Introduction The present paper is aimed at propagating new concepts of similarity more flexible and expressive than those underlying most case-based reasoning approaches today. So, it mainly deals with criticizing approaches in use, with motivating and introducing new notions and notations, and with first steps towards future applications. The investigations at hand originate from the author's work in learning theory. In exploring the relationship between inductive learning and case-based learning within a quite formal setting (cf. [Jan92b]), it turned out that both areas almost coincide, if sufficiently flexible similarity concepts are taken into acount. This provides some formal arguments for the necessity of non-symmetric similarity measures. Encouraged by these first results, the author tried to investigate more structured learning problems from the view point of case-based reasoning. It turned out that an appropriate handling requires formalisms allowing similarity concep

We outline the rationale and preliminary results of using the State Context Property (SCOP) formalism, originally developed as a generalization of quantum mechanics, to describe the contextual manner in which concepts are evoked, used, and combined to generate meaning. The quantum formalism was developed to cope with problems arising in the description of (1) the measurement process, and (2) the generation of new states with new properties when particles become entangled. Similar problems arising with concepts motivated the formal treatment introduced here. Concepts are viewed not as fixed representations, but entities existing in states of potentiality that require interaction with a context—a stimulus or another concept—to ‘collapse ’ to an instantiated form (e.g. exemplar, prototype, or other possibly imaginary instance). The stimulus situation plays the role of the measurement in physics, acting as context that induces a change of the cognitive state from superposition state to collapsed state. The collapsed state is more likely to consist of a conjunction of concepts for associative than analytic thought because more stimulus or concept properties take part in the collapse. We provide two contextual measures of conceptual distance—one using collapse probabilities and the other weighted properties—and show how they can be applied to conjunctions using the pet fish problem.

We describe an approach to user interface design based on ideas from social science, narratology (the theory of stories), cognitive science, and a new area called algebraic semiotics. Social analysis helps to identify certain roles for users with their associated requirements, and suggests ways to make proofs more understandable, while algebraic semiotics, which combines semiotics with algebraic specification, provides rigorous theories for interface functionality and for a certain technical notion of quality. We apply these techniques to designing user interfaces for a distributed cooperative theorem proving system, whose main component is a website generation and proof assistance tool called Kumo. This interface integrates formal proving, proof browsing, animation, informal explanation, and online background tutorials, drawing on a richer than usual notion of proof. Experience with using the interface is reported, and some conclusions are drawn.

Human concept learning presents a version of the classic problem of induction, which is made particularly difficult by the combination of two requirements: the need to learn from a rich (i.e. nested and overlapping) vocabulary of possible concepts and the need to be able to generalize concepts reasonably from only a few positive examples. I begin this thesis by considering a simple number concept game as a concrete illustration of this ability. On this task, human learners can with reasonable confidence lock in on one out of a billion billion billion logically possible concepts, after seeing only four positive examples of the concept, and can generalize informatively after seeing just a single example. Neither of the two classic approaches to inductive inference -- hypothesis testing in a constrained space of possible rules and computing similarity to the observed examples -- can provide a complete picture of how people generalize concepts in even this simple setting. This thesis prop...

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For decades, the Democrats have been viewed as the party of the poor, with the Republicans representing the rich. Recent presidential elections, however, have shown a reverse pattern, with Democrats performing well in the richer blue states in the northeast and coasts, and Republicans dominating in the red states in the middle of the country and the south. Through multilevel modeling of individuallevel survey data and county- and state-level demographic and electoral data, we reconcile these patterns. Furthermore, we find that income matters more in red America than in blue America. In poor states, rich people are much more likely than poor people to vote for the Republican presidential candidate, but in rich states (such as Connecticut), income has a very low correlation with vote preference.

: We describe a new approach to interface design called algebraic semiotics, combining semiotics with algebraic specification to give a rigorous theory of representation quality, and we apply it to the tatami distributed cooperative proving project. This project uses standard html, Java, etc. for remote proof browsing, servers for remote proof execution, a protocol to maintain truth of distributed cooperative proofs, and a tool combining proof assistance with website editing. Its proof paradigm reduces theorems to problems solvable by proof servers. ProofWebs integrate browsing, execution, animation, and informal explanation with formal proofs, and their design has been driven by semiotic ideas. 1 Introduction The landscape of theorem proving can be seen as two main peaks with a great plane between. These peaks represent fully automatic theorem provers and proof checking theorem provers; the plane represents the difficulty of combining their virtues. The peaks are steep and dark bec...

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. 1 Introduction The intention of the present paper is to introduce two new notions in incremental learning which allow a classification of phenomena finer than known so far in the area. These concepts are denoted by the phrases informationally incremental learning and operationally incremental learning, respectively. Roughly spoken, informationally incremental algorithms are required to work incrementally as usual, i.e. they have no permission to look back at the whole history of information presented during the learning process. Operationally incremental learning algorithms may have permission to look back, but they are not allowed to use information of the past in some effective way. ...

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Quantities are ubiquitous and an important part of our understanding about the world -- we talk of engine horsepower, size, mileage, price of cars; GDP, population, area of countries; wingspan, weight, surface area of birds, and so on. In this paper, we present cognitively plausible symbolic representations of quantity and principles for generating those representations. Bringing together evidence in linguistics and psychology, we argue that our representations must make two kinds of distinctions -- dimensional, those that denote changes of quantity, e.g., large and small; and structural, those that denote changes of quality, e.g. boiling point and poverty line.