Kenneth Wexler and Peter Culicover. Formal Principles of Language Acquisition. MIT Press, Cambridge, MA, 1980.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... and accuracy results in the model of learning in the limit introduced by Gold [11] During the last three decades much has been learned about the classes of formal languages and partial recursive functions that can successfully learned within Gold s [11] model and variations thereof (cf. e.g. [2, 5, 7, 8, 18, 24, 25, 27, 31]) We continue along these lines of research. In particular, we aim to investigate the principal learning capabilities of learners which perform incremental learning. For the purpose of motivation and discussion of our research, we introduce some notations. A positive presentation of a concept c ....

....to produce its actual guess exclusively from its previous one and the next element in the positive presentation. Iterative learning has been introduced by Wiehagen [26] who studied it in the setting of learning recursive functions. Further results concerning this learning model can be found in [7, 8, 13, 14, 18, 19, 25, 26, 29, 31]. Osherson et al. 18] also considered the variant that the learner has access to the last k elements, where k is a priori fixed. Interestingly enough, the latter approach does not increase the learning power. Alternatively, Fulk et al. 7] considered learners that are allowed to store k carefully ....

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K. Wexler and P. Culicover, "Formal Principles of Language Acquisition," MIT Press, Cambridge, Mass., 1980.

....summarize what has been known in this regard. The pattern languages can be learned by outputting descriptive patterns as hypotheses (cf. 1] The resulting learning algorithm is consistent and set driven. A learner is set driven iff its output depends only on the range of its input (cf. e.g. [20, 22]) In general, consistency and set drivenness considerably limit the learning capabilities (cf. e.g. 14, 22] But no polynomial time algorithm computing descriptive patterns is known, and hence already the update time is practically infeasible. Moreover, finding a descriptive pattern of ....

K. Wexler and P. Culicover. Formal Principles of Language Acquisition. MIT Press, Cambridge, MA, 1980.

....talk more about the here and now, and the child can observe the context and guess what the speaker might have meant. In fact, many models of language acquisition assume that the input the child receives consists not only of the sentence, but also of a representation of the meaning of the sentence ([Wexler and Culicover 1980], Pinker 1984] Berwick 1985] Briscoe 1999] among others) How much of the context surrounding the hearing of a sentence is used by children is an open question. Besides, as Landau and Gleitman [1985] observe, blind children have a severely limited access to non linguistic aspects of the ....

Wexler, K. and Culicover, P. Formal Principles of Language Acquisition. MIT Press, 1980.

....evidence that children are biased against acquiring homonyms (many to one mappings) at least cross categorially [10] Finally, most theories of the acquisition of syntax presuppose a bias against acquiring one to many mappings from meanings to syntactic structures (e. g the Uniqueness principle [20]) It has also been argued that a bias against many to one mappings from meanings to syntactic constructions can account for attested historical changes in language [3] 6 Conclusions I have presented an Iterated Learning Model of the cultural evolution of compositional structure. This model ....

K. Wexler and P. W. Culicover. Formal Principles of Language Acquisition. MIT Press, Cambridge, MA, 1980.

....Grammatical Inference. First, the grammar to be learned must be at least context free, as the power of natural languages is also at least context free ( Chomsky 57] Savitch 87] Second, to correctly simulate natural learning, the examples provided to the learner must exclusively be positive ( Wexler Culicover 80] But another more difficult constraint arises from natural situations. As a matter of fact, no one believes that children learn the grammar of their native language independent of meaning (semantics) and use (pragmatics) Feldman 98] Taking this claim seriously imposes to take at minimum ....

: K. Wexler, P. Culicover, Formal Principles of Language Acquisition, Cambridge, MIT Press, 1980.

....of Grammatical Inference from positive examples (or: from texts) consists in the design of algorithms able to identify a formal grammar from a sample of sentences it generates. This problem is a rough formal approximation of how children manage to learn the grammar of their mother language ([WC80]) From a theoretical point of view, identifying a formal grammar from texts is very dicult since regular (and therefore context free) grammars are not learnable from texts in usual learning models ( Gol67,Val84] 2.1 Categorial Grammars In the following, we will use formal grammars belonging ....

K. Wexler and P. Culicover. Formal Principles of Language Acquisition. MIT Press, 1980.

....for a large class of learning algorithms including the LWA. The point here is, that the LWA possesses two additional desirable properties, i.e. it is set driven (cf. Zeugmann [19] and conservative. A learner is said to be setdriven, if its outputs depends only on the range of its input (cf. [18]) Conservative learners maintain their actual hypotheses at least as long as they have not seen data contradicting them (cf. Angluin [2] learning algorithm. Then Pr(X t 1 X) 2 for all t 2 N . Proof. We divide the text (s 1 ; s 2 ; into blocks of length C . The probability that the ....

K. Wexler and P. Culicover. Formal Principles of Language Acquisition. MIT Press, Cambridge, MA, 1980.

....H 0 identifies C 0 . As it turned out, for proving some of the results below, it is conceptually simpler to use the characterization of conservative learning equating it with set driven inference (cf. Lange and Zeugmann [20] Set drivenness has been introduced by Wexler and Culicover [28] and describes the requirement that the output of an IIM is only allowed to depend on the range of its input. More formally, an IIM M is said to be set driven with respect to C iff, for all y; y 0 2 IN and all texts t; t for concepts in C, t y = t y 0 implies M(t y ) M( t y 0 ) ....

Wexler, K., and Culicover, P., "Formal Principles of Language Acquisition," MIT Press, 1980.

....see section 1.2.3. 5 1.2.3. Enumerative search and random search One of the oldest proposals for learning grammars is simple enumerative learning (Gold, 1967) An ordered list of the possible grammars is given, and the learner performs what has come to be known as error driven learning (Wexler Culicover, 1980). An error occurs when the learner encounters an overt form that cannot be successfully parsed (that is, assigned a grammatical structural description) by the learner s current grammar. The learner starts with the first grammar on the list; anytime an error occurs falsifying the learner s current ....

Wexler, K., & Culicover, P. (1980). Formal Principles of Language Acquisition. Cambridge, MA: MIT Press.

....shall concentrate on grammar acquisition. For our purposes the terms language acquisition device and universal grammar (Chomsky 1980, 1993) can be used synonymously. Universal grammar (UG) species the range of grammatical hypotheses that children entertain during language acquisition (see Wexler Culicover (1980); Lightfoot (1982) Many linguists believe that universal grammar is the consequence of specic genetically encoded structures within the human brain (Hornstein Lightfoot 1981; Pinker Bloom 1990; Jackendo 1997) It is important to note the dierence between universal grammar and the ....

Wexler, K. & Culicover, P. 1980 Formal principles of language acquisition. Cambridge MA: MIT Press.

....(Chomsky 1975; Crain Nakayama 1987; inter alia) On the other hand, a constrained grammar space is motivated by the remarkable similarities found in comparative studies of the world s languages. Virtually all previous formal models of language acquisition in the UG framework (Chomsky 1965; Wexler Culicover 1980; Berwick 1985; Gibson Wexler 1994; inter alia) are transformational , 2 borrowing a term from evolutionary biology (Lewontin 1983) In transformational models, the learner moves from one hypothesis grammar to another as input sentences are processed, and at any time, the state of the learner ....

....which a target grammar T is used, we say that learning converges to T if lim t## p T (E T , t) 1. 2.2 An acquisition algorithm Write E # s to indicate that a sentence s is an utterance in the linguistic environment E. Write s # G if G can analyze s, which, in a narrow sense, is parsability (Wexler Culicover 1980, Berwick 1985) Suppose that there are altogether N grammars in the population. For simplicity, write p i for p i (E, t) at time t, and p # i for p i (E, t 1) at time t 1. Learning takes place as follows: The Algorithm L: Given an input sentence s, the child 1. with the probability p i , ....

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Wexler, K. and P. Culicover (1980). Formal principles of language acquisition. Cambridge, MA: MIT Press.

....such that M i does not Resep identify (L i,f i , L # i,f i ) Let L C = L i,f i i # N # L # i,f i i # N . It follows that L C ## Reliablesep. # of Part (a) follows. Proposition 16 permits now to transfer the following noninclusions from the theory of learning functions [1, 4, 8, 17, 19, 21, 22, 24] to the theory of learning separations. Corollary 17 Recsep ## Reliablesep. Reliablesep ## Confidentsep. Confidentsep ## Reliablesep. Confidentsep ## Finitesep. Osherson, Stob and Weinstein [19, Exercise 4.4.2C] noted that a class which consists only of infinite sets has already a ....

K. Wexler and P. Culicover. Formal Principles of Language Acquisition. MIT Press, 1980.

....Lange, Gunter Grieser and Thomas Zeugmann Next, we define set driven IIMs. Intuitively speaking, the output of a set driven IIM depends exclusively on the content of its input, thereby ignoring the order as well as the frequency in which the examples occur. Definition 4 (Wexler and Culicover [19]) Let C 2 IC, let c be a concept, let H = h j ) j2N be a hypothesis space, and let a 2 N [ fg. An IIM M Sdr a Txt H identifies c iff M Lim a Txt H identifies c and, for all t; t 0 2 Text(C) and for all n; m 2 N , if content(t n ) content(t 0 m ) then M(t n ) M(t 0 m ) ....

K. Wexler and P. Culicover. Formal Principles of Language Acquisition. MIT Press, Cambridge, Mass., 1980.

....c. The learning type ConsvTxt is analogously defined as above. As it turned out, for proving some of the stated results, it is conceptually simpler to use the characterization of conservative learning equating it with set driven inference (cf. 10] Set drivenness has been introduced in [13] and describes the requirement that the output of an IIM is only allowed to depend on the range of its input. More formally, an IIM M is said to be set driven with respect to C iff M(t y ) M( t y 0 ) for all y; y 0 2 IN , and all texts t; t for concepts in C provided t y = t y 0 . ....

Wexler, K., and Culicover, P., "Formal Principles of Language Acquisition," MIT Press, 1980.

....type Consv a Txt is defined analogously to Definition 1. Next, we define set driven learning. Intuitively speaking, the output of a setdriven IIM depends exclusively on the content of its input, thereby ignoring the order as well as the frequency in which the examples occur. Definition 3 ([18]) Let C 2 IC, let c be a concept, let H = h j ) j2IN be a hypothesis space, and let a 2 IN [ fg. An IIM M Sdr a Txt H identifies c iff M Lim a Txt H identifies c and, for every t; t 0 2 Text(C) and for all n; m 2 IN, if content(t n ) content(t 0 m ) then M (t n ) M (t 0 m ) ....

K. Wexler and P. Culicover. Formal Principles of Language Acquisition. MIT Press, Cambridge, Mass., 1980.

....relies on the following notation, which will be ubiquitous in the sequel. The set f0; 1; 2 : g of natural numbers is denoted N . The symbol is used to denote N under its standard order, whereas denotes N ordered backwards. 5 This way of looking at things adapts a perspective due to [Wexler Culicover, 1980]. 4 Chapter I: Introduction I.2 A paradigm The paradigm is presented by stepping through the components listed in (1) I.2.1 Components Worlds. The potential realities, or worlds, are all the strict total orders OE over N . 6 For brevity, they are referred to in this chapter simply as ....

....in probabilistic contexts [Carnap, 1950, Sec. 45] it will be seen that the competence of memory limited scientists is reduced. II.4.1 Definition and examples The following definition isolates scientists whose current datum and current conjecture determine the next conjecture. 39) Definition: [Wexler Culicover, 1980] Scientist Psi is memory limited just in case Psi is total, and there is a total function f : pow(N) Theta N pow(N) such that for all oe 2 SEQ and x 2 N , Psi(oe x) f ( Psi(oe) x) Memory limited scientists have non negligeable competence, as illustrated by the following proposition. ....

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K. Wexler & P. Culicover. Formal Principles of Language Acquisition. M.I.T. Press, Cambridge MA, 1980.

....# 1999 Elsevier Science Ltd. All rights reserved. PII: S0893 6080(98)00139 7 otherwise cope with conditions of sparse input. However, these algorithms typically require that words in the input (or training) corpus be labelled or tagged in some way. For example, the algorithms presented in Wexler and Culicover (1980), Pinker (1984) and Berwick (1985) all require that lexical items be tagged with a syntactic role (e.g. as in Berwick) or with an argument position (relative to the verb, as in Pinker) This tagging approach is entirely reasonable provided we bear in mind that the algorithms in question are ....

Wexler, K., & Culicover, P. (1980). Formal principles of language acquisition.

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Kenneth Wexler and Peter Culicover. Formal Principles of Language Acquisition. MIT Press, Cambridge, MA, 1980.

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Kenneth Wexler and Peter W. Culicover. 1980. Formal Principles of Language Acquisition. MIT Press.

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Wexler, K., and Culicover, P. W. 1980. Formal Principles of Language Acquisition. MIT Press.

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WEXLER, K., and P. CULICOVER, 1980. Formal Principles of Lan- guage Acquisition. Cambridge, Mass.: MIT Press.

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Wexler, K. & Cullicover, P. 1980. Formal Principles of Language Acquisition. Cambridge: MIT Press.

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Wexler, K. and P. Culicover, Formal principles of language acquisition. 1980, Cambridge, MA: MIT Press.

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K. Wexler and P. Culicover, Formal Principles of Language Acquisition, MIT Press, Cambridge, Mass., 1980.

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K. Wexler and P. Culicover, Formal Principles of Language Acquisition. MIT Press, Cambridge, Mass., 1980.

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