Logic
Logical Environment
Physical Environment has rational rules that govern the properties of the physical world.
Physical Environment has rational rules that govern the properties of the physical world.
Grammars
Structure of grammar L is a language over an alphabet A then a grammar for L α → β α = strings of symbols taken from language A β = strings of symbols from a grammar disjoint from A. Can be interpreted as: replace α by β α produces β α rewrites β α reduces β --- Start symbol S → β Ex. Let A = { a, b, c }. S → Λ | aS | bS | cS Ex. Set of binary numerals that represent odd numbers O → B 1 B → Λ | B 0 | B 1. --- S → AB A → Λ | aA B → Λ | bB. Leftmost derivation S ⇒ AB ⇒ aAB ⇒ aaAB ⇒ aaB ⇒ aabB ⇒ aab . Rightmost Derivation S ⇒ AB ⇒ AbB ⇒ Ab ⇒ aAb ⇒ aaAb ⇒ aab . --- The Language of a Grammar (3.3.4) If G is a grammar with the start symbol S and the set of terminals T , then the language of G is the set L ( G ) = { s | s ∈ T * and S ⇒ + s }. Three simple grammars 1. {Λ, a, aa , …, a n , … } = { a n | n ∈ N}. • S → Λ | aS . 2. {Λ, ab, aabb , …, a n b n , … } = { a n b n
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