Human Language Complexity Human Language Complexity Linear Indexed Grammars Linear Indexed Grammars 1 Human Language Complexity Complexity and Character of Human Languages Chomsky Hierarchy Informatics 2A: Lecture 21 The Faculty of Language Strong and Weak Adequacy Mirella Lapata 2 Linear Indexed Grammars School of Informatics University of Edinburgh mlap@inf.ed.ac.uk Reading: J&M. Chapter 16.3–16.4; Hauser, Chomsky, and Fitch 04 November 2011 (2002) 1 / 24 2 / 24 Chomsky Hierarchy Chomsky Hierarchy Human Language Complexity Human Language Complexity The Faculty of Language The Faculty of Language Linear Indexed Grammars Linear Indexed Grammars Strong and Weak Adequacy Strong and Weak Adequacy Review Review Chomsky Hierarchy: classifies languages on scale of complexity: Regular languages: those whose phrases can be ‘recognized’ by a finite state machine. Context-free languages: most programming languages, and Regular many aspects of natural languages can be described at this level; the set of languages accepted by pushdown automata. Context−free Context-sensitive languages: equivalent with a linear bounded Context−sensitive nondeterministic Turing machine, also called a linear bounded automaton. Unrestricted Unrestricted languages: all languages that can in principle be defined via mechanical rules. 3 / 24 4 / 24
Chomsky Hierarchy Chomsky Hierarchy Human Language Complexity Human Language Complexity The Faculty of Language The Faculty of Language Linear Indexed Grammars Linear Indexed Grammars Strong and Weak Adequacy Strong and Weak Adequacy Review The Faculty of Language The “language fac- Regular ulty” has a broad sense and a narrow Context−free sense (Hauser, Chom- sky, and Fitch 2002). Context−sensitive Unrestricted Where do human languages fit within this complexity hierarchy? 4 / 24 5 / 24 Chomsky Hierarchy Chomsky Hierarchy Human Language Complexity Human Language Complexity The Faculty of Language The Faculty of Language Linear Indexed Grammars Linear Indexed Grammars Strong and Weak Adequacy Strong and Weak Adequacy The Faculty of Language (Broad Sense) The Faculty of Language (Narrow Sense) Sensory-motor system Abstract computational system for producing and perceiving linguistic communication one part of which is narrow syntax which generates spoken language: vocal track, auditory system representations internal to the mind/brain and maps them to: sign language: gestural system, visual system sensory-motor interface through phonological, gestural system; written language: writing system, visual or tactile system conceptual-intentional system through semantic (and pragmatic) systems. Conceptual-intentional system who to communicate with and what to communicate about A core property of narrow syntax is recursion: takes a fine set of generating mental states and attributing them to others; elements and yields a potentially infinite array of discrete acquiring conceptual representations that are non-linguistic; expressions. referring to entities and events. 6 / 24 7 / 24
Chomsky Hierarchy Chomsky Hierarchy Human Language Complexity Human Language Complexity The Faculty of Language The Faculty of Language Linear Indexed Grammars Linear Indexed Grammars Strong and Weak Adequacy Strong and Weak Adequacy Recursion Strong and Weak Adequacy The potential infiniteness of the language faculty has been Questions about the formal complexity of language are about the recognized by Galileo, Descartes, von Humboldt. computational power of syntax, as represented by a grammar Discrete Infinity that’s adequate for it. Sentences are built up by discrete units A strongly adequate grammar There are 6-word sentences, and 7-word sentences, but no 6.5 word sentences generates all and only the strings of the language; There is no longest sentence! assigns them the “right” structures — ones that support a correct representation of meaning. There is no non-arbitrary upper bound to sentence length! A weakly adequate grammar Mary thinks that John thinks that George thinks that Mary thinks generates all and only the strings of a language but assigns them that this course is boring! “wrong” structures. I ate lunch and slept and watched tv and went to the bathroom and had a coffee and got dressed . . . 8 / 24 9 / 24 Chomsky Hierarchy Chomsky Hierarchy Human Language Complexity Human Language Complexity The Faculty of Language The Faculty of Language Linear Indexed Grammars Linear Indexed Grammars Strong and Weak Adequacy Strong and Weak Adequacy Is Natural Language Regular? Is Natural Language Context Free? It is generally agreed that natural languages are not regular! It doesn’t look like it is context free either! Evidence comes from a Swiss German dialect and Bambara, a language spoken in Mali. Center-embedding Crossing dependencies [The cat 1 likes tuna fish 1 ]. [The cat 1 [the dog 2 chased 2 ] likes tuna fish 1 ]. omdat Wim 1 Jan 2 Henk 3 de kinderen 4 zag 1 helpen 2 leren 3 zwemmen 4 [The cat 1 [the dog 2 [the rat 3 bit 3 ] chased 2 ] likes tuna fish 1 ]. because Wim 1 Jan 2 Henk 3 the children 4 saw 1 help learn swim 4 because Wim saw Jan help Henk teach the children to learn to swim Idea of proof | zag | depends on | Wim | , and | helpen | depends on | Jan | , etc. (the+noun) n (transitive verb) n − 1 likes tuna fish. A = { the cat, the dog, the rat, the elephant, the kangaroo . . . } Idea of Proof B = { chased, bit, admired, ate, befriended . . . } Languages { xx | x ∈ { a , b } ∗ } are not context-free. Intersect /A* B* likes tuna fish/ with English Related a n b m c n d m language also not context -free. L = x n y n − 1 likes tuna fish , x ∈ A , y ∈ B Swiss German crossing dependencies equivalent to a n b m c n d m Use pumping lemma to show L is not regular 10 / 24 11 / 24
Chomsky Hierarchy Chomsky Hierarchy Human Language Complexity Human Language Complexity The Faculty of Language The Faculty of Language Linear Indexed Grammars Linear Indexed Grammars Strong and Weak Adequacy Strong and Weak Adequacy Is Natural Language Context Free? Is Natural Language Context Free? It doesn’t look like it is context free either! Evidence comes from a It doesn’t look like it is context free either! Evidence comes from a Swiss German dialect and Bambara, a language spoken in Mali. Swiss German dialect and Bambara, a language spoken in Mali. Crossing dependencies Crossing dependencies omdat Wim 1 Jan 2 Henk 3 de kinderen 4 zag 1 helpen 2 leren 3 zwemmen 4 omdat Wim 1 Jan 2 Henk 3 de kinderen 4 zag 1 helpen 2 leren 3 zwemmen 4 because Wim 1 Jan 2 Henk 3 the children 4 saw 1 help learn swim 4 because Wim 1 Jan 2 Henk 3 the children 4 saw 1 help learn swim 4 because Wim saw Jan help Henk teach the children to learn to swim because Wim saw Jan help Henk teach the children to learn to swim | zag | depends on | Wim | , and | helpen | depends on | Jan | , etc. | zag | depends on | Wim | , and | helpen | depends on | Jan | , etc. Idea of Proof Idea of Proof Languages { xx | x ∈ { a , b } ∗ } are not context-free. Languages { xx | x ∈ { a , b } ∗ } are not context-free. Related a n b m c n d m language also not context -free. Related a n b m c n d m language also not context -free. Swiss German crossing dependencies equivalent to a n b m c n d m Swiss German crossing dependencies equivalent to a n b m c n d m 11 / 24 11 / 24 Chomsky Hierarchy Chomsky Hierarchy Human Language Complexity Human Language Complexity The Faculty of Language The Faculty of Language Linear Indexed Grammars Linear Indexed Grammars Strong and Weak Adequacy Strong and Weak Adequacy Is Natural Language Context Free? Is Natural Language Context Free? It doesn’t look like it is context free either! Evidence comes from a It doesn’t look like it is context free either! Evidence comes from a Swiss German dialect and Bambara, a language spoken in Mali. Swiss German dialect and Bambara, a language spoken in Mali. Crossing dependencies Crossing dependencies omdat Wim 1 Jan 2 Henk 3 de kinderen 4 zag 1 helpen 2 leren 3 zwemmen 4 omdat Wim 1 Jan 2 Henk 3 de kinderen 4 zag 1 helpen 2 leren 3 zwemmen 4 because Wim 1 Jan 2 Henk 3 the children 4 saw 1 help learn swim 4 because Wim 1 Jan 2 Henk 3 the children 4 saw 1 help learn swim 4 because Wim saw Jan help Henk teach the children to learn to swim because Wim saw Jan help Henk teach the children to learn to swim | zag | depends on | Wim | , and | helpen | depends on | Jan | , etc. | zag | depends on | Wim | , and | helpen | depends on | Jan | , etc. Idea of Proof Idea of Proof Languages { xx | x ∈ { a , b } ∗ } are not context-free. Languages { xx | x ∈ { a , b } ∗ } are not context-free. Related a n b m c n d m language also not context -free. Related a n b m c n d m language also not context -free. Swiss German crossing dependencies equivalent to a n b m c n d m Swiss German crossing dependencies equivalent to a n b m c n d m 11 / 24 11 / 24
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