Logic Programming

What is Logic Programming?

• In contrast to all other types of programming encountered this semester, Logic Programming is nonprocedural
  • The focus is on what to compute as opposed to how to compute it
• A common example of this is sorting
  • Instead of coding how to do the sorting, describe what a sorted list looks like

$ sort(old\_list,new\_list) \subset permute(old\_list,new\_list) \cap sorted(new\_list) $

$ sorted(list) \subset \forall j \textrm{ such that } 1 \leq j \le n, list(j) \leq list(j + 1) $

Prolog

• Prolog is by far the most widely used logic programming language
• Was invented in the 70's
• Is based of a system of facts and rules
• Originally intended for theroem proving and natural language processing

Prolog on GL

• Like LISP and Scheme, there are many dialects of prolog
  • The one on GL is invoked using the command sicstus
• The prolog interpreter has two modes, entering facts and querying
  • The default mode is query
  • To enter the fact mode, enter [user]. and hit enter. Type ctrl+D to return to query mode
• To exit the interpreter, type ctrl+C followed by e

The Syntax of Prolog

• Prolog has a very limited set of valid statements
• Atom
  • Like an atom in LISP or Scheme, it is a symbolic value
  • Can contain underscores, letters, or numbers
  • Must start with a lowercase letter or be between single quotes
• Variable
  • Can also contain underscores, letters, or numbers
  • Must start with an uppercase letter

The Syntax of Prolog

• The third type of data in prolog is known as a structure
• The basic form is:

    functor(parameter list)

• The functor is any atom and is used to identify the structure
• The parameter list are atoms or variables separated by commas
• The functor can be though of as a relationship between the parameters in First-Order Logic

Fact Statements

• Prolog programs are made up of facts and rules to be consulted
• The facts in a program are a list of structures
• Every statement ends in a period

Fact Statement Examples

• The following facts describe the relationships between family members

  female(shelley).
  male(bill).
  female(mary).
  male(jake).
  father(bill, jake).
  father(bill, shelley).
  mother(mary, jake).
  mother(mary, shelley).

Fact Statement Practice

• Write statements for the following facts:
  • English,German,French,Spanish,Welsh,Russian,Persian,Hindu, and Gujarati are all languages
  • German and English are Germanic Languages
  • Spanish and French are Romance Languages
  • Welsh is a Celtic Language
  • Russian is a Slavic Language
  • Persian is a Iranian Language
  • Hindu and Gujarati are Indic Languges

Logic in Rule Statements

• When are are multiple structures in the antecedent, thare are connected by and clauses
• The statement below is read as "if antecedent1 and atencedent2 then consequence"

  consequence :- antecedent1, antecedent2.
  

• There is no explicit way to say or in prolog
  • Instead two statements are used

    consequence :- antecedentA.
    consequence :- antecedentB.
    

Using Variables in Rules

• It is perfectly legal, but very boring to have a rule with no variables

  ancestor(mary,shelley) :- mother(mary,shelley).
  

• When using variables in prolog, it is like adding the universal quantifier $\forall$ to the statement

  parent(X, Y) :- mother(X, Y).
  parent(X, Y) :- father(X, Y).
  grandparent(X, Z) :- parent(X, Y), parent(Y, Z).

Prolog Rule Practice

• Write rules for the following relationships
  • Iranian Language are a type of Indo-Iranian Language
  • Indic Languages are a type of Indo-Iranian Language
  • Indo-Iranian Languages are a type of Indo-European Language
  • Germanic Languages are a type of Indo-European Language
  • Romance Languages are a type of Indo-European Language
  • Celtic Languages are a type of Indo-European Language
  • Slavic Languages are a type of Indo-European Language

Querying Prolog

• Once we have defined the facts and rules in our program, we can use prolog to prove hypothesis
• At the most basic level, a query can be something like male(bill). to which the system will return yes or no
• More advanced queries are given with variables such as father(X,jake). which will return an answer if one exists.

A more efficent way to query

• Entering into user mode and having to enter all the facts is quite cumbersome
• Most prolog implementations have a way to store the database of facts and rules in a file
  • In scistus this is done using the consult call

    consult('file.pl')

• After this, all facts are loaded and the interpreter can be used to query

How Prolog Solves Queries

• The process of solving a query is known as unification because a variable and a symbol are unified during the process
  • It is similiar to assignment
  • It is better thought of as pattern matching
• There are two general algorithms
  • Forward Chaining starts with facts and attempts to derive the query through several steps
  • Backward Chaining starts with the query and matches rules and facts until variables are unified

How Prolog Solves Queries

• Sometimes, two rules or facts will work at a given stage
  • Here prolog must pick which statement to try first using either breath or depth first searching
• When the interpreter makes a wrong guess it needs to be able to backtrack to the last decision point and try another rule or fact
• The process of unification can be viewd by enabling tracing
  • In sicstus this is done by typing ctrl+C followed by t

Cons of Prolog

• Prolog can be very inefficent
  • If we had implemented the storting algorithm discussed at the beginning of lecture, prolog will just guess list permutations until it finds one that is sorted
• If a fact in not in the database, prolog assumes it is false
• Programming anything other than logic is cumbersome
  • Prolog is often more useful when used with another language