Logic Programming in Python


Keywords
logic-programming, neuro-symbolic-learning, prolog, python, symbolic-artificial-intelligence
License
MIT
Install
pip install pytholog==2.4.0

Documentation

pytholog

Write Prolog in Python

Build Status

Python library that enables using logic programming in python. The aim of the library is to explore ways to use symbolic reasoning with machine learning.

Now pytholog supports probabilities.

Pytholog gives facts indices (first term) and uses binary search to search for relevant facts instead of looping over all knowledge base. So when defining rules, make sure that the main search terms are in the first position to speed up the search queries.

OR can be implemented with defining the rules as many times as the OR facts. For example, to say "fly(X) :- bird(X) ; wings(X)." can be defined as two rules as follows: "fly(X) :- bird(X)." and "fly(X) :- wings(X)."

prolog syntax

Prolog takes facts and rules. A fact or a rule has a predicate which in “likes(noor, sausage)” is “likes” and in “friend(X, Y)” is “friend”. Rules have “Left Hand Side (LHS)” which has a predicate and “Right Hand Sides (RHS)” or “goals” to be searched to answer the queries about the rules. LHS and RHS in a rule are separated with “:-”. Each predicate has “Terms”. Prolog uses lowercased variables to describe “constant values” and uppercased values to describe “variables” that need to be updated from the query.

Let’s take an example: likes(noor, sausage) is a fact which has likes as a predicate and (noor and sausage) as terms. friend(X, Y) :- +(X = Y), likes(X, Z), likes(Y, Z) is a rule which defines that two persons are considered friends if they like the same dish. This rule has an LHS friend(X, Y) and RHS or goals [+(X = Y), likes(X, Z), likes(Y, Z)]. The comma separating the goals means and while ; will mean or. Variables in the fact are lowercased meaning they are truths and cannot change. While in a rule they are Uppercased meaning they need to be changed while in a query.

Prolog uses backtracking search to answer the questions and the queries.

I loved prolog and the idea of Symbolic Intelligence. So I decided to build a module or a framework in python that can allow me to use prolog inside python aiming to combine the power of machine learning and symbolic reasoning.

pytholog Implementation

Installation
pip install pytholog
import pytholog as pl

Defining a knowledge base object to store the facts and rules.

new_kb = pl.KnowledgeBase("flavor")
new_kb(["likes(noor, sausage)",
        "likes(melissa, pasta)",
        "likes(dmitry, cookie)",
        "likes(nikita, sausage)",
        "likes(assel, limonade)",
        "food_type(gouda, cheese)",
        "food_type(ritz, cracker)",
        "food_type(steak, meat)",
        "food_type(sausage, meat)",
        "food_type(limonade, juice)",
        "food_type(cookie, dessert)",
        "flavor(sweet, dessert)",
        "flavor(savory, meat)",
        "flavor(savory, cheese)",
        "flavor(sweet, juice)",
        "food_flavor(X, Y) :- food_type(X, Z), flavor(Y, Z)",
        "dish_to_like(X, Y) :- likes(X, L), food_type(L, T), flavor(F, T), food_flavor(Y, F)"])

Let’s do some queries in this database using its facts and rules.

new_kb.query(pl.Expr("likes(noor, sausage)"))
# ['Yes']
new_kb.query(pl.Expr("likes(noor, pasta)"))
# ['No']

I added Memoization to speed up the queries.

Wikipedia definition: In computing, memoization or memoisation is an optimization technique used primarily to speed up computer programs by storing the results of expensive function calls and returning the cached result when the same inputs occur again.

Let’s test it doing the same query twice and compare time used to do the query.

# query 1
from time import time
start = time()
print(new_kb.query(pl.Expr("food_flavor(What, sweet)")))
print(time() - start)

# [{'What': 'limonade'}, {'What': 'cookie'}]
# 0.0020236968994140625
# query 2
start = time()
print(new_kb.query(pl.Expr("food_flavor(Food, sweet)")))
print(time() - start)

# [{'Food': 'limonade'}, {'Food': 'cookie'}]
# 0.0

As you see, it took almost no time to return the same answer again and it also takes care of different Uppercased variable inputs as they anyways will be the same result no matter what they are.

Now we will use the dish_to_like rule to recommend dishes to persons based on taste preferences.

start = time()
print(new_kb.query(pl.Expr("dish_to_like(noor, What)")))
print(time() - start)

# [{'What': 'gouda'}, {'What': 'steak'}, {'What': 'sausage'}]
# 0.001992940902709961

Let’s test the Memoization again:

start = time()
print(new_kb.query(pl.Expr("dish_to_like(noor, What)")))
print(time() - start)

# [{'What': 'gouda'}, {'What': 'steak'}, {'What': 'sausage'}]
# 0.0
City Coloring problem

Image Source: Seven Languages in Seven Weeks book

The problem is Constraint Satisfaction Problem. The problem is to color each city using only three colors but no adjacent cities can be colored the same. The problem might seem so easy but it’s really challenging how to tell this to a machine. But using prolog logic it is kind of easier because all you have to do is to specify the rules of the problem and prolog will answer.

## new knowledge base object
city_color = pl.KnowledgeBase("city_color")
city_color([
    "different(red, green)",
    "different(red, blue)",
    "different(green, red)", 
    "different(green, blue)",
    "different(blue, red)", 
    "different(blue, green)",
    "coloring(A, M, G, T, F) :- different(M, T),different(M, A),different(A, T),different(A, M),different(A, G),different(A, F),different(G, F),different(G, T)"
])

Let’s query the answer:

## we will use [0] to return only one answer 
## as prolog will give all possible combinations and answers
city_color.query(pl.Expr("coloring(Alabama, Mississippi, Georgia, Tennessee, Florida)"), cut = True)

# {'Alabama': 'blue',
#  'Mississippi': 'red',
#  'Georgia': 'red',
#  'Tennessee': 'green',
#  'Florida': 'green'}

Now let's try to play with some probabilities. First in prolog "is" is used to assign the result of operations. For example, if we want to say "A = 3 * 4", we say "A is 3 * 4", not "A = 3 * 4" because this is unification not assignment.

Let's define some dummy knowledge base with probabilities and query them:

The numbers are totally dummy and have no meanings just to explain the functionality.
battery_kb = pl.KnowledgeBase("battery")
battery_kb([
	"battery(dead,P) :- voltmeter(battery_terminals,abnormal,P2), P is P2 + 0.5",
	"battery(dead,P) :- electrical_problem(P), P >= 0.8",
	"battery(dead,P) :- electrical_problem(P2), age(battery,old,P3), P is P2 * P3 * 0.9",
	"electrical_problem(0.7)",
	"age(battery,old, 0.8)",
	"voltmeter(battery_terminals,abnormal,0.3)"])
			
battery_kb.query(pl.Expr("battery(dead, Probability)"))

# [{'Probability': 0.8}, {'Probability': 'No'}, {'Probability': 0.504}]
# the second one is "No" because the condition has not been met.
for another example of nested probabilities, see friends_prob.md

Taking rules from Machine Learning model and feed them into knowledge base then try to predict new instances.

This shows beneficial for Explainable AI. One can explain why a model predicts specific prediction.

Let's suppose that we have these rules from a Decision Tree Model to classify iris flowers. And we have a new record for which we try to predict using the rules.

iris_kb = pl.KnowledgeBase("iris")
iris_kb([## Rules
	"species(setosa, Truth) :- petal_width(W), Truth is W <= 0.80", 
	"species(versicolor, Truth) :- petal_width(W), petal_length(L), Truth is W > 0.80 and L <= 4.95",
	"species(virginica, Truth) :- petal_width(W), petal_length(L), Truth is W > 0.80 and L > 4.95",
	## New record
	"petal_length(5.1)",
	"petal_width(2.4)"])

Now let's try to predict the class:

iris_kb.query(pl.Expr("species(Class, Truth)"))

# [{'Class': 'setosa', 'Truth': 'No'},
#  {'Class': 'versicolor', 'Truth': 'No'},
#  {'Class': 'virginica', 'Truth': 'Yes'}]

Now let's extract the rules for some goal or fact.

iris_kb.rule_search(pl.Expr("species(Species, Truth)"))

# [species(setosa,Truth):-petal_width(W),TruthisW<=0.80,
#  species(versicolor,Truth):-petal_width(W),petal_length(L),TruthisW>0.80andL<=4.95,
#  species(virginica,Truth):-petal_width(W),petal_length(L),TruthisW>0.80andL>4.95]

So now we can see the rules why a model chooses a prediction and explain the behavior.

clear_cache() is used to clean the cache inside the knowledge_base:

new_kb.clear_cache()

from_file() is used to read facts and rules from a prolog ,pl, or txt file:

example_kb = pl.KnowledgeBase("example")
example_kb.from_file("/examples/example.txt")
# facts and rules have been added to example.db
example_kb.query(pl.Expr("food_flavor(What, savory)"))
# [{'What': 'gouda'}, {'What': 'steak'}, {'What': 'sausage'}]

Also we can constructs rules or facts looping over dataframes:

import pandas as pd
df = pd.DataFrame({"has_work": ["david", "daniel"], "tasks": [8, 3]})
df
#	has_work  tasks
#0	   david	  8
#1	  daniel	  3
ex = pl.KnowledgeBase()
for i in range(df.shape[0]):
    ex([f"has_work({df.has_work[i]}, {df.tasks[i]})"])

ex.db
# {'has_work': {'facts': [has_work(david,8), has_work(daniel,3)],
#   'goals': [[], []],
#   'terms': [['david', '8'], ['daniel', '3']]}}

Graph Traversals with Pytholog

Let's define a weighted directed graph and see if we can get a path, hopefully the shortest, between two nodes using breadth first search.

Image source
graph = pl.KnowledgeBase("graph")
graph([
	"edge(a, b, 6)", "edge(a, c, 1)", "edge(b, e, 4)",
	"edge(b, f, 3)", "edge(c, d, 3)", "edge(d, e, 8)",
	"edge(e, f, 2)",
	"path(X, Y, W) :- edge(X , Y, W)",
	"path(X, Y, W) :- edge(X, Z, W1), path(Z, Y, W2), W is W1 + W2"])

answer, path = graph.query(pl.Expr("path(a, f, W)"), show_path = True)
print(answer)
print([x for x in path if str(x) > "Z"])

# [{'W': 9}, {'W': 12}, {'W': 14}]
# ['d', 'b', 'e', 'c']

Now with the show_path argument we can see the nodes the search passed by and we can see it gave all the possible answers and the first one is the best. So let's use the cut argument to get only the first result and stop the search.

answer, path = graph.query(pl.Expr("path(a, e, W)"), show_path = True, cut = True)
print(answer)
print([x for x in path if str(x) > "Z"])

# [{'W': 10}]
# ['b']

For another more complicated undirected graph example see graph traversals with pytholog

Future implementation will try to come up with ideas to combine this technique with machine learning algorithms and neural networks

Contribution, ideas and any kind of help will be much appreciated