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Reasoning

Reasoning. Automated Deduction. Reasonable Arguments. Argument : An attempt to demonstrate the truth of a conclusion from the truth of a set of premises. Reasoning The process that shape the argument To derive a conclusion from premises Two types of reasoning Types of reasoning

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Reasoning

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  1. Reasoning Automated Deduction

  2. Reasonable Arguments • Argument: An attempt to demonstrate the truth of a conclusion from the truth of a set of premises. • Reasoning • The process that shape the argument • To derive a conclusion from premises Two types of reasoning • Types of reasoning • Deductive reasoning • Inductive reasoning

  3. Deductive Reasoning • Starts with general case and deduces specific instances • If we assume the premises are true, then the conclusion cannot be false • Example • Gravity affects all matter on earth • The apple fell from the tree • Gravity affected the apple

  4. Deductions • Science • Take a general law and apply it to certain cases • Sherlock Holmes • Took general knowledge to derive details about the unsolved case

  5. Inductive Reasoning • From the specific to the general • If the premises are true, then the conclusion is true with some probability • Example • The sun has risen in the east every morning • The sun will rise in the east tomorrow

  6. Inductive Reasoning • Premises support the conclusion but do not ensure it • Depends on patterns of repeated experience • The conclusion is never guaranteed

  7. Example • Swans1 • This swan is white. (premise) • Therefore all swans are white. (conclusion) • Swans2 • All swans I have seen are white. • Therefore all swans are white. • Which one is a stronger argument?

  8. Induction Ladder • Assume P1 is true. • P1 implies P2 is true • P2 implies P3 is true • In general, Pk implies Pk+1 is true • Therefore Pn is true for n>=k

  9. Strong vs Weak Induction • Strength of the argument- • Based on the strength of the specific proposition • The strength of the general proposition cannot be greater than the strength of the specific proposition that lead to it • Weak induction if there has been an overgeneralization • Not quantifyable

  10. Cogent Arguments • The conclusion is likely • An argument is cogent if and only if the truth of the premise make the truth of the conclusion probable

  11. Strong or Weak Argument? • Jim pulled out 9 out of 10 loose socks in a sock drawer and all were black. • Therefore the next sock Jim pulls out will be black.

  12. Strong or Weak Argument? • Jim pulled one sock from among 10 pairs of loose socks in a sock drawer and it was black. • Therefore the next sock Jim pulls out will be black.

  13. Knowledge Discovery • Deduction • Does not add new knowledge • Conclusions self-contained within premises • Non-amplitive; does not increase one’s knowledge base • Induction • Adds new knowledge • Amplitive; increases ones knowledge base

  14. Automative Reasoning • The building of computer systems to reason by deduction • Automated theorem provers • Algorithms to implement a calculus (A calculus is a logical system which is used to prove valid formula.)

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