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Exploring the episodic structure of algebra story problem solving
This paper analyzes the quantitative and situational structure of algebra story problems, uses these materials to propose an interpretive framework for written problem-solving protocols, and then presents an exploratory study of the episodic structure of algebra story problem solving in a sizable group of mathematically competent subjects. Analyses of written protocols compare the strategic, tactical, and conceptual content of solution attempts, looking within these attempts at the interplay between problem comprehension and solution. Comprehension and solution of algebra story problems are complimentary activities, giving rise to a succession of problem solving episodes. While direct algebraic problem solving is sometimes effective, results suggest that the algebraic formalism may be of little help in comprehending the quantitative constraints posed in a problem text. Instead, competent problem solvers often reason within the situational context presented by a story problem, using various forms of "model-based reasoning" to identify, pursue, and verify quantitative constraints required for solution. The paper concludes by discussing the implications of these findings for acquiring mathematical concepts (e.g., related linear functions) and for supporting their acquisition through instruction
Bayesianism for Non-ideal Agents
Orthodox Bayesianism is a highly idealized theory of how we ought to live our epistemic lives. One of the most widely discussed idealizations is that of logical omniscience: the assumption that an agent’s degrees of belief must be probabilistically coherent to be rational. It is widely agreed that this assumption is problematic if we want to reason about bounded rationality, logical learning, or other aspects of non-ideal epistemic agency. Yet, we still lack a satisfying way to avoid logical omniscience within a Bayesian framework. Some proposals merely replace logical omniscience with a different logical idealization; others sacrifice all traits of logical competence on the altar of logical non-omniscience. We think a better strategy is available: by enriching the Bayesian framework with tools that allow us to capture what agents can and cannot infer given their limited cognitive resources, we can avoid logical omniscience while retaining the idea that rational degrees of belief are in an important way constrained by the laws of probability. In this paper, we offer a formal implementation of this strategy, show how the resulting framework solves the problem of logical omniscience, and compare it to orthodox Bayesianism as we know it
Knowledge-driven Natural Language Understanding of English Text and its Applications
Understanding the meaning of a text is a fundamental challenge of natural
language understanding (NLU) research. An ideal NLU system should process a
language in a way that is not exclusive to a single task or a dataset. Keeping
this in mind, we have introduced a novel knowledge driven semantic
representation approach for English text. By leveraging the VerbNet lexicon, we
are able to map syntax tree of the text to its commonsense meaning represented
using basic knowledge primitives. The general purpose knowledge represented
from our approach can be used to build any reasoning based NLU system that can
also provide justification. We applied this approach to construct two NLU
applications that we present here: SQuARE (Semantic-based Question Answering
and Reasoning Engine) and StaCACK (Stateful Conversational Agent using
Commonsense Knowledge). Both these systems work by "truly understanding" the
natural language text they process and both provide natural language
explanations for their responses while maintaining high accuracy.Comment: Preprint. Accepted by the 35th AAAI Conference (AAAI-21) Main Track
Online Handbook of Argumentation for AI: Volume 1
This volume contains revised versions of the papers selected for the first
volume of the Online Handbook of Argumentation for AI (OHAAI). Previously,
formal theories of argument and argument interaction have been proposed and
studied, and this has led to the more recent study of computational models of
argument. Argumentation, as a field within artificial intelligence (AI), is
highly relevant for researchers interested in symbolic representations of
knowledge and defeasible reasoning. The purpose of this handbook is to provide
an open access and curated anthology for the argumentation research community.
OHAAI is designed to serve as a research hub to keep track of the latest and
upcoming PhD-driven research on the theory and application of argumentation in
all areas related to AI.Comment: editor: Federico Castagna and Francesca Mosca and Jack Mumford and
Stefan Sarkadi and Andreas Xydi
A Dynamic Solution to the Problem of Logical Omniscience
The traditional possible-worlds model of belief describes agents as ‘logically omniscient’ in the sense that they believe all logical consequences of what they believe, including all logical truths. This is widely considered a problem if we want to reason about the epistemic lives of non-ideal agents who—much like ordinary human beings—are logically competent, but not logically omniscient. A popular strategy for avoiding logical omniscience centers around the use of impossible worlds: worlds that, in one way or another, violate the laws of logic. In this paper, we argue that existing impossible-worlds models of belief fail to describe agents who are both logically non-omniscient and logically competent. To model such agents, we argue, we need to ‘dynamize’ the impossible-worlds framework in a way that allows us to capture not only what agents believe, but also what they are able to infer from what they believe. In light of this diagnosis, we go on to develop the formal details of a dynamic impossible-worlds framework, and show that it successfully models agents who are both logically non-omniscient and logically competent
Boltzmann's H-theorem, its limitations, and the birth of (fully) statistical mechanics
A comparison is made of the traditional Loschmidt (reversibility) and Zermelo
(recurrence) objections to Boltzmann's H-theorem, and its simplified variant in
the Ehrenfests' 1912 wind-tree model. The little-cited 1896 (pre-recurrence)
objection of Zermelo (similar to an 1889 argument due to Poincare) is also
analysed. Significant differences between the objections are highlighted, and
several old and modern misconceptions concerning both them and the H-theorem
are clarified. We give particular emphasis to the radical nature of Poincare's
and Zermelo's attack, and the importance of the shift in Boltzmann's thinking
in response to the objections as a whole.Comment: 40 page
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