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Linguistic cues in the acquisition of number words
, 1997
"... Previous research has shown that children go through a stage in which they know that the number words each refer to a distinct numerosity, yet do not know which numerosity each number word picks out (Wynn, 1992). How do children attain this level of knowledge? We explore the possibility that particu ..."
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Previous research has shown that children go through a stage in which they know that the number words each refer to a distinct numerosity, yet do not know which numerosity each number word picks out (Wynn, 1992). How do children attain this level of knowledge? We explore the possibility that particular properties of how number words are used within sentences inform children of the semantic class to which they belong. An analysis of transcripts of the spontaneous speech of three one and twoyearold children and their parents (from the CHILDES database; MacWhinney & Snow, 1990) suggests that the relevant cues are available as input in parents ’ speech to children, and that children generally honour these properties of number words in their own speech. Implications of this proposal for word learning more generally are discussed.
Semantic Vector Products: Some Initial Investigations
"... Semantic vector models have proven their worth in a number of natural language applications whose goals can be accomplished by modelling individual semantic concepts and measuring similarities between them. By comparison, the area of semantic compositionality in these models has so far remained unde ..."
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Semantic vector models have proven their worth in a number of natural language applications whose goals can be accomplished by modelling individual semantic concepts and measuring similarities between them. By comparison, the area of semantic compositionality in these models has so far remained underdeveloped. This will be a crucial hurdle for semantic vector models: in order to play a fuller part in the modelling of human language, these models will need some way of modelling the way in which single concepts are put together to form more complex conceptual structures. This paper explores some of the opportunities for using vector product operations to model compositional phenomena in natural language. These vector operations
Using landing pages for sponsored search ad selection
 In WWW ’10: Proceedings of the 19th international conference on World wide web
, 2010
"... We explore the use of the landing page content in sponsored search ad selection. Specifically, we compare the use of the ad’s intrinsic content to augmenting the ad with the whole, or parts, of the landing page. We explore two types of extractive summarization techniques to select useful regions fro ..."
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We explore the use of the landing page content in sponsored search ad selection. Specifically, we compare the use of the ad’s intrinsic content to augmenting the ad with the whole, or parts, of the landing page. We explore two types of extractive summarization techniques to select useful regions from the landing pages: outofcontext and incontext methods. Outofcontext methods select salient regions from the landing page by analyzing the content alone, without taking into account the ad associated with the landing page. Incontext methods use the ad context (including its title, creative, and bid phrases) to help identify regions of the landing page that should be used by the ad selection engine. In addition, we introduce a simple yet effective unsupervised algorithm to enrich the ad context to further improve the ad selection. Experimental evaluation confirms that the use of landing pages can significantly improve the quality of ad selection. We also find that our extractive summarization techniques reduce the size of landing pages substantially, while retaining or even improving the performance of ad retrieval over the method that utilize the entire landing page.
Incorporating Generalized Quantifiers into Description Logic to Improve Source Selection

, 2001
"... ..."
Contextual Vocabulary Acquisition: From Algorithm to Curriculum
"... Deliberate contextual vocabulary acquisition (CVA) is a reader’s ability to figure out a (not the) meaning for an unknown word from its “context”, without external sources of help such as dictionaries or people. The appropriate context for such CVA is the “beliefrevised integration” of the reader’s ..."
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Deliberate contextual vocabulary acquisition (CVA) is a reader’s ability to figure out a (not the) meaning for an unknown word from its “context”, without external sources of help such as dictionaries or people. The appropriate context for such CVA is the “beliefrevised integration” of the reader’s prior knowledge with the reader’s “internalization” of the text. We discuss unwarranted assumptions behind some classic objections to CVA, and present and defend a computational theory of CVA that we have adapted to a new classroom curriculum designed to help students use CVA to improve their reading comprehension.
The growth of mathematical knowledge: an open world view
 The growth of mathematical knowledge, Kluwer, Dordrecht 2000
"... mathematical knowledge: “The advance of science is not comparable to the changes of a city, where old edifices are pitilessly torn down to give place to new ones, but to the continuous evolution of zoological types which develop ceaselessly and end by becoming unrecognizable to the common sight, but ..."
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mathematical knowledge: “The advance of science is not comparable to the changes of a city, where old edifices are pitilessly torn down to give place to new ones, but to the continuous evolution of zoological types which develop ceaselessly and end by becoming unrecognizable to the common sight, but where an expert eye finds always traces of the prior work of the centuries past ” (Poincaré 1958, p. 14). The view criticized by Poincaré corresponds to Frege’s idea that the development of mathematics can be described as an activity of system building, where each system is supposed to provide a complete representation for a certain mathematical field and must be pitilessly torn down whenever it fails to achieve such an aim. All facts concerning any mathematical field must be fully organized in a given system because “in mathematics we must always strive after a system that is complete in itself ” (Frege 1979, p. 279). Frege is aware that systems introduce rigidity and are in conflict with the actual development of mathematics because “in history we have development; a system is static”, but he sticks
Mathematical discourse vs. mathematical intuition
 Mathematical reasoning and heuristics, College Publications, London 2005
"... One of the most uninformative statements one could possibly make about mathematics is that the axiomatic method expresses the real nature of mathematics, i.e., that mathematics consists in the deduction of conclusions from given axioms. For the same could be said about several other subjects, for ex ..."
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One of the most uninformative statements one could possibly make about mathematics is that the axiomatic method expresses the real nature of mathematics, i.e., that mathematics consists in the deduction of conclusions from given axioms. For the same could be said about several other subjects, for example, about theology. Think of the first part of Spinoza’sEthica ordine geometrico demonstrata orofGödel’sproofof the existence of God, which are both fine specimens of Theologia ordine geometrico demonstrata. To the objection, ‘Surely theological entities are not mathematicalobjects’,one could answer:How do you know? If mathematics consists in the deduction of conclusions from given axioms, then mathematical objects are given by the axioms. So, if theological entities satisfy the axioms, why should not they be considered mathematical objects? Hilbert says: “Ifinspeakingofmypoints”,linesandplanes“I think of some system of things, e.g. the system: love, law, chimney sweep... and then assume all my axioms as relations between these things,thenmypropositions,e.g.Pythagoras’theorem,arealsovalidfor thesethings”. 1 Similarly he might have said: If in speaking of my points, lines and planes, I think of a suitable triad of theological entities, and assume all my axioms as relations between these things, then my propositions,e.g.Pythagoras’theorem,arealsovalidforthesethings. Indeed, if mathematics consists in the deduction of conclusions from given axioms, then it has no specific content. So it is simply imposibletodistinguishgeometricalobjects,suchas‘points,linesand planes’,from ‘love,law,chimney sweep’,ora suitable triad of theological entities.ThisisvividlyilustratedbyRusel’sstatementthat “mathematicsmaybedefinedasthesubject in which we never know whatwearetalkingabout,norwhetherwhatwearesayingistrue”. 2
THE CASE FOR PSYCHOLOGISM IN DEFAULT AND INHERITANCE REASONING
, 2005
"... Default reasoning occurs whenever the truth of the evidence available to the reasoner does not guarantee the truth of the conclusion being drawn. Despite this, one is entitled to draw the conclusion “by default” on the grounds that we have no information which would make us doubt that the inference ..."
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Default reasoning occurs whenever the truth of the evidence available to the reasoner does not guarantee the truth of the conclusion being drawn. Despite this, one is entitled to draw the conclusion “by default” on the grounds that we have no information which would make us doubt that the inference should be drawn. It is the type of conclusion we draw in the ordinary world and ordinary situations in which we find ourselves. Formally speaking, ‘nonmonotonic reasoning’ refers to argumentation in which one uses certain information to reach a conclusion, but where it is possible that adding some further information to those very same premises could make one want to retract the original conclusion. It is easily seen that the informal notion of default reasoning manifests a type of nonmonotonic reasoning. Generally speaking, default statements are said to be true about the class of objects they describe, despite the acknowledged existence of “exceptional instances” of the class. In the absence of explicit information that an object is one of the exceptions we are enjoined to apply the default statement to the object. But further information may later tell us that the object is in fact one of the exceptions. So this is one of the points where nonmonotonicity resides in default reasoning.
Predicative Fragments of Frege Arithmetic
, 2003
"... Frege Arithmetic (FA) is the secondorder theory whose sole nonlogical axiom is Hume’s Principle, which says that the number of F s is identical to the number of Gs if and only if the F s and the Gs can be onetoone correlated. According to Frege’s Theorem, FA and some natural definitions imply al ..."
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Frege Arithmetic (FA) is the secondorder theory whose sole nonlogical axiom is Hume’s Principle, which says that the number of F s is identical to the number of Gs if and only if the F s and the Gs can be onetoone correlated. According to Frege’s Theorem, FA and some natural definitions imply all of secondorder Peano Arithmetic. This paper distinguishes two dimensions of impredicativity involved in FA—one having to do with Hume’s Principle, the other, with the underlying secondorder logic—and investigates how much of Frege’s Theorem goes through in various partially predicative fragments of FA. Theorem 1 shows that almost everything goes through, the most important exception being the axiom that every natural number has a successor. Theorem 2 shows that the Successor Axiom cannot be proved in the theories that are predicative in either dimension. 1
SOMETHING ABOUT MARY*
"... Jackson’s blackandwhite Mary teaches us that the propositional content of perception cannot be fully expressed in language. In one of the earliest and best replies to Frank Jackson’s knowledge argument, Horgan claimed, in effect, that the argument illegitimately draws a metaphysical conclusion – t ..."
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Jackson’s blackandwhite Mary teaches us that the propositional content of perception cannot be fully expressed in language. In one of the earliest and best replies to Frank Jackson’s knowledge argument, Horgan claimed, in effect, that the argument illegitimately draws a metaphysical conclusion – that physicalism is false – from an epistemic premise – that physically omniscient Mary would not know everything. Horgan’s response has become standard. And, as it happens, I think it is correct. 1 But although physicalism survives unscathed, Jackson’s thought experiment does hold an important lesson. 2 It suggests, I shall argue, that the propositional content of perception is ineffable, in the sense that it cannot be fully expressed in language. This conclusion will be reached by considering a puzzle about perception posed by a slightly modified version of Jackson’s thought experiment. As will become clear, the puzzle has affinities * Earlier drafts were improved thanks to Michael Glanzberg, Benj Hellie,