Python Logic Programming With Example

What is Logic Programming?

Logic programming is a programming paradigm that sees computation as automatic reasoning over a database of knowledge made of facts and rules. It is a way of programming and is based on formal logic. A program in such a language is a set of sentences, in logical form, one that expresses facts and rules about a problem domain. Among others, Datalog is one such major logic programming language family.

Structure

Let’s talk about facts and rules. Facts are true statements — say, Bucharest is the capital of Romania. Rules are constraints that lead us to conclusions about the problem domain. These are logical clauses that express facts. We use the following syntax to write a rule (as a clause):

H -> B1, …, Bn.

We can read this as:

H if B1 and … and Bn.

Here, "H" is the head of the rule and "B1, …, Bn" is the body. A fact is a rule with no body:

H.

An example would be:

fallible(X) -> human(X)

Every logic program needs facts based on which to achieve the given goal. Rules are constraints that get us to conclusions.

Logic and Control

Think of an algorithm as a combination of logic and control.

Algorithm = Logic+Control

In a pure logic programming language, the logic component gets to the solution alone. We can, however, vary the control component for other ways to execute a logic program.

Getting Started With Python

Gearing up for logic programming with Python, we will install a couple of packages. Let’s use pip for this.

• Kanren: It lets us express logic as rules and facts and simplifies making code for business logic.

>>> pip install kanren

• SymPy: This is a Python library for symbolic mathematics. It is nearly a full-featured Computer Algebra System.

>>> pip install sympy

Python Logic Programming Example

With logic programming, we can compare expressions and find out unknown values. Consider the following piece of code:

>>> from kanren import run,var,fact
>>> from kanren.assoccomm import eq_assoccomm as eq
>>> from kanren.assoccomm import commutative,associative
>>> add='add' #Defining operations
>>> mul='mul'
>>> fact(commutative,mul) #Addition and multiplication are commutative and associative
>>> fact(commutative,add)
>>> fact(associative,mul)
>>> fact(associative,add)
>>> a,b,c=var('a'),var('b'),var('c') #Defining variables
>>> #2ab+b+3c is the expression we have'
>>> expression=(add, (mul, 2, a, b), b, (mul, 3, c))
>>> expression=(add,(mul,3,-2),(mul,(add,1,(mul,2,3)),-1)) #Expression
>>> expr1=(add,(mul,(add,1,(mul,2,a)),b),(mul,3,c)) #Expressions to match
>>> expr2=(add,(mul,c,3),(mul,b,(add,(mul,2,a),1)))
>>> expr3=(add,(add,(mul,(mul,2,a),b),b),(mul,3,c))
>>> run(0,(a,b,c),eq(expr1,expression)) #Calls to run()

((3, -1, -2),)

 >>> run(0,(a,b,c),eq(expr2,expression))  

((3, -1, -2),)

 >>> run(0,(a,b,c),eq(expr3,expression))  

()

You’ll see that the third expression gives us nothing. It is mathematically the same, but structurally different.

Checking for Prime Numbers in Python Logic Programming

If we have a list of numbers, we can find out which ones are prime and also generate such numbers. Let’s see how.

>>> from kanren import isvar,run,membero
>>> from kanren.core import success,fail,goaleval,condeseq,eq,var
>>> from sympy.ntheory.generate import prime,isprime
>>> import itertools as it
>>> def prime_test(n): #Function to test for prime
if isvar(n):
return condeseq([(eq,n,p)] for p in map(prime,it.count(1)))
else:
return success if isprime(n) else fail
>>> n=var() #Variable to use
>>> set(run(0,n,(membero,n,(12,14,15,19,21,20,22,29,23,30,41,44,62,52,65,85)),(prime_test,n)))

{41, 19, 29, 23}

>>> run(7,n,prime_test(n))

(2, 3, 5, 7, 11, 13, 17)

So, this was all in Python Logic Programming. Hope you like our explanation.

Conclusion – Python AI Logic Programming

In this Python AI Logic Programming tutorial, we discussed the meaning of logic programming in Python. Moreover, we saw the example of Python Logic Programming. Also, we discussed the checking for Prime Numbers. Still, if you have any doubt regarding Python Logic Programming, ask in the comment tab.