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Prolog

Prolog. Prolog: Programming in Logic Prolog programs consist of clauses and rules. Declarative programming Emphasis is on data and relations between objects. No familiar procedural controls. Built-in inference engine. Where is declarative programming useful?. Data-driven programming tasks

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Prolog

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  1. Prolog • Prolog: Programming in Logic • Prolog programs consist of clauses and rules. • Declarative programming • Emphasis is on data and relations between objects. • No familiar procedural controls. • Built-in inference engine.

  2. Where is declarative programming useful? • Data-driven programming tasks • Verification • Natural Language • Expert Systems • Relational Databases • Diagnostic Systems

  3. Logical Operators AND: Conjunction OR: Disjunction NOT: Inversion

  4. Logical Operators Implication Equivalence A->B is equivalent to !AvB A<->B is equivalent to: A->B ^ B->A (A ^ B) v (!A ^ !B)

  5. Propositional Calculus • Represent facts as symbols. • Homer_likes_beer. • Lisa_likes_tofu. • !(Bart_likes_school) • Bart_likes_school -> Bart_does_homework. • Lisa_likes_school ^ Lisa_likes_music • Easy, but overly verbose. • No reuse.

  6. Predicate Calculus • A predicate is a function that maps from zero or more objects to {T,F}. • Likes(Homer, beer) • !Likes(Bart, school) • Likes(Bart, school) -> Does(Bart, homework). • Happy(Lisa). • Gives(Moe, Homer, beer) -> Happy(Homer). • Predicates provides a syntactic shorthand for propositions. • No extra representational power.

  7. Inference Rules • AND-elimination: • If A^B is true, then A is true. • likes(Homer,beer) ^ likes(Homer, food)->likes(Homer,beer) • OR-introduction: • If A is true, then AvB is true. • likes(Homer,food)->likes(Homer,food)v likes(Homer,work). • Modus Ponens: • If A->B is true, and A is true, then B is true. • likes(Lisa,school)->does(Lisa,homework) ^ likes(Lisa,school) -> Does(Lisa,homework)

  8. Quantification • We would like to be able to express facts such as: • “Everyone who likes school does their homework.” • “No one who likes beef also likes tofu.” • “Someone likes beef.” • This requires us to be able to quantify over variables in the domain.

  9. First-Order Logic • First order logic allows quantification over objects. • Universal quantification: “For all x” x likes(x,school) -> does(x, homework). “Everyone who likes school does their homework.” • Existential quantification: “There exists an x” x likes(x,tofu). “There exists someone who likes tofu.”

  10. Computational Issues • Full FOL is too computationally difficult to work with. • Nested quantifiers are semi-decidable. xyz likes(x,y) ^ likes(y,z). “Everyone likes a person who likes everyone.” • Implications with an AND in the consequent are exponentially hard. x likes(x, school) -> does(x,homework) ^ attends(x,class) “Everyone who likes school does their homework and attends class.”

  11. Horn clauses • Horn clauses are implications of the form: x ^ y ^ z -> a • Only a single term in the consequent. • Horn clause inference is computationally tractable. • Prolog uses Horn clauses.

  12. Knowledge Representation in Prolog • Facts (unit clauses): • likes(homer, beer). • Constants are lower case. • Names of relations are lower case. • Conjunctions: • likes(homer,beer). • likes(homer,food). • Statement is represented as separate Prolog clauses. <- ends with a period

  13. Knowledge Representation in Prolog • Rules • does(lisa,homework) :- likes(lisa,school). • Equivalent to: • likes(lisa,school) ->does(lisa,homework) • Read as: “Lisa does homework if she likes school.” or … • “To prove that Lisa does homework, prove that she likes school.”

  14. Variables • Variables are all upper-case. • Universal quantification is achieved by using variables in rules. • does(X,homework) :- likes(X,school). • “Everyone who likes school does their homework.” • “To prove that someone does their homework, prove that they like school.”

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