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Introduction to Reasoning and Logic in Artificial Intelligence

This session covers types of reasoning such as deterministic, propositional logic, and predicate logic, with a focus on Aristotle's basic forms and deduction principles. It explores how logical reasoning operates with uncertain or changing information using dynamic and non-monotonic logic. Key topics include Boolean logic, connectives, truth values, and quantifiers in predicate logic. The session also discusses rules of inference and managing uncertainty in reasoning.

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Introduction to Reasoning and Logic in Artificial Intelligence

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Presentation Transcript

  1. Knowledge Processing 1 Artificial Intelligence Techniques

  2. Aims of session • Introduce types of reasoning • Deterministic • Propositional logic • Predicate logic

  3. Deterministic • Artistole (384-322BC) • Basic form • If-Then • First part of rule is either true or false, if true then second part of part activated this can also be true or false. • If first part is true then system can initiate an action to make the second part true • Deduction-truth of a fact can be deducted from another.

  4. Example (Taken from Johnson and Picton) • IF image contains unknown object THEN take evasive action • The known fact “The image has an unknown object” is true • Deduced fact “take evasive action”is true

  5. George Boole worked out how new statements can be deduced by linking them with AND and OR (connectives). • Using with the previous example the previous known fact can be split into two facts • “image contains an object” is true AND “object cannot be matched in database” is true. • The known facts have been combined into a single statement which is • “image contains an object” AND “object cannot be matched in database” is true.

  6. Using Boolean logic we can work out the truth of a proposition given the truth values of the sub-propositions. • Propostional logic

  7. Predicate logic • Evaluates truth values of compound propositions for the quantifiers • “for all” (Universal quantifier) • “there exists” (existential quantifier)

  8. Dynamic reasoning • Logical reasoning does allow functioning when faced with incomplete or inconsistent information to deal with a rapidly changing environment. • A classic example (taken from Johnson and Picton 1995) “Tweety is a bird” is true and we know “birds fly” is true deduce “Tweety can fly”

  9. Problem is a new fact is introduced “Tweety is a penguin” is true and “penguins cannot fly” is true, “Tweety can fly” is false. • What happened?

  10. Original deduction was based on two propositions and default knowledge. Deterministic logic assumes no default knowledge-so we have a problem. • Non-monotonic logic allows deduction to change as new evidence arrives, so avoiding needing extra quantifiers.

  11. Non-deterministic logic • Introduce extra logic values such as “unknown” • Probability

  12. Proposition and truth • T(X) is true if X is true • T(X) is false if X is false • T(X)=T(Y)

  13. Why is T(X)=T(Y) not the same as X=Y?

  14. Connectives • X ^Y means X AND Y • X v Y means X OR Y • ¬X means NOT X • XY means X implies Y (only false when X is true and Y is False).

  15. Implies • Taken from Johnson and Picton • X is inside Y so if Y is false X cannot be true. Y X

  16. Predicate Logic • In predicate logic we use variable and have quantifiers. • Proposition in predicate logic are split into a subject (argument) and predicate.

  17. Hot(water) • argument:water • predicate:Hot • True if water is hot • False if water is not hot. • Hot(x) only when a specifc item substituted for x will there it have a truth value. • Predicate can have more than one argument.

  18. Quantifiers • (universal qualifier) For all x, P(x) is true • (existential qualifier) There exists for x such that P(x) is true.

  19. Example • If ( on (sensor x)) • Then on(alarm) • The predicate on(sensor x) is true if sensor x is ON, on(alarm) is true if the alarm is sounding. Therefore there exists a value of x such that the predicate on(sensor x) is true then sound the alarm.

  20. Next week • Rules of inference • Uncertainty in reasoning

  21. References • Johnson J and Picton P (1995) Mechatronics : designing intelligent machines. - Vol.2 : concepts in artificial intelligence Oxford : Butterworth-Heinemann pg 175-187

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