LING 320 Lecture Notes - Lecture 8: Noam Chomsky, Universal Instantiation, Modus Ponens
25 Oct 2018
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Inside a proposition, you"ll find terms, predicates, quantifiers: connectors: &, ~, =, --> Example1: everybody in this class read 2 books by chomsky. X x books by chomsky (y) (x read y) X books by chomsky (y) x (x read y) Example 2: john wants to marry a norwegian. Inference rules: rules that allow us to make logical deductions. F(a) --> g(b) = ~f(a) or g(b) or f(x) --> g(y) = ~f(x) or g(y) [f(a) = g(b)] therefore ,[ f(a) --> g(b)] & [g(b) -> f(a)] Existential generalization: ex: socrates is mortal, therefore, socrates is mortal https://www. cs. odu. edu/~cs381/cs381content/logic/pred_logic/inference/univ_inst. html. Ex1: p: all men are mortal, q: socrates is a man, r: socrates is mortal: x [m (x) -> d(x), m(s) Proofing: m(s) -> d(s) (from substitution of identification in 3, d(s) (from 6 and 2, modus ponens, m(x) -> d(x) (from 1, universal instantiation, assume m(x) from 3, x m(x) (from universal generalization)
