1 / 19

Intelligent systems

Intelligent systems. Lection 3. Part 2. Logic. propositional logic – unsuitable tool for knowledge representation For example: 1) Distance between Earth and Son is 150000000 km 2) Distance between Earth and Mars is 56000000 km

xanthus-little
Download Presentation

Intelligent systems

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Intelligent systems Lection 3. Part 2.

  2. Logic propositional logic – unsuitable tool for knowledge representation For example: 1) Distance between Earth and Son is 150000000 km 2) Distance between Earth and Mars is 56000000 km We see similarity of this sentences, but in propositional logic its are absolutely noncomparable. So predicate logic was invented or 1-order logic.

  3. 1-order logic 1) Distance(Earth, Son, 150000000) 2) Distance(Earth, Mars, 56000000) These are structures which are comparable by comparison of its parts.

  4. 1-order logic (syntax) Formal theory:

  5. 1-order logic (syntax) F(x1, x2 … xn) predicate (logical function), xi – variable of area, n – arity of predicate. f(x1, x2 … xm) – function determined on area forxi, it may be argument of predicate as variable

  6. 1-order logic (syntax) Formula consists ofpredicates, logical connective &, V, ¬, generality quantifier and existential quantifier And also implication: FromF1(x1)=true followF2(x2)=true.

  7. 1-order logic (semantics) For all value of x F(x) is true Exist at least one value of x for which F(x) is true

  8. Interpretation of 1-logic for knowledge representation (semantics) F(x) – property of object x; High(tower), green(tree), good(student) F(x,y) – relation between objects x and y Mother(Maria,John), study(John,”Kyung Hee”) Under(cloude,earth), hot(weather,Korea)

  9. Conjunction Normal Form (CNF) • Formulas of 1-order logic are transformed to set of clauses (CNF) • Without generality quantifiers (its have in mind) • Without existential quantifiers (its are replaced by set of predicates-facts with concrete constants as arguments) • Clauses not include conjunctions &

  10. For CNF algorithms of proof exist. First of them was “resolution” of Robinson Logic of Horn is basis of logic programming and Prolog

  11. Example of program in Prolog (part) /* description of objects */ cube(“Cube_1", 10). cylinder(“Cyl_1”, 10, 20). /* description of location */ object(“cube_1", “table"). object(“Cyl_1", “box"). /* description of any actions (commands) */ take(_):- in_arm(_), /* checking of free of arm */ write(“arm is not free”)), nl, !. take(X):- object(X,Y), /*recognition of location ofX*/ turn_to(Y), select_object(X,Coord_X,Coord_Y), position(Coord_X,Coord_Y), get, /* set of arm */ assert(in_arm(X)). /*save what is in arm*/

  12. put(X,Y):- in_arm(Z), /* recognition what is in arm*/ Z<>X, write(“arm is not free"), nl, !. put(X,Y):- in_arm(X), turn_to(Y), center(Y, Coord_X,Coord_Y), position(Coord_X,Coord_Y), off, retract(in_arm(X)), !. put(X,Y):- not(in_arm(_)), object(X,Y), write(“Object "), write(X), write(" is already in "), write(Y), nl, !. put(X,Y):- not(in_arm(_)), take(X), put(X,Y).

  13. And-OR-tree of inference take OR Rule 1 for “take” Rule 2 for take AND AND … In_arm write object Turn_to …

  14. Disadvantages of 1-order logic for knowledge representation • Monotonic reasoning • Impossibility of using of uncertainty. • Impossible of using of predicates as arguments of other predicates • not enough powerful devices of description of structures

More Related