Download Functional Programming

Logic Programming
By
P. S. Suryateja
Asst. Professor, CSE
Vishnu Institute of Technology
Vishnu Institute of technology – Website: www.vishnu.edu.in
Introduction
• Programs are expressed in the form of symbolic logic and logical
inferencing process is used to produce results.
• Logic programs are declarative rather than procedural.
• Programs in logic programming languages are collections of facts
and rules.
• Programming that uses a form of symbolic logic as a programming
languages is often called logic programming.
• Example of logic programming language is Prolog.
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Predicate Calculus
•
Predicate calculus is the basis of logic programming.
•
A proposition is a logical statement that may or may not be true.
•
Formal logic is a method for describing propositions.
•
Symbolic logic can be used for three basic needs of formal logic:
– To express propositions
– To express relationships between propositions
– To describe how new propositions can be inferred from other propositions
that are assumed to be true.
• The form of symbolic logic that is used for logic programming is called
first-order predicate calculus.
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Predicate Calculus : Propositions
• The objects in propositions are represented by
constants or variables.
• A constant is a symbol that represents an object.
• A variable is a symbol that can represent
different objects at different times.
• The simplest proposition is an atomic
proposition which consists of compound terms.
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Predicate Calculus : Propositions (cont...)
• A compound term is composed of two parts: a functor
and an ordered list of parameters.
• A functor is the function symbol that names the relation.
• A compound term with a single parameter is a 1-tuple, one
with two parameters is a 2-tuple and so on.
Examples of 1-tuple and 2-tuple compound terms:
man(jake)
like(bob, steak)
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Predicate Calculus : Propositions (cont...)
• A compound proposition have two or more
atomic propositions which are connected by
logical connectors, or operators.
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Predicate Calculus : Propositions (cont...)
• Examples of compound propositions:
a∩bƆc
aϹbUc
• Variables can be used in propositions but only
when they are introduced by special symbols
called quantifiers.
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Predicate Calculus : Clausal Form
• One problem with predicate calculus is that there are
too many different ways of stating propositions that
have the same meaning.
• A standard form for stating propositions is clausal
form.
• A proposition in clausal form has the following
syntax:
B1 U B2 U ... U Bn Ϲ A1 ∩ A2 ∩ ... ∩ Am
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Predicate Calculus : Clausal Form (cont...)
• The meaning of the clausal form is: if all the A’s
are true then at least one of the B’s is true.
• Characteristics of clausal form:
– Existential quantifiers are not required and universal
quantifiers are implicit.
– No operators other than conjunction and disjunction
are supported.
– Disjunction should appear on the left hand side and
conjunction on the right hand side.
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Predicate Calculus : Clausal Form (cont...)
• The right side of clausal form proposition is
called the antecedent and the left side is
called consequent.
Ex:
likes(bob, trout) Ϲ likes(bob, fish) ∩ fish(trout)
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Prolog
• Prolog was developed by Colmerauer and
Roussel in 1972.
• A program in Prolog is made up of several
statements.
• Each statement is made up of terms.
• A Prolog term is a constant, a variable, or a
structure.
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Prolog (cont...)
• A constant is either an atom or an integer.
• Atoms are symbolic values of Prolog.
• A variable is a string of letters, digits, and underscores
that begins with a uppercase letter or an underscore ( _ ) .
• A structure represents the atomic propositions of
predicate calculus, and their form is:
functor(parameter-list)
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Prolog (cont...)
• Prolog has three basic kinds of statements:
– Fact statements
– Rule statements
– Goal statements
• A fact statement is a proposition that is assumed to be true.
• A fact statement is represented as a headless Horn clause.
Ex:
female(shelly).
male(bill).
father(bill, jake).
mother(bill, shelly).
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Prolog (cont...)
• A rule statement specifies rules of implication between
propositions.
• A rule statement is represent as headed Horn clause.
• The right side is the antecedent or if part and the left
side is the consequent of then part.
• The consequent is a single term and the antecedent can
be either a single term or a conjunction.
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Prolog (cont...)
• In Prolog conjunction is specified as a comma.
• General form of a Prolog rule statement is:
consequence :- antecedent
Ex:
ancestor(mary, shelley) :- mother(mary, shelley)
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Prolog (cont...)
• In Prolog a theorem is in the form of proposition that
we want the system to either prove or disprove. Such
propositions are called goals or queries.
• The syntax of a Prolog goal statement is same as that
of a fact statement.
Ex:
man(fred).
father(X, mike).
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Prolog : Inferencing Process
• Resolution is an inferencing process that allows
inferred propositions to be computed from given
propositions.
• Queries are called goals. When a goal is a compound
proposition, each of the facts is called a sub goal.
• To prove that a goal is true, the inferencing process
must find a chain of inference rules or facts in the
database that connect the goal to one or more facts in
the database.
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Prolog : Inferencing Process (cont...)
• For example, if Q is a goal, then either Q
must be a fact in the database or the
inferencing process must find a fact P1 and a
sequence of propositions P2, P3, ..., Pn such
that:
P2 :- P1
P3 :- P2
...
Q :- Pn
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Prolog : Inferencing Process (cont...)
• There are two approaches for attempting to match a given goal to a
fact in the database:
– Top-down resolution or backward chaining
– Bottom-up resolution or forward chaining
• If the system starts with the goal and attempts to find a sequence of
matching propositions that lead to some set of original facts in the
database is known as top-down resolution or backward chaining.
• If the system starts with the facts and rules of the database and
attempts to find a sequence of matches that lead to a goal is known
as bottom-up resolution or backward chaining.
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Prolog : Inferencing Process (cont...)
Example:
Database:
father(bob).
man(X) :- father(X).
Query:
man(bob).
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Prolog : Inferencing Process (cont...)
• Solution search is done in one of the two ways:
– Depth-first
– Breadth-first
• A depth-first search finds the complete sequence
of propositions, a proof, for the first sub goal
before working on others.
• A breadth-first search works on all sub goals of a
given goal in parallel.
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Prolog : Inferencing Process (cont...)
• Prolog implementations use backward
chaining for resolution and depth-first as its
search process.
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Applications of Logic Programming
• Relational Database Management Systems
– RDBMS is similar logic programming.
– Tables can be represented using Prolog structures and relationships between
tables can be described by Prolog rules and the retrieval process is inherent in
resolution operation.
– The goal statements of Prolog provide the queries for the RDBMS.
– One advantage of using logic programming to implement an RDBMS is that
only a single language is required.
– Another advantage of using logic programming to implement RDMS is that
deductive capability is built in.
• Expert Systems
– Expert systems are computer systems designed to emulate human expertise in
some particular domain.
– Prolog can be used to construct expert systems.
– Prolog’s facts, rules and inference mechanism can be used to implement
expert systems.
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Applications of Logic Programming (cont...)
– Missing from Prolog is the automatic ability of the system to
query the user for additional information when it is needed.
• Natural Language Processing
– Natural language interfaces to computer systems can be easily
implemented using logic programming languages.
– For describing language syntax, logic programming is
equivalent to context-free grammar.
– Inferencing process (backward chaining) in logic programming
is equivalent to parsing strategies.
– Some kinds of semantics of natural languages can be made
clear by modeling the languages with logic programming.
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