Quantification and the language of thought

Home
/
Papers
/
Quantification and the language of thought

Proceedings Article•

Quantification and the language of thought

Charles Kemp¹•Institutions (1)

07 Dec 2009-Vol. 22, pp 943-951

TL;DR: To support this proposal, behavioral results from a concept learning study inspired by the work of Shepard, Hovland and Jenkins are presented and it is shown that the language of thought allows first order quantification more readily than second-order quantification.

read less

Abstract: Many researchers have suggested that the psychological complexity of a concept is related to the length of its representation in a language of thought. As yet, however, there are few concrete proposals about the nature of this language. This paper makes one such proposal: the language of thought allows first order quantification (quantification over objects) more readily than second-order quantification (quantification over features). To support this proposal we present behavioral results from a concept learning study inspired by the work of Shepard, Hovland and Jenkins.

...read moreread less

Content maybe subject to copyright Report

Citations

PDF

Open Access

More filters

Journal Article•DOI•

The logical primitives of thought: Empirical foundations for compositional cognitive models.

[...]

Steven Piantadosi¹, Joshua B. Tenenbaum², Noah D. Goodman³•Institutions (3)

University of Rochester¹, Massachusetts Institute of Technology², Stanford University³

14 Apr 2016-Psychological Review

TL;DR: This work shows how different sets of LOT primitives, embedded in a psychologically realistic approximate Bayesian inference framework, systematically predict distinct learning curves in rule-based concept learning experiments, and shows how specific LOT theories can be distinguished empirically.

...read moreread less

Abstract: The notion of a compositional language of thought (LOT) has been central in computational accounts of cognition from earliest attempts (Boole, 1854; Fodor, 1975) to the present day (Feldman, 2000; Penn, Holyoak, & Povinelli, 2008; Fodor, 2008; Kemp, 2012; Goodman, Tenenbaum, & Gerstenberg, 2015). Recent modeling work shows how statistical inferences over compositionally structured hypothesis spaces might explain learning and development across a variety of domains. However, the primitive components of such representations are typically assumed a priori by modelers and theoreticians rather than determined empirically. We show how different sets of LOT primitives, embedded in a psychologically realistic approximate Bayesian inference framework, systematically predict distinct learning curves in rule-based concept learning experiments. We use this feature of LOT models to design a set of large-scale concept learning experiments that can determine the most likely primitives for psychological concepts involving Boolean connectives and quantification. Subjects' inferences are most consistent with a rich (nonminimal) set of Boolean operations, including first-order, but not second-order, quantification. Our results more generally show how specific LOT theories can be distinguished empirically. (PsycINFO Database Record

...read moreread less

117 citations

Cites background or methods or result from "Quantification and the language of ..."

...We build on recently developed computational tools and empirical techniques that have allowed detailed modeling of how people learn symbolically structured concepts across a variety of domains (e.g., Nosofsky, Palmeri, & McKinley, 1994; Kemp, Goodman, & Tenenbaum, 2008a; Kemp, 2009; Piantadosi, 2011; Kemp, 2012; Ullman et al., 2012)....
[...]
...This provides strong evidence for quantification in the LOT, in line with Kemp (2009); the superiority of a grammar with multiple types of quantifiers indicates that, like the Boolean results, quantificational operations in the LOT do not make use of a “minimal” basis of operations (such as just…...
[...]
...We find it compelling that, despite these differences, we find qualitatively similar results, including a tendency for quantification over objects but not features (Kemp, 2009, 2012)....
[...]
...Building on Kemp (2009, 2012), and motivated by both classic work in formal semantics (Montague, 1973), AI (Levesque et al., 1998; Muggleton & De Raedt, 1994; Milch et al., 2004; Russell & Norvig, 2009; Domingos & Richardson, 2007; Richardson & Domingos, 2006; Goodman, Mansinghka, et al. 2008;…...
[...]
...…tools and empirical techniques that have allowed detailed modeling of how people learn symbolically structured concepts across a variety of domains (e.g., Nosofsky, Palmeri, & McKinley, 1994; Kemp, Goodman, & Tenenbaum, 2008a; Kemp, 2009; Piantadosi, 2011; Kemp, 2012; Ullman et al., 2012)....
[...]

Dissertation•

Learning and the language of thought

[...]

Steven Piantadosi

01 Jan 2011

TL;DR: An inductive statistical model is presented over a compositionally structured representation system, a language of thought (LOT) (Fodor, 1975), that formalizes an optimal Bayesian trade-off between representational complexity and fit to the observed data.

...read moreread less

Abstract: Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Brain and Cognitive Sciences, 2011.

...read moreread less

24 citations

Cites result from "Quantification and the language of ..."

...Building off of previous experimental and computational studies (Kemp, 2009; Piantadosi et al., 2009), we extend the modeling results to the wider range of concepts from our experiment that involve quantification and relational terms....
[...]

Journal Article•

Review: George Boole, An Investigation of the Laws of Thought, on Which are Founded the Mathematical Theories of Logic and Probabilities

[...]

Alonzo Church

01 Sep 1951-Journal of Symbolic Logic

10 citations

Journal Article•

Inferring priors in compositional cognitive models.

[...]

Eric Bigelow, Steven Piantadosi

01 Jan 2016-Cognitive Science

TL;DR: A data analysis technique is developed for a family of compositional “Language of Thought” (LOT) models which permits discovery of subjects’ prior probability of mental operations in this domain and reveals high correlations between model mean predictions and subject generalizations.

...read moreread less

2 citations

Cites methods from "Quantification and the language of ..."

...To test these assumptions, different particular LOTs have been tested to compare, for instance, LOT theories with distinct types of quantification or varying sets of boolean operations (Kemp, 2009, 2012; S. Piantadosi, 2011; S. T. Piantadosi, Tenenbaum, & Goodman, under review)....
[...]

References

PDF

Open Access

More filters

Book•

The Language of Thought

[...]

Jerry A. Fodor

01 Jan 1975

TL;DR: In this article, Fodor argues that, while our best current theories of cognitive psychology view many higher processes as computational, computation itself presupposes an internal medium of representation, which is the speculative approach to the philosophy of mind.

...read moreread less

Abstract: In a compelling defense of the speculative approach to the philosophy of mind, Jerry Fodor argues that, while our best current theories of cognitive psychology view many higher processes as computational, computation itself presupposes an internal medium of representation. Fodor's prime concerns are to buttress the notion of internal representation from a philosophical viewpoint, and to determine those characteristics of this conceptual construct using the empirical data available from linguistics and cognitive psychology.

...read moreread less

4,289 citations

Proceedings Article•DOI•

Cheap and Fast -- But is it Good? Evaluating Non-Expert Annotations for Natural Language Tasks

[...]

Rion Snow¹, Brendan O'Connor, Dan Jurafsky¹, Andrew Y. Ng¹•Institutions (1)

Stanford University¹

25 Oct 2008

TL;DR: This work explores the use of Amazon's Mechanical Turk system, a significantly cheaper and faster method for collecting annotations from a broad base of paid non-expert contributors over the Web, and proposes a technique for bias correction that significantly improves annotation quality on two tasks.

...read moreread less

Abstract: Human linguistic annotation is crucial for many natural language processing tasks but can be expensive and time-consuming. We explore the use of Amazon's Mechanical Turk system, a significantly cheaper and faster method for collecting annotations from a broad base of paid non-expert contributors over the Web. We investigate five tasks: affect recognition, word similarity, recognizing textual entailment, event temporal ordering, and word sense disambiguation. For all five, we show high agreement between Mechanical Turk non-expert annotations and existing gold standard labels provided by expert labelers. For the task of affect recognition, we also show that using non-expert labels for training machine learning algorithms can be as effective as using gold standard annotations from experts. We propose a technique for bias correction that significantly improves annotation quality on two tasks. We conclude that many large labeling tasks can be effectively designed and carried out in this method at a fraction of the usual expense.

...read moreread less

2,237 citations

Book•

A mathematical introduction to logic

[...]

Herbert B. Enderton

01 Jan 1972

TL;DR: A comparison of first- and second-order logic in the case of SETs shows that the former is more likely to be correct and the latter is less likely.

...read moreread less

Abstract: USEFUL FACTS ABOUT SETS. SENTENTIAL LOGIC. FIRST-ORDER LOGIC. UNDECIDABILITY. SECOND-ORDER LOGIC.

...read moreread less

2,216 citations

"Quantification and the language of ..." refers background in this paper

...If partitions that differ only up to a permutation of the features (Domain 3) or objects (Domain 4) are grouped into equivalence classes, there are ten of these classes, and a representative of each is shown in Figure 1b. Previous researchers [6] have pointed out that the stimuli in Domain 1 can be…...
[...]

Journal Article•DOI•

Games with a purpose

[...]

L. von Ahn¹•Institutions (1)

Carnegie Mellon University¹

01 Jun 2006-IEEE Computer

TL;DR: "Games with a purpose" have a vast range of applications in areas as diverse as security, computer vision, Internet accessibility, adult content filtering, and Internet search, and any game designed to address these and other problems must ensure that game play results in a correct solution and, at the same time, is enjoyable.

...read moreread less

Abstract: Through online games, people can collectively solve large-scale computational problems. Such games constitute a general mechanism for using brain power to solve open problems. In fact, designing such a game is much like designing an algorithm - it must be proven correct, its efficiency can be analyzed, a more efficient version can supersede a less efficient one, and so on. "Games with a purpose" have a vast range of applications in areas as diverse as security, computer vision, Internet accessibility, adult content filtering, and Internet search. Any game designed to address these and other problems must ensure that game play results in a correct solution and, at the same time, is enjoyable. People will play such games to be entertained, not to solve a problem - no matter how laudable the objective

...read moreread less

1,057 citations

Book•

An investigation of the laws of thought, on which are founded the mathematical theories of logic and probabilities

[...]

George Boole

17 Jan 2007

TL;DR: In this paper, the authors use the symbolic language of mathematics to establish a method to examine the nature of the human mind using logic and the theory of probabilities, and they consider language not just as a mode of expression, but as a system one can use to understand human mind.

...read moreread less

Abstract: Self-taught mathematician and father of Boolean algebra, George Boole (1815–1864) published An Investigation of the Laws of Thought in 1854. In this highly original investigation of the fundamental laws of human reasoning, a sequel to ideas he had explored in earlier writings, Boole uses the symbolic language of mathematics to establish a method to examine the nature of the human mind using logic and the theory of probabilities. Boole considers language not just as a mode of expression, but as a system one can use to understand the human mind. In the first 12 chapters, he sets down the rules necessary to represent logic in this unique way. Then he analyses a variety of arguments and propositions of various writers from Aristotle to Spinoza. One of history's most insightful mathematicians, Boole is compelling reading for today's student of intellectual history and the science of the mind.

...read moreread less

890 citations