Programming in Logic Prolog Introduction Reading Read Chapter

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Programming in Logic: Prolog Introduction Reading: Read Chapter 1 of Bratko MB: 26 Feb Programming in Logic: Prolog Introduction Reading: Read Chapter 1 of Bratko MB: 26 Feb 2001 CS 360 - Lecture 1 1

Declarative Programming Declarative programming describes what to compute rather than how to compute it. Declarative Programming Declarative programming describes what to compute rather than how to compute it. n E. g. , blueprints for a house are declarative, they describe what to build not how to build it. n Describing “what” is often much easier than describing “how” (but not always). n Algorithm = Logic + Control (R. Kowalski, 1979) n Logic expressions are declarative. n MB: 26 Feb 2001 CS 360 - Lecture 1 2

Advantages of Declarative Style of Programming Simply encode your knowledge without worrying how the Advantages of Declarative Style of Programming Simply encode your knowledge without worrying how the knowledge will be used. n The underlying inference engine uses that knowledge to answer the user’s queries. n Knowledge can be used in many ways: n – – – Is Mary Peter’s sister? Who is whose sister? MB: 26 Feb 2001 CS 360 - Lecture 1 3

Knowledge Bases n A Knowledge Base has: – Knowledge in the form of: n Knowledge Bases n A Knowledge Base has: – Knowledge in the form of: n Facts (e. g. , Socrates is a man) n Rules (e. g. , All men are mortals) – n An inference engine A Knowledge Base uses its facts, rules, and inference engine to answer questions. – – Is Socrates mortal? yes MB: 26 Feb 2001 CS 360 - Lecture 1 4

Logic Programming & Knowledge Bases Logic programming languages are one way to implement knowledge Logic Programming & Knowledge Bases Logic programming languages are one way to implement knowledge bases. n Encode your knowledge base and your queries then the underlying inference engine will attempt to answer your queries. n The inference engine answers your queries by building constructive proofs that your queries are entailed by the knowledge base. n MB: 26 Feb 2001 CS 360 - Lecture 1 5

Simple Example: Families n Define the relevant relationships: – n Store the basic facts: Simple Example: Families n Define the relevant relationships: – n Store the basic facts: – n mother, father, brother, sister, aunt, uncle, cousin, ancestor, descendant parents, siblings, and gender Ask your queries: – Who is whose sister? MB: 26 Feb 2001 CS 360 - Lecture 1 6

Some Rules mother. Of(M, O) : - parent. Of(M, O), female(M). n sister. Of(S, Some Rules mother. Of(M, O) : - parent. Of(M, O), female(M). n sister. Of(S, P) : - sibling. Of(S, P), female(S). n aunt. Of(A, N) : - sister. Of(A, X), parent. Of(X, N). n grandmother. Of(G, P) : mother. Of(G, X), parent. Of(P). n ancestor(A, P) : - parent. Of(A, X), ancestor(X, P). n. . . n MB: 26 Feb 2001 CS 360 - Lecture 1 7

Some Facts male(john). n female(mary). n male(peter). n parent. Of(john, mary). n sibling. Of(mary, Some Facts male(john). n female(mary). n male(peter). n parent. Of(john, mary). n sibling. Of(mary, peter). n parent. Of(ann, john). n parent. Of(mark, ann). n. . . n MB: 26 Feb 2001 CS 360 - Lecture 1 8

Some Queries ? - sister. Of(mary, peter). n ? - sister. Of(mary, Who). n Some Queries ? - sister. Of(mary, peter). n ? - sister. Of(mary, Who). n ? - sister. Of(Sis, peter). n ? - sister. Of(Sister, Sibling). n ? - ancestor. Of(A, P). n MB: 26 Feb 2001 CS 360 - Lecture 1 9

Their Answers n ? - sister. Of(mary, peter). – n ? - sister. Of(mary, Their Answers n ? - sister. Of(mary, peter). – n ? - sister. Of(mary, Who). – – n yes Who = peter ? ; no ? - sister. Of(Sis, peter). – – Sis = mary ? ; no MB: 26 Feb 2001 CS 360 - Lecture 1 10

More Answers n ? - sister. Of(Sister, Sibling). – – – Sibling = peter, More Answers n ? - sister. Of(Sister, Sibling). – – – Sibling = peter, Sister = mary ? ; no MB: 26 Feb 2001 CS 360 - Lecture 1 11

Last Answer n ? - ancestor. Of(A, P). – – – – – A Last Answer n ? - ancestor. Of(A, P). – – – – – A = john, P = mary ? ; A = ann, P = john ? ; A = mark, P = ann ? ; A = ann, P = mary ? ; . . . MB: 26 Feb 2001 CS 360 - Lecture 1 12

Running Prolog Create knowledge base using favorite editor. n Type /usr/local/bin/prolog on cs 26. Running Prolog Create knowledge base using favorite editor. n Type /usr/local/bin/prolog on cs 26. n Load that knowledge base into Prolog: n – n Ask queries: – n [‘my. Knowledge. Base. pl’]. sister. Of(X, Y). Exit Prolog: – halt. MB: 26 Feb 2001 CS 360 - Lecture 1 13

Prolog Knowledge Base Anatomy n Knowledge Base – Relations n. Clauses – Terms MB: Prolog Knowledge Base Anatomy n Knowledge Base – Relations n. Clauses – Terms MB: 26 Feb 2001 CS 360 - Lecture 1 14

Terms n Terms are things like atoms, numbers, variables, and structures: – n tom, Terms n Terms are things like atoms, numbers, variables, and structures: – n tom, 25. 3, X, name(mike, barley) In happy(P) : - paid(P, X), spend(P, Y), X>Y happy(P), : -, paid(P, X), spend(P, Y), X>Y, P, X, and Y are all terms. MB: 26 Feb 2001 CS 360 - Lecture 1 15

Anatomy of a Clause All clauses terminated by full-stop(“. ”). n Clauses have the Anatomy of a Clause All clauses terminated by full-stop(“. ”). n Clauses have the form: n head : - body. n MB: 26 Feb 2001 CS 360 - Lecture 1 16

Head of a Clause n The head may be the relation name with arguments Head of a Clause n The head may be the relation name with arguments or may be missing, Examples: – – – likes(X, Z) : - likes(X, Y), likes(Y, Z). likes(mike, X) : - true. : - write(***). likes(mike, X) : - true. likes(mike, X). n Clauses with missing bodies are called facts. n Facts with variables are called universal facts. n MB: 26 Feb 2001 CS 360 - Lecture 1 17

Body of a Clause Body is an expression composed of terms. n When the Body of a Clause Body is an expression composed of terms. n When the clause head is missing then the body is executed at load-time. n MB: 26 Feb 2001 CS 360 - Lecture 1 18

Anatomy of a Relation n A relation is identified by its name and its Anatomy of a Relation n A relation is identified by its name and its arity (# of arguments) - name/arity – n likes/2 is a different relation from likes/3 A relation is defined by the clauses whose heads match the relation id, e. g. , the clause – ancestor(A, P) : - parent. Of(A, P). is part of the definition of ancestor/2 MB: 26 Feb 2001 CS 360 - Lecture 1 19

Anatomy of a Query Queries are input by the user (rather than part of Anatomy of a Query Queries are input by the user (rather than part of the knowledge base). n Queries have clause body syntax & semantics, notably variables are existentially quantified. n When query has variables, & Prolog succeeds in proving it follows from KB, Prolog displays variable bindings used in proof. n MB: 26 Feb 2001 CS 360 - Lecture 1 20

Quick Quiz What do you ignore (at least initially) in declarative-style programming? n What Quick Quiz What do you ignore (at least initially) in declarative-style programming? n What are the two main components of a knowledge-based system? n What is the type of knowledge encoded in a Prolog knowledge base? n MB: 26 Feb 2001 CS 360 - Lecture 1 21

Quick Quiz cont’d By what two things are relations identified? n In a Prolog Quick Quiz cont’d By what two things are relations identified? n In a Prolog knowledge base, what constitutes the definition of a relation? n What forms can a clause take? n What are the two parts of a clause? n What terminates a clause? n Give examples of different types of terms. n MB: 26 Feb 2001 CS 360 - Lecture 1 22

Summary Declarative programming focuses on specifying what you want, not on how to get Summary Declarative programming focuses on specifying what you want, not on how to get it. n Knowledge based systems provide an underlying inference engine, the user provides (in declarative form) the knowledge and the queries. n Prolog can be viewed as a type of knowledge based programming system. n MB: 26 Feb 2001 CS 360 - Lecture 1 23

Summary cont’d Prolog knowledge base = relation collection. n Relation identified by name/arity. n Summary cont’d Prolog knowledge base = relation collection. n Relation identified by name/arity. n Relation defined by clauses whose heads agree with that id (i. e. , name & number of arguments) n MB: 26 Feb 2001 CS 360 - Lecture 1 24

Summary cont’d n Clauses have following forms: – – – n head : - Summary cont’d n Clauses have following forms: – – – n head : - body. head. : - body. Queries are entered by the user (i. e. , not in knowledge base) and have form of clause body. MB: 26 Feb 2001 CS 360 - Lecture 1 25




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