SAD as a mathematical assistant—how should we go from here to there?

The System for Automated Deduction (SAD) is developed in the framework of the Evidence Algorithm research project and is intended for automated processing of mathematical texts. The SAD system works on three levels of reasoning: (a) the level of text presentation where proofs are written in a formal natural-like language for subsequent verification; (b) the level of foreground reasoning where a particular theorem proving problem is simplified and decomposed; (c) the level of background deduction where exhaustive combinatorial inference search in classical first-order logic is applied to prove end subgoals.

We present an overview of SAD describing the ideas behind the project, the system's design, and the process of problem formalization in the fashion of SAD. We show that the choice of classical first-order logic as the background logic of SAD is not too restrictive. For example, we can handle binders like Σ or lim without resort to second order or to a full-powered set theory. We illustrate our approach with a series of examples, in particular, with the classical problem .     

Learning the form of causal relationships using hierarchical bayesian models

People learn quickly when reasoning about causal relationships, making inferences from limited data and avoiding spurious inferences. Efficient learning depends on abstract knowledge, which is often domain or context specific, and much of it must be learned. While such knowledge effects are well documented, little is known about exactly how we acquire knowledge that constrains learning. This work focuses on knowledge of the functional form of causal relationships; there are many kinds of relationships that can apply between causes and their effects, and knowledge of the form such a relationship takes is important in order to quickly identify the real causes of an observed effect. We developed a hierarchical Bayesian model of the acquisition of knowledge of the functional form of causal relationships and tested it in five experimental studies, considering disjunctive and conjunctive relationships, failure rates, and cross-domain effects. The Bayesian model accurately predicted human judgments and outperformed several alternative models.     

What’s in the name? Or how rocks and stones are different from bunnies and rabbits

Labels have been shown to play an important role in inductive generalization; however, the mechanism by which labels contribute to generalization early in development remains unclear. We investigated two factors that may influence the inductive potential of labels: semantic similarity and co-occurrence probability. Results suggested that adults and 6-year-olds rely on semantic similarity of labels and that their generalizations are not affected by co-occurrence probability. Specifically, generalization patterns were qualitatively similar for co-occurring semantically similar labels (e.g., bunny-rabbit) and non-co-occurring semantically similar labels (e.g., rock-stone) in 6-year-olds and adults. Unlike 6-year-olds and adults, 4-year-olds were likely to generalize co-occurring labels but not non-co-occurring labels. Possible mechanisms by which co-occurrence probability may influence label generalization in young children are discussed.     

Incorporating Demographic Embeddings Into Language Understanding

Meaning depends on context. This applies in obvious cases like deictics or sarcasm as well as more subtle situations like framing or persuasion. One key aspect of this is the identity of the participants in an interaction. Our interpretation of an utterance shifts based on a variety of factors, including personal history, background knowledge, and our relationship to the source. While obviously an incomplete model of individual differences, demographic factors provide a useful starting point and allow us to capture some of this variance. However, the relevance of specific demographic factors varies between situations—where age might be the key factor in one context, ideology might dominate in another. To address this challenge, we introduce a method for combining demographics and context into situated demographic embeddings—mapping representations into a continuous geometric space appropriate for the given domain, showing the resulting representations to be functional and interpretable. We further demonstrate how to make use of related external data so as to apply this approach in low‐resource situations. Finally, we show how these representations can be incorporated into improve modeling of real‐world natural language understanding tasks, improving model performance and helping with issues of data sparsity.     

Generating Relations Elicits a Relational Mindset in Children

Relational reasoning is a hallmark of human higher cognition and creativity, yet it is notoriously difficult to encourage in abstract tasks, even in adults. Generally, young children initially focus more on objects, but with age become more focused on relations. While prerequisite knowledge and cognitive resource maturation partially explains this pattern, here we propose a new facet important for children's relational reasoning development: a general orientation to relational information, or a relational mindset. We demonstrate that a relational mindset can be elicited, even in 4‐year‐old children, yielding greater than expected spontaneous attention to relations. Children either generated or listened to an experimenter state the relationships between objects in a set of formal analogy problems, and then in a second task, selected object or relational matches according to their preference. Children tended to make object mappings, but those who generated relations on the first task selected relational matches more often on the second task, signaling that relational attention is malleable even in young children.     

An examination of the SEP candidate analogical inference rule within pure inductive logic

Within the framework of (Unary) Pure Inductive Logic we investigate four possible formulations of a probabilistic principle of analogy based on a template considered by Paul Bartha in the Stanford Encyclopedia of Philosophy [1] and give some characterizations of the probability functions which satisfy them. In addition we investigate an alternative interpretation of analogical support, also considered by Bartha, based not on the enhancement of probability but on the creation of possibility.     

Intrinsic cognitive models

Theories concerning the structure, or format, of mental representation should (1) be formulated in mechanistic, rather than metaphorical terms; (2) do justice to several philosophical intuitions about mental representation; and (3) explain the human capacity to predict the consequences of worldly alterations (i.e., to think before we act). The hypothesis that thinking involves the application of syntax‐sensitive inference rules to syntactically structured mental representations has been said to satisfy all three conditions. An alternative hypothesis is that thinking requires the construction and manipulation of the cognitive equivalent of scale models. A reading of this hypothesis is provided that satisfies condition (1) and which, even though it may not fully satisfy condition (2), turns out (in light of the frame problem) to be the only known way to satisfy condition (3).     

儿童类比推理的影响因素及干预促进

类比推理这一重要认知能力能够帮助儿童在未经历过的复杂情况下进行推断和学习。近年来研究者主要从行为研究、计算机模型和眼动技术的角度探究了儿童抑制控制和工作记忆在类比推理中的交互作用模式及类比推理策略对类比推理的影响。在此基础上,研究者围绕语言标签和物理表征两方面对儿童类比推理进行了干预研究。儿童类比推理的未来研究应着眼于改进研究方法、关注类比推理各加工阶段影响因素及加强儿童类比推理策略的干预应用研究。     

The computational value of debate in defeasible reasoning

Defeasible reasoning is concerned with the logics of non-deductive argument. As is described in the literature, the study of this type of reasoning is considerably more involved than the study of deductive argument, even so that, in realistic applications, there is often a lack of resources to perform an exhaustive analysis. It follows that, in a theory of defeasible reasoning, the order and direction in which arguments are developed, i.e. theprocedure, is important. The aim of this article is to show that debate is the most efficient procedure to argue in the presence of limited resources. To do so, there is first some general theory on defeasible argumentation, which is followed by an introduction to the problem of dialectical search. The problem of dialectical search is (or at least, should be) the essential issue in every theory on argumentation, and emerges at every occasion that involves adjudication on competing arguments. Starting with an example, it is explained that dialectical search can be best scheduled according to classical debating techniques, that work along well-tried methods. These methods (which include various forms of curtailment, interruption, and interpretation) have proven their value in keeping debating efforts within reasonable bounds. How they apply in a theory of formal argument, will be shown in this article.This research was made possible by SION, and is financed by NWO under contract number 612-316-019. Part of this research has been conducted at the Vrije Universiteit Amsterdam. This article contains fragments of Chapter 6 and Chapter 7 of the author's dissertation. Studies in Defeasible Argumentation (1993).