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Lang & Logic (Propositional Logic (Sequent notation - P→O, ¬O : ¬P, If…
Lang & Logic
Propositional Logic
Sequent notation - P→O, ¬O : ¬P
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^Introduction - A, B ⊢ A^B
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vElimination - (AvB, A⊢C, B⊢C) ⊢ C
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→Elimination - A→B, A ⊢ B
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Predicate Calculus
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∀Elimination - ∀x[A(x)→B(x)], A(a) ⊢ B(a)
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∃Elimination - (∃x[φ(x)], φ(a)⊢C) ⊢ C
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=Elimination - a=b, φ(a) ⊢ φ(b)
Relationships - Describes a relationship between objects. Eg. L(x, y) means x loves y
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Definitions
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Atomic propositions - Propositions that cannot be broken down any further. Eg. "If the cat is sat, then it will meow". "The cat is sat" and "the cat will meow" are atomic
Grammar
Definition - A set of rules which must be followed. It defines the grammar of a given language, so that all possible "words" can be achieved with no illegal values
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Eg. Non Terminals (Vn): N, D
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Production rules (P): N→D, N→ND, D→1, D→0
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Validity
Semantic - Whenever all of the premises are true, the conclusion is true. Eg. Truth tables
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