1. CSNB143 – Discrete Structure Topic 11 – Language

2. Learning Outcomes Student should identify the basic components in language Students should be able to produce phrase structure grammar

3. Topic 11 – Language Understanding Language If set W = {all characters from a, b, c, …….., z, A, B, C, ……., Z}, then set W* = {all words that can be formed from W} = {aabb, bus, lamp, pqrs, ….}, either it has any meaning or not. Let say set S = {all possible words} = W*, then Then set S* = {all possible sentences that can be formed from S} = {I like to play, the dog is running, aabb shine pqrst, ….}, either it has any meaning or not. Then we can say that language consists of three basic things, that are: – S; a set of all possible words, – S*; a set of properly constructed sentences, (this is what we called as syntax, that differentiate between a properly constructed sentence and not a properly constructed sentence.) – The meaning of the sentences (referred to as semantic)

4. Topic 11 – Language Understanding Language Example 1 : Consider the two sentences below: Going to the store John George to sing. This sentence is a valid sentence in S*, but it doesn’t constructed properly. The order of noun and verb is not valid. Noiseless blue sounds sit cross-legged under the mountaintop. This sentence is correct in structure, but it doesn’t have any meaning.

5. Topic 11 – Language Understanding Language The need to identify syntax has expanding the formal language, to a new set of rules, we determine that: – Sentence must be built from noun phrase and verb phrase. – Noun phrase must be built from an article and adjective, followed by noun. – Noun phrase must be built from an article and noun. – Verb phrase must be built from verb and adverb. – Verb phrase must be built from verb. – Article is either a or the – Adjective is either large or hungry – Noun is either rabbit or doctor – Verb is either eats or hops – Adverb is either quickly or wildly

6. Topic 11 – Language Understanding Language Can make sentence using the order of valid replacement Other sentences are: – a hungry doctor eats wildly – a large doctor hops wildly – the hungry rabbit eats quickly,.....and so on.

7. Topic 11 – Language Phrase Structure Grammar Syntax being used to produce valid sentences with meaning Referred to as G, that consists of four elements: – V; a finite set of elements, consists of S together with some other symbols – S; a subset of V that consists of terminal symbols, S is a set of all allowed words in a language. – v 0 ; where v 0  V – S, it is the element v 0 of V is the starting point for substitution –  a finite relation on V*. The relation  on V* specifies allowable replacements, e.g if w  w’, we may replace w with w’ whenever string w occurs, either alone or as combination with other string. We call  the production relation. Phase Structure Grammar is written as G = (V, S, v 0,  ) Traditionally, the statement w  w’ called a production of G. w and w’ are termed the left and right sides of the production.

8. Topic 11 – Language Phrase Structure Grammar Example: G = (V, S, v 0,  ) Let S = {John, Jill, drives, jogs, carelessly, rapidly, frequently}; N = {sentence, noun, verbphrase, verb, adverb} and V = S  N. Let v 0 = sentence (starting point of substitution) and relation  on V* (all possible sentence that can be formed from the words) are defined as: – Noun  John – Noun  Jill – Verbphrase  verb + adverb – Verb  drives – Verb  jogs – Adverb  carelessly – Adverb  rapidly – Adverb  frequently

9. Topic 11 – Language Phrase Structure Grammar Answer: Then we can have few sentences that syntactically correct, for example:

10. Topic 11 – Language Phrase Structure Grammar - the language of G, L(G) In phrase structure grammars G, correct syntax simply refers to the process by which a sentence is formed. A set of all properly constructed sentences that can be produced using a grammar G is called the language of G, denoted by L (G)

11. Topic 11 – Language The language of G, L(G) Example: Let V = {v 0, w, a, b, c}; S = {a, b, c} and  is relations on V* given by : (1) v 0  aw(2) w  bbw(3) w  c Derive a proper L(G) (can use substitution approach and derivation tree approach)

12. Topic 11 – Language The language of G, L(G) Answer: Let V = {v 0, w, a, b, c}; S = {a, b, c} and  is relations on V* given by : (1) v 0  aw(2) w  bbw(3) w  c Derive a proper L(G). To derive the language of L(G), necessary to perform successive substitution, until all symbols are eliminated other than the terminal symbols (in this case a,b,c). Since v 0 is the substitution starting point, we will usually start with production (1), v 0  aw. Result after trying both substitution and tree derivation approach, the L(G) obtained will be a(bb) n c