The redundancy of recursion and infinity for natural language

Luuk, Erkki; Luuk, Hendrik

doi:10.1007/s10339-010-0368-6

Cited by 18 publications

(6 citation statements)

References 42 publications

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“…Frequently, we find an isomorphism between procedure and structure, i.e., recursive processes often generate recursive structures. However, this isomorphism does not always occur (Lobina, 2011;Luuk & Luuk, 2010;Martins, 2012). In this manuscript we explicitly focus on a third level of analysis, which is the level of representation.…”

Section: An Empirically Useful Definition Of Recursionmentioning

confidence: 99%

A novel approach to investigate recursion and iteration in visual hierarchical processing

Martins

Martins²,

Fitch

2015

Behav Res

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We describe a new method to explore recursive cognition in the visual domain. We define recursion as the ability to represent multiple hierarchical levels using the same rule, entailing the ability to generate new levels beyond those previously encountered. With this definition recursion can be distinguished from general hierarchical embedding. To investigate this recursion/hierarchy distinction in the visual domain, we developed two novel methods: The Visual Recursion Task (VRT), in which an inferred rule is used to represent new hierarchical levels, and the Embedded Iteration Task (EIT), in which additional elements are added to an existing hierarchical level. We found that adult humans can represent recursion in the visuo-spatial domain, and that this ability is distinct from both general intelligence and the ability to represent iterative processes embedded within hierarchical structures. Compared with embedded iteration, visual recursion correlated positively with other recursive planning tasks (Tower of Hanoi), but not with specific visuo-spatial resources (spatial short-term memory and working memory). We conclude that humans are able to use recursive representations to process complex visuo-spatial hierarchies and that our visual recursion task taps into specific cognitive resources. This method opens exciting opportunities to explore the relationship between visual recursion and language.Keywords Recursion . Iteration . Cognition . Vision . Fractals . RepresentationThe capacity to understand and generate complex hierarchies is one of the most fascinating features of human cognition. In many domains, including language, music, problem-solving, action-sequencing, and spatial navigation, humans organize basic elements into higher-order groupings and structures (Badre, 2008;Chomsky, 1957;Hauser, Chomsky, & Fitch, 2002; Nardini, Jones, Bedford, & Braddick, 2008;Unterrainer & Owen, 2006;Wohlschlager, Gattis, & Bekkering, 2003). This ability to encode the relationship between basic elements (words, people, etc.) and the broader structures in which these are embedded (sentences, corporations, etc.), affords flexibility to human behavior. For example, in action sequencing, and unlike pure serial associative behavior, hierarchical representations allow the omission or modification of certain steps, without impairing the overall goal.Here, we define hierarchies as non-cyclical tree-like organizations, where higher levels incorporate multiple lower levels in structural representations (Fitch & Martins, 2014), i.e., in which elements are embedded within other elements. This embedding can refer to the grouping of constituents within a higher order set, such as the grouping of individuals within a family (family = {ind1; ind2; ind3}), or it can refer to the establishment of asymmetrical dominance-subordination relationships between constituents, such as in social hierarchies (ind1 dominant over ind2, ind2 dominant over ind3, etc.).Electronic supplementary material The online version of this article

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Section: An Empirically Useful Definition Of Recursionmentioning

confidence: 99%

A novel approach to investigate recursion and iteration in visual hierarchical processing

Martins

Martins²,

Fitch

2015

Behav Res

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“…How to compress these vectors into one sentence representation is still unclear. Since natural language has the redundancy mechanism [59], different words have different contributions to sentence semantics. Moreover, self-attention can select the important parts at different positions from a single sequence [13].…”

Section: B Global Sentence Encodingmentioning

confidence: 99%

LadRa-Net: Locally-Aware Dynamic Re-read Attention Net for Sentence Semantic Matching

Zhang,

Lv,

et al. 2021

Preprint

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Sentence semantic matching requires an agent to determine the semantic relation between two sentences, which is widely used in various natural language tasks, such as Natural Language Inference (NLI), Paraphrase Identification (PI), and so on. Much recent progress has been made in this area, especially attention-based methods and pre-trained language model based methods. However, most of these methods focus on all the important parts in sentences in a static way and only emphasize how important the words are to the query, inhibiting the ability of attention mechanism. In order to overcome this problem and boost the performance of attention mechanism, we propose a novel dynamic re-read attention, which can pay close attention to one small region of sentences at each step and re-read the important parts for better sentence representations. Based on this attention variation, we develop a novel Dynamic Re-read Network (DRr-Net) for sentence semantic matching. Moreover, selecting one small region in dynamic re-read attention seems insufficient for sentence semantics, and employing pre-trained language models as input encoders will introduce incomplete and fragile representation problems. To this end, we extend DRr-Net to Locally-Aware Dynamic Re-read Attention Net (LadRa-Net), in which local structure of sentences is employed to alleviate the shortcoming of Byte-Pair Encoding (BPE) in pre-trained language models and boost the performance of dynamic reread attention. Extensive experiments on two popular sentence semantic matching tasks demonstrate that DRr-Net can significantly improve the performance of sentence semantic matching. Meanwhile, LadRa-Net is able to achieve better performance by considering the local structures of sentences. In addition, it is exceedingly interesting that some discoveries in our experiments are consistent with some findings of psychological research.

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“…The publication of Hauser et al (2002) generated a number of reactions against the suggestion that recursion is the sole property of the FLN (Bickerton, 2009;Luuk & Luuk, 2011, Ott, 2009Sauerland & Trotzke, 2011). Luuk and Luuk (2011) argued that recursion is not required for natural language, but a process of iteration is necessary. Recursion involves self-reference and invokes another instance of itself, as in the example above.…”

Section: Introductionmentioning

confidence: 99%

Beyond Recursion: Critique of Hauser, Chomsky, and Fitch

Taraban¹,

Ахінта²

2017

eejpl

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In 2002, Hauser, Chomsky, and Fitch published an article in which they introduced a distinction between properties of language that are exclusively part of human communication (i.e., the FLN) and those properties that might be shared with other species (i.e., the FLB). The sole property proposed for the FLN was recursion. Hauser et al. provided evidence for their position based on issues of evolution. The question of the required properties of human language is central to developing theories of language processing and acquisition. In the present critique of Hauser et al. we consider two examples from non-English languages that argue against the suggestion that recursion is the sole property within the human language faculty. These are i) agreement of inflectional morphemes across sentence constructions, and ii) synthetic one-word constructions. References Adger, D. (2003). Core Syntax: A Minimalist Approach. Oxford: Oxford University Press. Bates, E., & MacWhinney, B. (1989). Functionalism and the Competition Model. In: The Crosslinguistic Study of Sentence Processing, (pp 3-76). B. MacWhinney and E. Bates (Eds.). New York: Cambridge University Press. Bickerton, D (2009). Recursion: core of complexity or artifact of analysis? In: Syntactic Complexity: Diachrony, Acquisition, Neuro-Cognition, Evolution, (pp. 531–543). T. Givón and M. Shibatani (Eds.). Amsterdam: John Benjamins. Chomsky, N. (1957). Syntactic Structures (2nd edition published in 2002). Berlin: Mouton Chomsky, N. (1959). On certain formal properties of grammars. Information and Control, 2, 137–167. Chomsky, N. (1995). The Minimalist Program for Linguistic Theory. Cambridge, MA: MIT Press. Hauser, M. D., Chomsky, N., Fitch, W. T. (2002). The faculty of language: What it is, who has it, and how did it evolve? Science, 298, 1569-1579. Luuk, E., & Luuk, H. (2011). The redundancy of recursion and infinity for natural language. Cognitive Processing 12, 1–11. Marantz, A. (1997). No escape from syntax: Don't try morphological analysis in the privacy of your own lexicon. University of Pennsylvania Working Papers in Linguistics, 4(2), A. Dimitriadis, L. Siegel, et. al. (eds.), 201- 225. MacWhinney, B. & O’Grady, W. (Eds.) (2015). Handbook of Language Emergence. New York: Wiley. Nevins, A., Pesetsky, D., & Rodrigues, C. (2009). Pirahã exceptionality: A reassessment. Language, 85(2), 355–404. Ott, D. (2009). The evolution of I-language: Lexicalization as the key evolutionary novelty. Biolinguistics, 3, 255–269. Sauerland, U., & Trotzke, A. (2011). Biolinguistic perspectives on recursion: Introduction to the special issue. Biolinguistics, 5, 1–9. Trotzke, A., Bader, M. & Frazier, L. (2013). Third factors and the performance interface in language design. Biolinguistics, 7, 1–34.

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The redundancy of recursion and infinity for natural language

Cited by 18 publications

References 42 publications

A novel approach to investigate recursion and iteration in visual hierarchical processing

A novel approach to investigate recursion and iteration in visual hierarchical processing

LadRa-Net: Locally-Aware Dynamic Re-read Attention Net for Sentence Semantic Matching

Beyond Recursion: Critique of Hauser, Chomsky, and Fitch

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