Reasoning Automated Deduction. Reasonable Arguments Argument: An attempt to demonstrate the truth of a conclusion from the truth of a set of premises.

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Presentation transcript:

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 Deductive reasoning Inductive reasoning

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

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

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

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

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?

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

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

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

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.

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.

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

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.)