Combining Models of Approximation with Partial Learning

In Gold's framework of inductive inference, the model of partial learning requires the learner to output exactly one correct index for the target object and only the target object infinitely often. Since infinitely many of the learner's hypotheses may be incorrect, it is not obvious whether a partial learner can be modifed to "approximate" the target object. Fulk and Jain (Approximate inference and scientific method. Information and Computation 114(2):179--191, 1994) introduced a model of approximate learning of recursive functions. The present work extends their research and solves an open problem of Fulk and Jain by showing that there is a learner which approximates and partially identifies every recursive function by outputting a sequence of hypotheses which, in addition, are also almost all finite variants of the target function. The subsequent study is dedicated to the question how these findings generalise to the learning of r.e. languages from positive data. Here three variants of approximate learning will be introduced and investigated with respect to the question whether they can be combined with partial learning. Following the line of Fulk and Jain's research, further investigations provide conditions under which partial language learners can eventually output only finite variants of the target language. The combinabilities of other partial learning criteria will also be briefly studied.Comment: 28 page

A Description Logic of Typicality for Conceptual Combination

We propose a nonmonotonic Description Logic of typicality able to account for the phenomenon of combining prototypical concepts, an open problem in the fields of AI and cognitive modelling. Our logic extends the logic of typicality ALC + TR, based on the notion of rational closure, by inclusions p :: T(C) v D (“we have probability p that typical Cs are Ds”), coming from the distributed semantics of probabilistic Description Logics. Additionally, it embeds a set of cognitive heuristics for concept combination. We show that the complexity of reasoning in our logic is EXPTIME-complete as in ALC

Raising argument strength using negative evidence: A constraint on models of induction

Both intuitively, and according to similarity-based theories of induction, relevant evidence raises argument strength when it is positive and lowers it when it is negative. In three experiments, we tested the hypothesis that argument strength can actually increase when negative evidence is introduced. Two kinds of argument were compared through forced choice or sequential evaluation: single positive arguments (e.g., “Shostakovich’s music causes alpha waves in the brain; therefore, Bach’s music causes alpha waves in the brain”) and double mixed arguments (e.g., “Shostakovich’s music causes alpha waves in the brain, X’s music DOES NOT; therefore, Bach’s music causes alpha waves in the brain”). Negative evidence in the second premise lowered credence when it applied to an item X from the same subcategory (e.g., Haydn) and raised it when it applied to a different subcategory (e.g., AC/DC). The results constitute a new constraint on models of induction

Child categorization

Categorization is a process that spans all of development, beginning in earliest infancy yet changing as children's knowledge and cognitive skills develop. In this review article, we address three core issues regarding childhood categorization. First, we discuss the extent to which early categories are rooted in perceptual similarity versus knowledge-enriched theories. We argue for a composite perspective in which categories are steeped in commonsense theories from a young age but also are informed by low-level similarity and associative learning cues. Second, we examine the role of language in early categorization. We review evidence to suggest that language is a powerful means of expressing, communicating, shaping, and supporting category knowledge. Finally, we consider categories in context. We discuss sources of variability and flexibility in children's categories, as well as the ways in which children's categories are used within larger knowledge systems (e.g., to form analogies, make inferences, or construct theories). Categorization is a process that is intrinsically tied to nearly all aspects of cognition, and its study provides insight into cognitive development, broadly construed. WIREs Cogn Sci 2011 2 95–105 DOI: 10.1002/wcs.96 For further resources related to this article, please visit the WIREs websitePeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/78491/1/96_ftp.pd

Compositionality and Concepts

In this chapter I aim to explain how psychology understands concepts, and why there is a need for semantic theory to take on the challenge of psychological data. All of the contributors to this volume are (presumably) in the business of trying to understand and explain how language has meaning, and the primary source of evidence for this has to be our intuitions of what things mean. Furthermore, if my semantic intuitions (as a theorist) are out of kilter with those of the common language user, then it is my theory which should be called into question and not the lay intuition. This chapter describes a range of results from my research program over the last 30 years, some old and some new, with the aim of giving a general account of using Prototype Theory as a way to explain semantic intuitions

The Tacit ‘Quantum’ of Meeting the Aesthetic Sign; Contextualize, Entangle, Superpose, Collapse or Decohere

The semantically ambiguous nature of the sign and aspects of non-classicality of elementary matter as described by quantum theory show remarkable coherent analogy. We focus on how the ambiguous nature of the image, text and art work bears functional resemblance to the dynamics of contextuality, entanglement, superposition, collapse and decoherence as these phenomena are known in quantum theory. These quantumlike properties in linguistic signs have previously been identified in formal descritions of e.g. concept combinations and mental lexicon representations and have been reported on in the literature. In this approach the informationalized, communicated, mediatized conceptual configuration—of e.g. the art work—in the personal reflected mind behaves like a quantum state function in a higher dimensional complex space, in which it is time and again contextually collapsed and further cognitively entangled (Aerts et al. in Found Sci 4:115–132, 1999; in Lect Notes Comput Sci 7620:36–47, 2012). The observer–consumer of signs becomes the empowered ‘produmer’ (Floridi in The philosophy of information, Oxford University Press, Oxford, 2011) creating the cognitive outcome of the interaction, while loosing most of any ‘classical givenness’ of the sign (Bal and Bryson in Art Bull 73:174–208, 1991). These quantum-like descriptions are now developed here in four example aesthetic signs; the installation Mist room by Ann Veronica Janssens (2010), the installation Sections of a happy moment by David Claerbout (2010), the photograph The Falling Man by Richard Drew (New York Times, p. 7, September 12, 2001) and the documentary Huicholes. The Last Peyote Guardians by Vilchez and Stefani (2014). Our present work develops further the use of a previously developed quantum model for concept representation in natural language. In our present approach of the aesthetic sign, we extend to individual—idiosyncratic—observer contexts instead of socially shared group contexts, and as such also include multiple idiosyncratic creation of meaning and experience. This irreducible superposition emerges as the core feature of the aesthetic sign and is most critically embedded in the ‘no-interpretation’ interpretation of the documentary signal

Contradictory reasoning network:an EEG and FMRI study

Contradiction is a cornerstone of human rationality, essential for everyday life and communication. We investigated electroencephalographic (EEG) and functional magnetic resonance imaging (fMRI) in separate recording sessions during contradictory judgments, using a logical structure based on categorical propositions of the Aristotelian Square of Opposition (ASoO). The use of ASoO propositions, while controlling for potential linguistic or semantic confounds, enabled us to observe the spatial temporal unfolding of this contradictory reasoning. The processing started with the inversion of the logical operators corresponding to right middle frontal gyrus (rMFG-BA11) activation, followed by identification of contradictory statement associated with in the right inferior frontal gyrus (rIFG-BA47) activation. Right medial frontal gyrus (rMeFG, BA10) and anterior cingulate cortex (ACC, BA32) contributed to the later stages of process. We observed a correlation between the delayed latency of rBA11 response and the reaction time delay during inductive vs. deductive reasoning. This supports the notion that rBA11 is crucial for manipulating the logical operators. Slower processing time and stronger brain responses for inductive logic suggested that examples are easier to process than general principles and are more likely to simplify communication. © 2014 Porcaro et al

Human and Machine Learning

In this paper, we consider learning by human beings and machines in the light of Herbert Simon’s pioneering contributions to the theory of Human Problem Solving. Using board games of perfect information as a paradigm, we explore differences in human and machine learning in complex strategic environments. In doing so, we contrast theories of learning in classical game theory with computational game theory proposed by Simon. Among theories that invoke computation, we make a further distinction between computable and computational or machine learning theories. We argue that the modern machine learning algorithms, although impressive in terms of their performance, do not necessarily shed enough light on human learning. Instead, they seem to take us further away from Simon’s lifelong quest to understand the mechanics of actual human behaviour

Philosophical issues about concepts

In this article, we review some important controversies about concepts in the philosophy of psychology, focusing particularly on the theories of concepts developed in philosophy, on the debate about the homogeneity of concepts, on neo-empiricism, and on concept learning. © 2012 John Wiley & Sons, Ltd