Introduction to Cognitive Science

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Introduction to Cognitive Science

• Linguistics Component

• Topic Formal Grammars
• Generating and Parsing
• Lecturer Dr Bodomo

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Introduction

• In my previous lectures, we discussed how tacit
  linguistic knowledge can be represented at
  various levels of phonology, morphology, syntax,
  semantics, pragmatics, and their interfaces,
  including morphophonology, morphosyntax, and the
  syntax-semantics interrelationships.
• In this lecture, we shall look closely at how
  these linguistic knowledge representations can be
  formalised into an algorithm, a computational
  procedure for processing this linguistic
  knowledge.

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Keywords

• Constituent structure rules
• initial symbol
• terminal symbol
• non-terminal symbol
• generative grammar
• formal grammar

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Formal devices and notation

• The symbol ? indicates that a node is
  rewritten as or consists of, or has the
  constituents
• This is used in rewrite rules of the type S ? NP
  VP
• a sentence, S, has the constituents noun phrase
  (NP) and verb phrase (VP)
• Optionality in the grammar is expressed as X,
  Y . This means apply either X or Y but not both

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Formal devices and notation (cont.)

• The symbol is used to indicate constituent
  boundary
• e.g. _ is word initial while _ is word final
• The notation X (Y) implies that X is obligatory
  and may be followed by Y

• Initial symbol the symbol from which a rewrite
  rule begins (e.g. S)
• Terminal symbol the end symbols from which no
  constituent structure can be further developed
  (N, V, Art). All others are non-terminal symbols
  (e.g. NP, VP).

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Two main aspects of grammatical information
processingGenerating and Parsing sentences

• Before we begin let us illustrate with a simple
  grammar and lexicon, using the following
  sentence
• The students greeted the teacher .

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The students greeted the teacher.

• Lexicon 1
• Greeted V, - NP
• Students N
• The Art
• Teacher N

• Grammar
• S ? NP VP
• VP ? V NP
• NP ? Art N

This grammar can also generate (i.e. produce)
the following sentences The teacher
greeted the students The teacher scared the
students The child ate an apple
But you have to augment i.e. increase the lexicon
as follows Lexicon2 An Art Greeted,
scared, ate V, - NP Apple N Students N
Child N Teacher N The Art
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Sentence Generationthe algorithm

• To produce a sentence we need three things
• A set of phrase structure rules (as illustrated
  above)
• A lexicon (as illustrated above), and
• A lexical insertion rule (as explained below)
• A lexical insertion rule is an instruction to
  select the right word from a lexicon
• The following is an example of a lexical rule

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Lexical insertion rule

• For each terminal symbol of a phrase structure
  rule, select a word from the lexicon that
  satisfies the following conditions
• It is a member of the class of terminal symbol
  (e.g. N, V)
• its subcategorization frame matches that of the
  terminal symbol (e.g. V, _NP). Attach this word
  as the daughter of this terminal symbol.
• The set of rules above constitutes what is known
  as a sentence generator.

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• The whole procedure of beginning with an initial
  symbol and then working through phrase structure
  rules to adding the lexical items via lexical
  insertions rules is driven by an algorithm or a
  set of instructions.
• Let us set out an algorithm for the generation
  (production) of the sentence The students
  greeted the teacher, a grammar and a lexicon as
  follows

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The students greeted the teacher
Lexicon1 Greeted V, - NP Students N The
Art Teacher N
Grammar PS Rule1 S ? NP VP PS Rule2 VP ? V
NP PS Rule3 NP ? Art N

• i. Start with the initial symbol, S.
• ii. For every non-terminal symbol, X, find a
  phrase structure rule with X as left-hand symbol
  and others as the right hand symbol(s), and
  develop a rewrite rule with X as the mother and
  the right hand symbols as ordered daughters.
• iii. Apply rule ii. until all branches end in
  terminal symbols.
• iv. Apply lexical rule iteratively until every
  terminal symbol is replaced by a lexical item.

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Illustrating the algorithm

• Applying rule i we get S

• Applying rule ii and iii. We get

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• From the above we can see that we have started
  from an initial string and have ended with
  terminal strings with lexical items as their
  daughters. A sentence has thus been generated
  (produced), telling us how this sentence is built
  up.
• Now, let us see how we can begin with an existing
  sentence and then break it down into its
  component parts by applying rules.

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Sentence parsing the algorithm

• To parse a sentence means to analyse it into its
  constituent parts by the systematic application
  of lexical insertion rules and some phrase
  structure rules. It is like the reverse process
  of generation.

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Some sentence parsing rules which constitute a
PARSER

• For a sentence, S
• i. Determine from the lexicon the word class of
  every item and develop a partial tree for each
  word where the word class label dominates the
  word.
• ii. Find a PS rule of the type X ? Y, Z and
  where the right hand symbols match some sequence
  of categories in the structure so far, and
  develop a partial tree with X as the mother and
  the right hand symbols as ordered daughters.
• iii. Continue rule ii. until the root, S, is
  reached and there are no unattached strings.

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The man drank the tea.
Lexicon1 drank V, - NP man N The Art Tea
N
Grammar PS Rule1 S ? NP VP PS Rule2 VP ? V
NP PS Rule3 NP ? Art N
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Conclusion

• Parsing and generation of natural language data
  is a very important area of linguistics,
  especially in computer applications of natural
  languages which has become an important aspect of
  the computer or information processing industry.
• In the next lecture, we shall be looking at the
  last topic of the linguistics segment i.e. how
  linguistic knowledge is acquired/learnt by
  speakers of a language, from the point of view of
  spoken language and from the point of literacy
  (reading and writing).