Logic Programming Tarik Booker

What will we cover?  Introduction  Definitions  Predicate Calculus  Prolog  Applications

What is Logic Programming?  Simply programming that uses a form of symbolic logic (predicate calculus) as a programming language  Languages based on this type of programming are called Logic Programming Languages  (Also known as declarative languages)

Definitions (1) Predicate Calculus:  Proposition – a logical statement that may or may not be true  Atomic – consist of compound terms  Compound Terms – element of a mathematical relation  Functor – function symbol that names the relation  Ordered list – parameters man(bob) like(bob, steak)

Definitions (2) Clausal Form: B 1  B 2  B 3  A 1  A 2  A 3  Antecedent – right side of a clausal form  Consequent – left side of a clausal form  Declarative Semantics – there is a simple way to determine the meaning of each statement

Prolog  Logic Programming Language  Definitions:  Term – a constant, variable or structure  Constant – only an atom (synbolic value) or an integer  Variable – any string of letters, digits, or underscores that begins with an uppercase letter  Structure – atomic propositions of predicate calculus  Ex: mystruct(parameter list)  Instantiation – a binding of a value to a variable

Sample Prolog (Fact Statements) Fact Statements:  male(bill).  male(jack).  father(bill, jack). Which is Correct?  Bill is Jack’s father?  Jack is Bill’s father?

(Answer)  Either way!  There are no intrinsic semantics in Prolog (just like Predicate Calculus)  Can be interpreted by the programmer in any way he/she likes.

Sample Prolog (Rule Statements)  Consequence_1 :- Antecedent_expression  Examples:  female(shelley), child(shelley).  ancestor(mary, shelley) :- mother(mary, shelley). (If Mary is the mother of Shelley, then Mary is the ancestor of Shelley)

Goal Statements  Queries are known as goals in Prolog.  Example: father(jason, freddy). father(X, freddy).

Inferencing  You want a goal.  When the goal is a compound proposition, each of the facts (structures) is called a subgoal  To prove a goal is true, the inferencing process muse connect the goal to one or more facts in the database  Proving a subgoal is known as satisfying the subgoal

Inferencing Example  Database contains:  father(bob).  man(X) :- father(X).  Your goal (query):  man(bob).  Forward Chaining – bottom-up resolution (start with facts, find goal)  Backward Chaining – top-down resolution(start with goal, find facts)

Inferencing (2)  Forward Chaining: better when the number of possible correct answers is large  Backward Chaining: better when there is a reasonable small set of candidate answers  When goal has more than one structure, we must search:  Depth-first – finds a proof for the first subgoal beforw working on the others  Breadth-first – works on all subgoals in parallel  Prolog uses depth-first, because it utilizes fewer resources  Backing up in a goal to a previously proven subgoal is known as backtracking

Applications of Logic Programming  Relational Database Management Systems  Expert Systems – emulate human expertise in some particular domain  Natural Language Processing

Resources Used Sebesta, Robert W. Concepts of Programming Languages (4 th Edition)