1 / 13

Chapter 8: The Logical Paradigm

Chapter 8: The Logical Paradigm. Lecturer: Xinming (Simon) Ou CIS 505: Programming Languages Fall 2010 Kansas State University. What we have covered so far:. Imperative paradigm Computes effects Functional paradigm Computes values Used ML as an example Logical paradigm

varana
Download Presentation

Chapter 8: The Logical Paradigm

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. Chapter 8: The Logical Paradigm Lecturer: Xinming (Simon) Ou CIS 505: Programming Languages Fall 2010 Kansas State University

  2. What we have covered so far: • Imperative paradigm • Computes effects • Functional paradigm • Computes values • Used ML as an example • Logical paradigm • Computes relations • Use Prolog as an example

  3. Example relations • Parent relation: • parent(A, B) means A is B’s parent • e.g. parent(bill, mary). parent(mary, john). • Ancestor relation • Can be defined inductively: A is B’s ancestor if A is B’s parent. A is B’s ancestor if A is C’s ancestor, and C is B’s ancestor • The resulting relation is the smallest one that satisfies the above two rules.

  4. Some definitions for Prolog • Atoms: • Any sequence of alpha-numeric characters that starts with a lower-case letter, or a single-quoted string, or a number e.g. mary, john01, ‘Mary Doe’, 100 • Variables: • Any sequence of alpha-numeric characters that starts with an upper-case letter, or an underscore “_” • e.g. Mary, _mary, _ • Literal • predicate(t1, …, tk), where tiis either an atom, a variable, or a data-structure (function applied to parameters). • e.g. parent(mary, john). parent(mother(john), john). ancestor(mother(father(john)), john).

  5. Horn Clauses • A Horn clause is a logical clause with a single positive literal: L0∨ L1∨ … Ln • This is equivalent to L1∧ …∧Ln=> L0 In Prolog, we use “,” to mean logical and, and write implication “backward”. Each clause is concluded with a “.” L0 :- L1, …, Ln. • Example: ancestor(A, B) :- parent(A, B). ancestor(A, B) :- parent(A, C), ancestor(C, B). • We call the left-hand side of the clause its head, and the right-hand side of the clause its body. • A clause may have an empty body. e.g. parent(mother(X), X).

  6. Variables in Clauses • All variables are implicitly universally bound at the beginning of the clause • e.g. ancestor(A, B) :- parent(A, B). Logically it is equivalent to: Forall A, B. parent(A,B) => ancestor(A, B) Thus A and B can be instantiated with any term. • An underscore “_” is a wild card and can match anything. • e.g. isParent(A) :- ancestor(A, _).

  7. Query in Prolog • A query is in the form of a literal. The answer to the query is all the instantiations of the variables that make the literal true. • e.g. ? - ancestor(X,Y). X = bill Y = mary; X = mary Y = john; X = bill Y = john; no • Logically it is equivalent to “exists X, Y. ancestor(X,Y)?”

  8. Execution Semantics of Prolog • When a query is issued, it is “compared” against the head of all the clauses one by one. • If a “match” is found, the body of the clause becomes the new goals • This process will iterate and may either succeed or fail. • In either case the execution will backtrack to the first “choice point”, and try another match. • This is called “SLD resolution”

  9. Example SLD resolution ancestor(X,Y) :- parent(X,Y). ancestor(X,Y) :- parent(X,Z), ancestor(Z,Y). parent(bill,mary). parent(mary,john). • ?- ancestor(X, Y). • ?- parent(X,Y). • ?- parent(X,Z), ancestor(Z,Y). • X=bill • Y=mary • X=mary • Y=john • X=mary • Z=john • X=bill • Z=mary • ?- • Success ?- ancestor(john,Y). • ?- • Success ?- ancestor(mary,Y). • … • Failure ?- parent(mary,Y). ?- parent(mary,Z2), ancestor(Z2,Y). • Y=john • Z2=john ?- ancestor(john,Y). • ?- • Success • … • Failure

  10. Logic deduction as a program • The advantage of Prolog is that it has both a logic meaning, and an execution semantics • Ideally you do not need to think about the SLD resolution process when writing Prolog code • A Prolog program is simply a collection of logical statements. A query is simply asking whether a fact can be derived as a logical consequence of the statements. • However… • When the result does not match your expectation, knowing the SLD resolution process will help in debugging. • Moreover, Prolog is not always declarative, which we will see in the next lecture.

  11. Practice XSB • We will be using the XSB Prolog system • Is installed on all the departmental Linux machines • Can be downloaded from: http://xsb.sourceforge.net/ Installation is relatively hassle-free. However, if you need to compile XSB under Mac OS X Snow Leopard, please let me know and there will be special instructions.

  12. The first simple Prolog program • Put the following Prolog statements in a text file named “ancestor.P” parent(bill, mary). parent(mary, john). ancestor(A, B) :- parent(A, B). ancestor(A, B) :- parent(A, C), ancestor(C, B). Load the file in XSB: bash-3.2$ xsb [xsb_configuration loaded] [sysinitrc loaded] XSB Version 3.2 (Kopi Lewak) of March 15, 2009 [i386-apple-darwin10.4.0; mode: optimal; engine: slg-wam; scheduling: local; word size: 64] | ?- [ancestor].

  13. Experiment with it • Issue various queries: e.g. ?- ancestor(X,Y). ?- ancestor(bill, X). ?- ancestor(john, X). … • Change the order of the clauses and see what will happen: parent(bill, mary). parent(mary, john). ancestor(A, B) :- parent(A, C), ancestor(C, B). ancestor(A, B) :- parent(A, B).

More Related