Recursive definitions and proof stratergies Flashcards

1
Q

What are the three parts of a recursive definition?

A
  1. A basic clause - for the “starting” elements
  2. An inductive clause - to build other elements
  3. An extremal clause - to eliminate unwanted elements
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2
Q

How do you define a recursively defined function?

A
  1. Specify the value of the function at zero
  2. Give a rule for finding its value at any integer from its values at smaller integers
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3
Q

What are two common features of a proof strategy?

A
  • A proof starts with an assumptions (called premises, conditions or pre-conditions)
  • A proof has a goal
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4
Q

What are elimination stratergies?

A

Eliminating a logical element in order to reduce the distance to the goal.

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5
Q

What are introduction strategies?

A

Introducing logical elements in order in to get closer to the goal.

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6
Q

What is modus ponens?

A

If P implies Q and P is true then Q is true

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7
Q

What is modus tollens?

A

If P implies Q and not Q then not P follows

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