Inductive Inference

In his most recent work, The Large-Scale Structure of Inductive Inference (2024), John Norton defends the two fundamental aspects of his material theory of induction: (i) there is no universal schema or template for justifying inductive inferences; and (ii) all inductions are materially and locally justified. Moreover, Norton uses this work to clarify some points that were missing in his earlier work.

Higman essentially showed that if A is any language then SUBSEQ(A) is regular, where SUBSEQ(A) is the language of all subsequences of strings in A. Let s1, s2, s3, . . . be the standard lexicographic enumeration of all strings over some finite alphabet. We consider the following inductive inference problem: given A(s1), A(s2), A(s3), . . . , learn, in the limit, a DFA for SUBSEQ(A). We consider this model of learning and the variants of it that are usually studied in Inductive Inference: anomalies, mindchanges, teams, and combinations thereof. This paper is a significant revision and expansion of an earlier conference version [10]. We denote this by x y. Notation 1.2. If A is a set of strings, then SUBSEQ(A) is the set of subsequences of strings in A.

We generalize the classical notion of Vapnik-Chernovenkis (VC) dimension to ordinal VC-dimension, in the context of logical learning paradigms. Logical learning paradigms encompass the numerical learning paradigms commonly studied in Inductive Inference. A logical learning paradigm is defined as a set W of structures over some vocabulary, and a set D of first-order formulas that represent data. The sets of models of in W, where varies over D, generate a natural topology W over W. We show that if D is closed under boolean operators, then the notion of ordinal VC-dimension offers a perfect characterization for the problem of predicting the truth of the members of D in a member of W, with an ordinal bound on the number of mistakes. This shows that the notion of VC-dimension has a natural interpretation in Inductive Inference, when cast into a logical setting. We also study the relationships between predictive complexity, selective complexity-a variation on predictive complexity-and mind change complexity. The assumptions that D is closed under boolean operators and that W is compact often play a crucial role to establish connections between these concepts. We then consider a computable setting with effective versions of the complexity measures, and show that the equivalence between ordinal VC-dimension and predictive complexity fails. More precisely, we prove that the effective ordinal VC-dimension of a paradigm can be defined when all other effective notions of complexity are undefined. On a better note, when W is compact, all effective notions of complexity are defined, though they are not related as in the noncomputable version of the framework.

Most theoretical models of inductive inference make the idealized assumption that the data available to a learner is from a single and accurate source. The subject of inaccuracies in data emanating from a single source has been addressed by several authors. The present paper argues in favor of a more realistic learning model in which data emanates from multiple sources, some or all of which may be inaccurate. Three kinds of inaccuracies are considered: spurious data (modeled as noisy texts), missing data (modeled as incomplete texts), and a mixture of spurious and missing data (modeled as imperfect texts). Motivated by the above argument, the present paper introduces and theoretically analyzes a number of inference criteria in which a learning machine is fed data from multiple sources, some of which may be infected with inaccuracies. The learning situation modeled is the identification in the limit of programs from graphs of computable functions. The main parameters of the investigation are: kind of inaccuracy, total number of data sources, number of faulty data sources which produce data within an acceptable bound, and the bound on the number of errors allowed in the final hypothesis learned by the machine. Sufficient conditions are determined under which, for the same kind of inaccuracy, for the same bound on the number of errors in the final hypothesis, and for the same bound on the number of inaccuracies, learning from multiple texts, some of which may be inaccurate, is equivalent to learning from a single inaccurate text. The general problem of determining when learning from multiple inaccurate texts is a restriction over learning from a single inaccurate text turns out to be combinatorially very complex. Significant partial results are provided for this problem. Several results are also provided about conditions under which the detrimental effects of multiple texts can be overcome by either allowing more errors in the final hypothesis or by reducing the number of inaccuracies in the texts. It is also shown that the usual hierarchies resulting from allowing extra errors in the final program (results in increased learning power) and allowing extra inaccuracies in the texts (results in decreased learning power) hold. Finally, it is demonstrated that in the context of learning from multiple inaccurate texts, spurious data is better than missing data which in turn is better than a mixture of spurious and missing data.

Identification of grammars (r. e. indices) for recursively enumerable languages from positive data by algorithmic devices is a well studied problem in learning theory. The present paper considers identification of r. e. languages by machines that have access to membership oracles for noncomputable sets. It is shown that for any set A there exists another set B such that the collections of r. e. languages that can be identified by machines with access to a membership oracle for B is strictly larger than the collections of r. e. languages that can be identified by machines with access to a membership oracle for A. In other words, there is no maximal inference degree for language identification.

Identification of programs for computable functions from their graphs and identification of grammars (r. e. indices) for recursively enumerable languages from positive data are two extensively studied problems in the recursion theoretic framework of inductive inference. In the context of function identification, Freivalds, Kinber, and Wiehagen have shown that only those collections of functions, S, are identifiable in the limit for which there exists

We define a class of functions termed "Computable in the Limit", based on the Machine Learning paradigm of "Identification in the Limit". A function is Computable in the Limit if it defines a property Pp of a recursively enumerable class A of recursively enumerable data sequences S ∈ A, such that each data sequence S is generated by a total recursive function φs that enumerates S. Let the index s represent the data sequence S. The property Pp(s) = x is computed by a partial recursive function φp(s, t) such that there exists a u where φp(s, u) = x and for all t ≥ u, φp(s, t) = x if it converges. Since the index s is known, this is not an identification problem -instead it is computing a common property of the sequences in A. We give a Normal Form Theorem for properties that are Computable in the Limit, similar to Kleene's Normal Form Theorem. We also give some examples of sets that are Computable in the Limit, and derive some properties of Canonical and Complexity Bound Enumerations of classes of total functions, and show that no full enumeration of all indices of Turing machines T M i that compute a given total function f (x) can be Computable in the Limit.

Schwichtenberg developed the program called "Proofs as Programs" by measuring the "complexity" of proofs as programs using the Curry-Howard correspondence. In particular, he precisely characterized the complexity of proofs in arithmetic using proof-theoretic tools. In this paper, we extend this result to parameter-free subsystems of Girard's System F having the strength of Π 1 1-CA0, determining the expected complexity of terms in them (instead of proofs). This abstract setting of System F provides a new perspective on Schwichtenberg's result. His original goal was to determine the complexity of programs, relying on the Curry-Howard correspondence. In contrast, our approach directly determines the complexity of terms in System F , which are essentially programs themselves. Another advantage of this approach should be that our approach for these fragments is more uniform than the original, owing to the abstract setting of System F.

Conceptual understanding is essential to learn physics principles, for this the Case method is considered, the design of a Case study and two objectives: a) describe the systematic process of designing a Case, by ERVE model: structure, review, validation and evaluation; The dimensions were validated by judges: clarity, coherence, relevance, sufficiency; Aiken statistic was calculated; The evaluation involved piloting student opinion and data triangulation. b) Implement the method with the IGBE model: individual activity, Case reading; focus group; plenary; anecdotal log; evaluation judges dimensions understanding; diagnostic surveys and verification of experimental and control groups. The validation and evaluation results of the design showed optimal levels of relevance and sufficiency; with coincidences in acceptable assessments that the Case is not totally coherent with a linear reality but rather a complex one. When implementing the method, the judges evaluated plenary discussion, with high levels of understanding. When evaluating logs, the results showed medium and high levels. When implementing diagnostic surveys, similar levels of preconceptions were observed in both groups. When comparing results from verification surveys, higher levels of understanding were observed in the experimental group than in the control group; The method favorably impacts understanding through dialogic socialization. But it is of little application in engineering and the existence of designed cases as well. Both models are effective for designing and qualifying Cases, due to their systematic processes that improve the dimensions of design and understanding, they can be replicated and related to learning through inductive reasoning.

Recent research suggests that inductive inference may be based on salient relations between premise and/or conclusion categories . The types of relations deemed relevant may be influenced by experience (e.g. . Novices in a given domain have been shown to rely primarily on taxonomic relationships to guide their inductive inferences. In contrast, experts show flexible use of both taxonomic and non-taxonomic relations. Previous research has assessed induction using forced choice tasks or ratings of argument strength, measures that may underestimate the salience of non-taxonomic relations for novices. The present study investigated the use of taxonomic and non-taxonomic relations among novices in the domain of local animal species using an open-ended task. Participants were given 12 pairs of taxonomically or ecologically related animals both known to have a certain property and asked to list other animals that might also have that property. Results show that relations among premise pairs had systematic effects on open-ended inferences. Overall, responses based on ecological relations were more frequent than taxonomic responses for novices. These results suggest that given an open-ended task, novices do demonstrate sensitivity to relevant relations among premise categories in generating inductive inference.

Partial recursive functions which equal the amount of time or space required by computations have special properties which distinguish them from arbitrary partial recursive functions. Our mmin result illustrates a property of running times similar in interpretation to Borodin's gap theorem. The proof is based on the construction of difficult to co_ute characteristic functions which take the value one very infrequently.

Los procesos metacognitivos implicados en la comprensión lectora han sido objeto de estudio desde los años 70 en el ámbito de la investigación psicológica. Flavell en el año 1977 de-fine la metacognición como el conocimiento que uno tiene sobre los propios procesos y productos cognitivos o sobre cualquier aspecto relacionado con éstos. , se refiere a la metacognición como el control deliberado y consciente de las acciones cognitivas, dando al comportamiento estratégico un papel principal en la actividad cognitiva y diferenciando la cognición, inconsciente y automática, de la metacognición consciente y deliberada. Posteriormente,

El estudio de los trastornos de la lectura, la escritura y la dislexia ha cobrado una gran importancia hoy en día debido a que este desorden implica cada vez a más niños y niñas, como demuestran estudios como los de Fluss et al. ( ), que revelan la existencia de una alta tasa de alumnos con retraso significativo en la lectura. Por este motivo, numerosas investigaciones se han centrado en el análisis y

We show that using nonextensive entropy can lead to spontaneous symmetry breaking when a parameter changes its value from that applicable for a symmetric domain, as in field theory. We give the physical reasons and also show that even for symmetric Dirichlet priors, such a definition of the entropy and the parameter value can lead to asymmetry when entropy is maximized.

What is the relation between human and nonhuman animals? As adults, we construe this relation flexibly, depending in part on the situation at hand. From a biological perspective, we acknowledge the status of humans as one species among many (as in Western science), but at the same time may adopt other perspectives, including an anthropocentric perspective in which human characteristics are attributed to nonhuman animals (as in fables and popular media). How do these perspectives develop? The predominant view in developmental cognitive science is that young children universally possess only one markedly anthropocentric vantage point, and must undergo fundamental conceptual change, overturning their initially human-centered framework before they can acquire a distinctly biological framework. Evidence from two experiments challenges this view. By developing a task that allows us to test children as young as 3 years of age, we are able to demonstrate that anthropocentrism is not the fir...

This paper presents a nonmonotonic ILP approach for the automatic revision of metabolic networks through the logical analysis of experimental data. The method extends previous work in two respects: by suggesting revisions that involve both the addition and removal of information; and by suggesting revisions that involve combinations of gene functions, enzyme inhibitions, and metabolic reactions. Our proposal is based on a new declarative model of metabolism expressed in a nonmonotonic logic programming formalism. With respect to this model, a mixture of abductive and inductive inference is used to compute a set of minimal revisions needed to make a given network consistent with some observed data. In this way, we describe how a reasoning system called XHAIL was able to correctly revise a state-of-the-art metabolic pathway in the light of real-world experimental data acquired by an autonomous laboratory platform called the Robot Scientist.

This paper presents a nonmonotonic ILP approach for the automatic revision of metabolic networks through the logical analysis of experimental data. The method extends previous work in two respects: by suggesting revisions that involve both the addition and removal of information; and by suggesting revisions that involve combinations of gene functions, enzyme inhibitions, and metabolic reactions. Our proposal is based on a new declarative model of metabolism expressed in a nonmonotonic logic programming formalism. With respect to this model, a mixture of abductive and inductive inference is used to compute a set of minimal revisions needed to make a given network consistent with some observed data. In this way, we describe how a reasoning system called XHAIL was able to correctly revise a state-of-the-art metabolic pathway in the light of real-world experimental data acquired by an autonomous laboratory platform called the Robot Scientist.

CF-induction is a sound and complete hypothesis finding procedure for full clausal logic which uses the principle of inverse entailment to compute a hypothesis that logically explains a set of examples with respect to a prior background theory. Currently, CF-induction computes hypotheses by applying combinations of several complex generalisation operators to an intermediate theory called a bridge formula. In this paper we propose an alternative approach whereby hypotheses are derived from a bridge formula using a single deductive operator and a single inductive operator. We show that our simplified procedure preserves the soundness and completeness of CF-induction.

We study consistency problems of the following form for some family (Lk) of language classes: Given a finite language F and some parameter k, is there some language L⊇ F contained in Lk? We derive non-trivial complexity results for languages of structures of categorial grammars, in terms of classical complexity, as well as in terms of parameterized complexity and approximability.

Traditional attempts to understanding inductive reasoning in science have typically involved analyzing language, focusing on statements or propositions. However, recent arguments suggest that this approach misconceives induction, prompting the need for a new perspective. This study offers a fresh view on induction by integrating William Whewell's theory of induction, which distinguishes two forms of reasoning: interpretation and representation. This perspective suggests that induction can be seen as a reasoning process based on semantic and pragmatic models rather than statements or propositions.

Conceptual understanding is essential when learning engineering. For that, the design of a case
study is considered, as well as the method of the case and two objectives: a) describe the design
process, using the SRJU model: structure, review, judges validation and user evaluation; the
dimensions of clarity, coherence, relevance, sufficiency were validated by judges; the
evaluation involved piloting of student opinions and data triangulation. b) Apply the method
with the IGAA model by activities: individual case reading; focal groups; plenary; anecdotal
logs; assessment by judges of the dimensions of understanding; diagnostic surveys and
verification of the experimental and control group. The results of the validation and evaluation
of the design showed optimal levels of relevance and sufficiency; with coincidences in
acceptable assessments that the case is not totally coherent with a linear reality but rather
complex. When implementing the method, the judges evaluated discussion in plenary, with
high levels of understanding. When evaluating logs, the results showed medium and high
levels. When implementing diagnostic surveys, similar levels of preconceptions were observed
in both groups. When comparing results of verification surveys, higher levels of understanding
were observed in the experimental group than in the control group; the method favorably
impacts understanding through dialogic socialization. However, it is rarely applied in physics
and the existence of designed cases is also limited. Both models are effective for designing and
qualifying Cases, due to their systematic processes that improve the dimensions of design and
understanding and replicated.

Research advances are presented whose objective is to test and qualify the viability of
implementing Rational Thought of the ancient classical pedagogical area, in digital classrooms
of foreign languages; and answer the questions: what are the current theoretical foundations
and on which thematic digital teaching should be built in multilingual diversity classrooms?;
How does rational thought modify in students of different languages, research and
conceptualization related to linguistic, literary and cultural topics? How does classical
pedagogy help the development of didactics in the digital context, allowing the teacher to teach
and the student to build knowledge? The first stage consisted of theoretically basing classical
pedagogy, with the rational thought of ancient Greece and its derivation in scientific thought
as its guiding axis. Design that implied contrast in ways of thinking about thematic diversity.
With the following organization: methodological, theoretical and procedural foundation. For
the test design, an interaction matrix is proposed to order and interpret data that reflect the level
of conceptualization to be collected by written language; according to types of structured
thought: rational logical, methodical and narrative; For each type of thought, dimensions of
content, purpose and structure are evaluated. The methodology used for this stage is qualitative;
In the second stage, test design will be applied. As a result of the first stage, methodological,
theoretical and test design foundations were achieved, implementing the scientific method,
supported by preliminary conclusions and an annex of examples to address multiple topics.

Rūsiņš Mārtiņš Freivalds has played a key role in the development of theoretical computer science in Latvia. While also being recognised internationally and taking an active part in the computer scientists’ community, he managed to make a major contribution to the formation of the Latvian school of computer science.
In order to pay tribute to Freivalds’ scientific legacy and honour a beloved colleague, teacher, and Professor his fellow academics at the Computer Science Department of the University of Latvia, as well as some of his close Finnish, German, Japanese, and other international collaborators have contributed to this BJMC volume containing scientific papers and essays sharing personal memories of Freivalds.
This volume begins with Professor Freivalds’ academic genealogy and publications. The essay section reveals a profound sense of Freivalds’ responsibility for the future of computer science. The recollections of his lifelong scientific contributions also serve as testimony of the man’s inner freedom, and spiritual strength living under a totalitarian rule for half of his scientific career.

Presented is an algorithm (for learning a subclass of erasing regular pattern languages) which can be made to run with arbitrarily high probability of success on extended regular languages generated by patterns π of the form x 0 α 1 x 1 ...α m x m for unknown m but known c , from number of examples polynomial in m (and exponential in c ), where x 0 , . . . , x m are variables and where α 1 , ..., α m are each strings of terminals of length c . This assumes that the algorithm randomly draws samples with natural and plausible assumptions on the distribution. With the aim of finding a better algorithm, we also explore computer simulations of a heuristic.

Abstract—reasoning is an important part of many fields like logic, artificial intelligence, philosophy of science, and so on. Reasoning can either be deductive (deduction) or it can be inductive (induction). The decisions based on induction are very helpful in research but ...

We present a model of inductive inference that includes, as special cases, Bayesian reasoning, case-based reasoning, and rulebased reasoning. This unified framework allows us to examine how the various modes of inductive inference can be combined and how their relative weights change endogenously. For example, we establish conditions under which an agent who does not know the structure of the data generating process will decrease, over the course of her reasoning, the weight of credence put on Bayesian vs. non-Bayesian reasoning. We illustrate circumstances under which probabilistic models are used until an unexpected outcome occurs, whereupon the agent resorts to more basic reasoning techniques, such as case-based and rule-based reasoning, until enough data are gathered to formulate a new probabilistic model.

& Inductive inference underlies much of human cognition. The essential component of induction is hypothesis selection based on some criterion of relevance. The purpose of this study was to determine the neural substrate of inductive inference, particularly hypothesis selection, using fMRI. Ten volunteers were shown stimuli consisting of novel animals under two task conditions, and asked to judge whether all the animals in the set were the same type of animal. In one condition, subjects were given a rule that specified the criteria for``same type of animal''. In the other condition, subjects had to infer the rule without instruction. The two conditions were further factored into easy and difficult components. Rule inference was specifically associated with bilateral hippocampal activation while the task by difficulty interaction was associated with activation in right lateral orbital prefrontal cortex. We interpret the former in terms of semantic encoding of novel stimuli, and the latter in terms of hypothesis selection. Thus, we show an anatomical dissociation between task implementation and task difficulty that may correspond to a critical psychological distinction in the processes necessary for inductive inference. &

We study learning of predicate logics formulas from "elementary facts," i.e. from the values of the predicates in the given model. Several models of learning are considered, but most of our attention is paid to learning with belief levels. We propose an axiom system which describes what we consider to be a human scientist's natural behavior when trying to explore these elementary facts. It is proved that no such system can be complete. However we believe that our axiom system is "practically" complete. Theorems presented in the paper in some sense confirm our hypothesis.

This research was supported in part by NSF Grant GP-2880, ARPA grant SD-146, and 2) We use L L C" to denote proper inclusion, and ''2" for improper inclusion. DSR 79457 under Project MAC. I) The operation of substitution consists of composition of functions and explicit transformation. *) We use ' ' Z,," as an abbreviation for "x1, x2, . . . , x,,".

When an empirical prediction E of hypothesis H is observed to be true, such observation is said to confirm, i.e., support (although not prove) the truth of the hypothesis. But why? What justifies the claim that such evidence supports the hypothesis? The widely accepted answer is that it is justified by induction. More specifically, it is commonly held that the following argument: (1) If H then E; (2) E; (3) Therefore, (probably) H—here referred to as ‘hypothetico-deductive con-firmation argument’—is inductively strong. Yet this argument looks nothing like an inductive generalisation, i.e., it doesn’t seem inductive in the term's traditional, enumerative sense. If anything, it has the form of the fallacy of affirming the consequent. This paper aims to solve this puzzle. True, in recent decades, ‘in-duction’ has been sometimes used more broadly to encompass any non-deductive, i.e., ampliative, argument. Applying Bayesian confirmation theory has famously demonstrated that hypothetico-deductive confirmation is indeed inductive in this broader, ampliative sense. Nonetheless, it will be argued here that, despite appearance, hypothetico-deductive confirmation can also be recast as a strong enumerative induction. Hence, by being enumeratively inductive, the scientific method of hypothetico-deductive confirmation is justified through this traditional, more restrictive type of induction rather than merely by ampliative induction.

Higman essentially showed that if A is any language then SUBSEQ(A) is regular, where SUBSEQ(A) is the language of all subsequences of strings in A. Let s1, s2, s3,. .. be the standard lexicographic enumeration of all strings over some finite alphabet. We consider the following inductive inference problem: given A(s1), A(s2), A(s3),. .. , learn, in the limit, a DFA for SUBSEQ(A). We consider this model of learning and the variants of it that are usually studied in Inductive Inference: anomalies, mindchanges, teams, and combinations thereof. This paper is a significant revision and expansion of an earlier conference version [10]. S1. Introduction. Our work is based on a remarkable theorem of Higman [22], 1 given below as Theorem 1.3. Convention: Σ is a finite alphabet. Definition 1.1. Let x, y ∈ Σ *. We say that x is a subsequence of y if x = x 1 • • • x n and y ∈ Σ * x 1 Σ * x 2 • • • x n−1 Σ * x n Σ *. We denote this by x y. Notation 1.2. If A is a set of strings, then SUBSEQ(A) is the set of subsequences of strings in A. Higman [22] showed the following using well-quasi-order theory. Theorem 1.3 (Higman [22]). If A is any language over Σ * , then SUBSEQ(A) is regular. In fact, for any language A there is a unique minimum (and finite) set S of strings such that SUBSEQ(A) = {x ∈ Σ * : (∀z ∈ S)[z x]}. (1) The original proof of this theorem is nonconstructive. Nerode's Recursive Mathematics Program [27, 9] attempts to pin down what it means for a proof to be noneffective. In [11] we showed that there can be no effective proof. In particular we showed (among other things) that there is no partial computable

In this work, we present the Hierarchical Grounded Truth Preservation Theorem (HGTPT), a novel framework for constructing and verifying a grounded truth predicate within axiomatic extensions of formal arithmetic. The theorem proposes a structured hierarchy of grounded truth sets, effectively avoiding inconsistencies associated with self-reference while preserving the expressive power of the truth predicate within the context of Peano Arithmetic (PA). This approach maintains logical consistency, provides a hierarchy-based semantic interpretation, and introduces new insights into the interaction of truth, provability, and conservativity in formal systems.

The main goal is to exhibit the relationship between research work on non-monotonic reasoning and recursion-theoretically based approaches to inductive learning. There are introduced the concepts of monotonic and weakly monotonic inductive inference. It is proved that these concepts are considerably distinguished from other classical concepts of inductive inference, i.e. non-monotonic reasoning is inherently required in several approaches to inductive inference.

This paper presents the novel use of storyboards for composing, organizing and visualizing tactical agents designed to serve as computer generated forces. These tactical agents represent enemy forces that act and react to trainee actions and are specifically used here to populate military training scenarios. The tactical agents are based on the Context-based Reasoning human behavior representation paradigm. This application of storyboards facilitates the use and visualization of the contextual elements that make up the composed agents. The use of the approach is described and an informal qualitative evaluation is conducted.

This paper is intended to introduce a closer look at incremental learning by developing the two concepts of informationally incremental learning and operationally incremental learning. These concept are applied to the problem of learning containment decision lists for demonstrating its relevance.

A study investigated how young children understand natural kind terms by examining how 3-and 4-year-olds rely on category membership to draw inductive inferences about objects. One hundred four children (53 girls and 51 boys) from six preschools in California and Michigan participated in the study. The children were shown 10 sets of pictures of natural objects or creatures, told something about the items shown, and asked to draw inferences about other natural kind pictures. Two conditions were added: word only condition and picture only condition. Results suggest that even the youngest children assume that objects with the same name share underlying similarities. When given just labels, the children used them as a base for making inductions, and when labels and appearances conflicted, they relied more on labels than appearances. Even when no labels were given, the children sometimes figured out what categories the pictures belonged to and used this inference to decide about other properties. It is concluded that children are clearly sensitive to the power of language for organizing and extending language, and that words that refer, even common nouns, serve to identify objects as well as foster inductions. (MSE)

This essay examines the proposal that psychological essentialism re s u l t s f rom a history of natural selection acting on human re p resentation and inference systems. It has been argued that the features that distinguish essentialist re p resentational systems are especially well suited for re p resenting natural kinds. If the evolved function of essentialism is to exploit the rich inductive potential of such kinds, then it must be subserved by cognitive mechanisms that carry out at least three distinct functions: identifying these kinds in the environment, constructing essentialized re p resentations of them, and constraining inductive inferences about kinds. More o v e r, there are different kinds of kinds, ranging from nonliving substances to biological taxa to within-species kinds such as sex, and the causal processes that render these categories coherent for the purposes of inductive generalization vary. If the evolved function of essentialism is to support inductive generalization under ignorance of tru e causes, and if kinds of kinds vary in the implicit assumptions that support valid inductive i n f e rences about them, then we expect different, functionally incompatible modes of essentialist thinking for different kinds. In part i c u l a r, there should be differences in how biological and nonbiological substances, biological taxa, and biological and social role kinds are essentialized. The functional differences between these kinds of essentialism are discussed.

In celebration of the work of Richard Threlkeld Cox, we explore inductive logic and its role in science touching on both experimental design and analysis of experimental results. In this exploration we demonstrate that the duality between the logic of assertions and the logic of questions has important consequences. We discuss the conjecture that the relevance or bearing, b, of a question on an issue can be expressed in terms of the probabilities, p, of the assertions that answer the question via the entropy. In its application to the scientific method, the logic of questions, inductive inquiry, can be applied to design an experiment that most effectively addresses a scientific issue. This is performed by maximizing the relevance of the experimental question to the scientific issue to be resolved. It is shown that these results are related to the mutual information between the experiment and the scientific issue, and that experimental design is akin to designing a communication channel that most efficiently communicates information relevant to the scientific issue to the experimenter. Application of the logic of assertions, inductive inference (Bayesian inference) completes the experimental process by allowing the researcher to make inferences based on the information obtained from the experiment.

The problem of source separation is by its very nature an inductive inference problem. There is not enough information to deduce the solution, so one must use any available information to infer the most probable solution. We demonstrate that source separation problems are well-suited for the Bayesian approach which provides a natural and logically consistent method by which one can incorporate prior knowledge to estimate the most probable solution given that knowledge. We derive the Bell-Sejnowski ICA algorithm from first principles, i.e. Bayes' Theorem and demonstrate how the Bayesian methodology makes explicit the underlying assumptions. We then further demonstrate the power of the Bayesian approach by deriving two separation algorithms that incorporate additional prior information. One algorithm separates signals that are known a priori to be decorrelated and the other utilizes information about the signal propagation through the medium from the sources to the detectors.

This work falls into two parts. In the flrst part, we characterize the sets of all ƒ2 and all B(§1) (= boolean combinations of §1) theorems of Iƒ¡ 1 in terms of restricted exponentiation; and use these characterizations to prove that both sets are not deductively equivalent. In the second part, we investigate how these results generalize to Iƒ¡ 2 . We present a new model{theoretic approach to Iƒ ¡ 2 that allows us to obtain informative characterizations of the set of all ƒ2 and all B(§2) theorems of Iƒ¡ 2 ; and to give a model{theoretic proof of a conservation result by L. Beklemishev's stating that Iƒ¡ 2 is a B(§2) conservative extension of I§ ¡ 1 .

Riassunto Nel presente lavoro sono esaminati alcuni esempi proposti dal filosofo Luigi Bàrbera (1829-1904) nel trattato Lezioni di logica inventiva (Pisa, 1866). Dal punto di vista didattico, tali esempi possono essere commentati criticamente per sottolineare l'importanza della ricerca euristica e della dimostrazione, sia in matematica che nella pratica didattica.

Generic statements play a crucial role in concept learning, communication and education. Despite many efforts, the semantics of generics remain a controversial issue, as they do not seem to fit our standard theories of meaning. In this article, we attempt to shed light on this problem by focusing on how these sentences function in reasoning. Drawing on a distinction between property and diagnostic generics, we defend three theses: First, property generics are not about facts but express relations between concepts. Second, generics play an important role in everyday reasoning by interacting with our expectations about the world. Third, diagnostic generics emphasise properties that separate the category in the generics from other categories in the same contrast class. We use the theory of conceptual spaces to advance measures of typicality and diagnosticity capable of modelling different
aspects of generics and apply them to the modifier effect and the inverse conjunction fallacy. Finally, we discuss the pragmatics of gene

Ergonomik memainkan peranan yang penting dalam rekabentuk kerusi sekolah. Postur duduk yang janggal akibat daripada rekabentuk kerusi yang tidak sesuai mampu menyumbang ke arah kesan yang negatif kepada kesihatan kanak-kanak. Isu ini dapat dilihat melalui penyelidikan yang mempersoalkan tentang kesesuaian ukuran kerusi yang terdapat di sekolah rendah yang digunakan oleh Murid Sekolah Rendah Tahap Satu (MSRTS). Seramai 108 orang responden telah terlibat dalam penyelidikan ini yang terdiri daripada MSRTS yang berumur 7, 8 dan 9 tahun dari 12 buah Sekolah Rendah Kebangsaan di Perlis, Kedah dan Pulau Pinang. Penyelidikan ini menggabungkan kaedah kuantitatif dan kualitatif dalam mengenalpasti ketidak-sepadanan antropometri responden dengan ukuran kerusi yang digunakan di sekolah. Antropometer, goniometer, penimbang berat badan dan pita ukur digunakan bagi memperolehi data antropometri responden dan ukuran kerusi dari setiap sekolah. Data antropometri dan ukuran kerusi dianalisa menggunakan perisian SPSS (Statistical Package for Social Science). Postur duduk responden ketika sesi pembelajaran di dalam kelas turut dirakam dan dianalisa bagi menyokong data SPSS yang diperolehi. Dapatan kajian mencatatkan data antropometri MSRTS tidak sepadan dengan ukuran kerusi yang digunakan di sekolah. Oleh itu, pertimbangan terhadap faktor ergonomik dalam rekabentuk kerusi sekolah adalah perlu bagi memastikan kesihatan dan keselesaan MSRTS di sekolah. Kata Kunci: Ergonomik, Murid Sekolah Rendah Tahap Satu (MSRTS), Antropometri, Kerusi sekolah PENGENALAN "Ergonomics (or human factors) is the scientific discipline concerned with the understanding of interactions among humans and other elements of a system, and the profession that applies theory, principles, data and methods to design in order to optimize human well-being and overall system performance".

We combine computable structure theory and algorithmic learning theory to study learning of families of algebraic structures. Our main result is a model-theoretic characterization of the class Inf Ex-, consisting of the structures whose isomorphism types can be learned in the limit. We show that a family of structures is Inf Ex--learnable if and only if the structures from K can be distinguished in terms of their Σ inf 2 -theories. We apply this characterization to familiar cases and we show the following: there is an infinite learnable family of distributive lattice; no pair of Boolean algebras is learnable; no infinite family of linear orders is learnable.

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.