural analogy” between a sentence and previous sentences, which is formalized by the most probable shortest combination of subtrees from all trees of previous sentences. Corpus‐based experiments with this model on the Penn Treebank and the Childes database indicate that it can learn both exemplar‐based and rule‐based aspects of language, ranging from phrasal verbs to auxiliary fronting. By having learned the syntactic structures of sentences, we have also learned the grammar implicit in these structures, which can in turn be used to produce new sentences. We show that our model mimicks children’s language development from item‐based constructions to abstract constructions, and that the model can simulate some of the errors made by children in producing complex questions. (shrink)

We present a reference model for finding evidence of discrimination in datasets of historical decision records in socially sensitive tasks, including access to credit, mortgage, insurance, labor market and other benefits. We formalize the process of direct and indirect discrimination discovery in a rule-based framework, by modelling protected-by-law groups, such as minorities or disadvantaged segments, and contexts where discrimination occurs. Classification rules, extracted from the historical records, allow for unveiling contexts of unlawful discrimination, where the degree of burden (...) over protected-by-law groups is evaluated by formalizing existing norms and regulations in terms of quantitative measures. The measures are defined as functions of the contingency table of a classification rule, and their statistical significance is assessed, relying on a large body of statistical inference methods for proportions. Key legal concepts and reasonings are then used to drive the analysis on the set of classification rules, with the aim of discovering patterns of discrimination, either direct or indirect. Analyses of affirmative action, favoritism and argumentation against discrimination allegations are also modelled in the proposed framework. Finally, we present an implementation, called LP2DD, of the overall reference model that integrates induction, through data mining classification rule extraction, and deduction, through a computational logic implementation of the analytical tools. The LP2DD system is put at work on the analysis of a dataset of credit decision records. (shrink)

Multi-level teaching has been proven to be more effective than a one-size-fits-all learning approach. This study aimed to develop and implement a multi-level remedial teaching scheme in various high school classes containing students of a wide range of learning levels and to determine its effect of their learning. The deterministic inputs noisy and gate model of cognitive diagnosis theory was used to classify students at multiple levels according to their knowledge and desired learning outcomes. A total of 680 senior (...) high school students from central provinces in China participated in the initial cognitive diagnostic test, and 1,615 high school sophomores from seven high schools in China participated in a formal cognitive diagnosis test. Thirty-six high school students from Southwestern China participated in the think-aloud protocols, and 258 seniors from three high schools in southwest China participated in the remedial teaching experiment. Through an analysis of students’ think-aloud protocols, cognitive errors of students at all levels were determined, and multi-level remedial teaching programs were designed to address these common cognitive errors. The remedial teaching programs were then implemented in three schools and compared with a control group. The results indicated that the students in the experimental group showed a more significant improvement. In this study, the steps of designing multi-level remedial teaching include assessment, classification, and preparing a teaching scheme, which are feasible and can have remarkable teaching effects. This process can be used for reference by teachers of various subjects. (shrink)

Calibration inductive logics are based on accepting estimates of relative frequencies, which are used to generate imprecise probabilities. In turn, these imprecise probabilities are intended to guide beliefs and decisions — a process called “calibration”. Two prominent examples are Henry E. Kyburg's system of Evidential Probability and Jon Williamson's version of Objective Bayesianism. There are many unexplored questions about these logics. How well do they perform in the short-run? Under what circumstances do they do better or worse? What is (...) their performance relative to traditional Bayesianism? -/- In this article, we develop an agent-based model of a classic binomial decision problem, including players based on variations of Evidential Probability and Objective Bayesianism. We compare the performances of these players, including against a benchmark player who uses standard Bayesian inductive logic. We find that the calibrated players can match the performance of the Bayesian player, but only with particular acceptance thresholds and decision rules. Among other points, our discussion raises some challenges for characterising “cautious” reasoning using imprecise probabilities. Thus, we demonstrate a new way of systematically comparing imprecise probability systems, and we conclude that calibration inductive logics are surprisingly promising for making decisions. (shrink)

This study investigated the cognitive processes involved in inductive reasoning. Sixteen undergraduates solved quadratic function–finding problems and provided concurrent verbal protocols. Three fundamental areas of inductive activity were identified: Data Gathering, Pattern Finding, and Hypothesis Generation. These activities are evident in three different strategies that they used to successfully find functions. In all three strategies, Pattern Finding played a critical role not previously identified in the literature. In the most common strategy, called the Pursuit strategy, participants created new quantities from (...) x and y, detected patterns in these quantities, and expressed these patterns in terms of x. These expressions were then built into full hypotheses. The processes involved in this strategy are instantiated in an ACT‐based model that simulates both successful and unsuccessful performance. The protocols and the model suggest that numerical knowledge is essential to the detection of patterns and, therefore, to higher‐order problem solving. (shrink)

Prima facie, accounts of scientific representation should illuminate how models support justified surrogative reasoning while remaining neutral on the nature of inductive inference. We argue that doing both at once is harder than it first appears. Accounts like “DEKI,” which distinguish justified and unjustified surrogative inferences by appealing to a distinction between derivational and factual correctness, cannot accommodate non-formal, non-rule-based accounts of inference such as John Norton’s material theory of induction. In contrast, a recent expressivist-inferentialist account appears compatible (...) with material inference, but at the cost of abandoning inductive neutrality. (shrink)

Hilary Kornblith (1993) has recently offered a reliabilist defense of the use of the Law of Small Numbers in inductive inference. In this paper I argue that Kornblith's defense of this inferential rule fails for a number of reasons. First, I argue that the sort of inferences that Kornblith seeks to justify are not really inductive inferences based on small samples. Instead, they are knowledge-based deductive inferences. Second, I address Kornblith's attempt to find support in the work of (...) Dorrit Billman and I try to show that close attention to the workings of her computational model reveals that it does not support Kornblith's argument. While the knowledge required to ground the inferences in question is perhaps inductively derived, Billman's work does not support the notion that small samples provide a reliable basis for our generalizing inferences. (shrink)

My dissertation explores the ways in which Rudolf Carnap sought to make philosophy scientific by further developing recent interpretive efforts to explain Carnap’s mature philosophical work as a form of engineering. It does this by looking in detail at his philosophical practice in his most sustained mature project, his work on pure and applied inductive logic. I, first, specify the sort of engineering Carnap is engaged in as involving an engineering design problem and then draw out the complications of design (...) problems from current work in history of engineering and technology studies. I then model Carnap’s practice based on those lessons and uncover ways in which Carnap’s technical work in inductive logic takes some of these lessons on board. This shows ways in which Carnap’s philosophical project subtly changes right through his late work on induction, providing an important corrective to interpretations that ignore the work on inductive logic. Specifically, I show that paying attention to the historical details of Carnap’s attempt to apply his work in inductive logic to decision theory and theoretical statistics in the 1950s and 1960s helps us understand how Carnap develops and rearticulates the philosophical point of the practical/theoretical distinction in his late work, offering thus a new interpretation of Carnap’s technical work within the broader context of philosophy of science and analytical philosophy in general. (shrink)

A new approach to Hume's problem of induction that justifies the optimality of induction at the level of meta-induction. Hume's problem of justifying induction has been among epistemology's greatest challenges for centuries. In this book, Gerhard Schurz proposes a new approach to Hume's problem. Acknowledging the force of Hume's arguments against the possibility of a noncircular justification of the reliability of induction, Schurz demonstrates instead the possibility of a noncircular justification of the optimality of (...) class='Hi'>induction, or, more precisely, of meta-induction (the application of induction to competing prediction models). Drawing on discoveries in computational learning theory, Schurz demonstrates that a regret-based learning strategy, attractivity-weighted meta-induction, is predictively optimal in all possible worlds among all prediction methods accessible to the epistemic agent. Moreover, the a priori justification of meta-induction generates a noncircular a posteriori justification of object induction. Taken together, these two results provide a noncircular solution to Hume's problem. Schurz discusses the philosophical debate on the problem of induction, addressing all major attempts at a solution to Hume's problem and describing their shortcomings; presents a series of theorems, accompanied by a description of computer simulations illustrating the content of these theorems (with proofs presented in a mathematical appendix); and defends, refines, and applies core insights regarding the optimality of meta-induction, explaining applications in neighboring disciplines including forecasting sciences, cognitive science, social epistemology, and generalized evolution theory. Finally, Schurz generalizes the method of optimality-based justification to a new strategy of justification in epistemology, arguing that optimality justifications can avoid the problems of justificatory circularity and regress. (shrink)

In base rate problems the estimated probability must equal the base rate only where random sampling is assumed. Otherwise there is uncertainty over and above that which can be included in any probability model and inductive inference is involved. Subjects should use base rates to the extent that the problem suggests a simple random sampling model.

A central question in cognitive research concerns how new properties are generalized to categories. This article introduces a model of how generalizations involve a process of causal inference in which people estimate the likely presence of the new property in individual category exemplars and then the prevalence of the property among all category members. Evidence in favor of this causal‐based generalization (CBG) view included effects of an existing feature’s base rate (Experiment 1), the direction of the causal relations (...) (Experiments 2 and 4), the number of those relations (Experiment 3), and the distribution of features among category members (Experiments 4 and 5). The results provided no support for an alternative view that generalizations are promoted by the centrality of the to‐be‐generalized feature. However, there was evidence that a minority of participants based their judgments on simpler associative reasoning processes. (shrink)

This paper critiques a number of standard ways of understanding the role of the metalanguage in a semantic theory for natural language, including the idea that disquotation plays a nontrivial role in any explanatory natural language semantics. It then proposes that the best way to understand the role of a semantic metalanguage involves recognizing that semantics is a model-based science. The metalanguage of semantics is language for articulating features of the theorist's model. Models are understood as mediating (...) instruments---idealized structures used to represent select aspects of the world, aspects the theorist is seeking some theoretical understanding of. The aspect of reality we are seeking some understanding of in semantics is a dimension of human linguistic competence---informally, knowledge of meaning. (shrink)