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Generalized Modus Ponens (GMP)

  • Apply modus ponens reasoning to generalized rules

  • Combines Universal-Elimination, and Modus Ponens

    • E.g, from P(c) and Q(c) and x (P(x) Q(x)) R(x) derive R(c)

  • GMP requires substitutions for variable symbols

    • subst(θ, α) denotes the result of applying a set of substitutions defined by θ to the sentence α

    • A substitution list θ = {v1/t1, v2/t2, ..., vn/tn} means to replace all occurrences of variable symbol vi by term ti

    • Substitutions are made in left-to-right order in the list

    • subst ({x/IceCream, y/Ziggy}, eats(y,x)) = eats (Ziggy, IceCream)

Speaker notes:

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