natlog 0.4.1

Prolog-like interpreter and tuple store

A lightweight Prolog-like interpreter with a natural-language style syntax and neuro-symbolic tuple database interface

We closely follow Einstein's "Everything should be made as simple as possible, but no simpler."

At this point, we rely on Python's natural error checking, without doing much to warn about syntactic or semantic errors. This can be added, but this is meant as an executable specification of an otherwise simple and natural logic language that we hereby name Natlog.

Natlog : a succinct overview

• Terms are represented as nested tuples.

• A parser and scanner for a simplified Prolog term syntax is used to turn terms into nested Python tuples.

Surface syntax of facts, as read from strings, is just whitespace separated words (with tuples parenthesized) and sentences ended with . or ?. Like in Prolog, variables are capitalized, unless quoted. Example programs are in folder natprogs, for instance tc.nat:

cat is feline.
tiger is feline.
mouse is rodent.
feline is mammal.
rodent is mammal.
snake is reptile.
mammal is animal.
reptile is animal.

tc A Rel B : A Rel B.
tc A Rel C : A Rel B, tc B Rel C.

To query it, try:

>>> n=natlog(file_name="natprogs/tc.nat")
>>> n.query("tc Who is animal ?")

It will return the transitive closure of the is relation.

GOAL PARSED: (('tc', 0, 'is', 'animal'),)
ANSWER: ('tc', 'cat', 'is', 'animal')
ANSWER: ('tc', 'tiger', 'is', 'animal')
ANSWER: ('tc', 'mouse', 'is', 'animal')
ANSWER: ('tc', 'feline', 'is', 'animal')
ANSWER: ('tc', 'rodent', 'is', 'animal')
ANSWER: ('tc', 'snake', 'is', 'animal')
ANSWER: ('tc', 'mammal', 'is', 'animal')
ANSWER: ('tc', 'reptile', 'is', 'animal')

List processing is also supported as in:

app () Ys Ys. 
app (X Xs) Ys (X Zs) : app Xs Ys Zs.

The interpreter supports a yield mechanism, similar to Python's own. Something like ^ my_answer X resulting in my_answer X to be yield as an answer.

The interpreter has also been extended to handle simple function and generator calls to Python using the same prefix operator syntax:

• `f A B .. Z R, resulting in Python function f(A,B,C) being called and R unified with its result
• ``f A B .. Z R, resulting in Python generator f(A,B,C) being called and R unified with its multiple yields, one a time
• ~R A B .. Z for unifying ~ R A B .. Z with matching facts in the term store
• f A B .. Z, resulting in f(A,B,C,..,Z) being called with no result returned

A nested tuple store for unification-based tuple mining

An indexer in combination with the unification algorithm is used to retrieve ground terms matching terms containing logic variables.

Indexing is on all constants occurring in ground facts placed in a database.

As facts are ground, unification has occurs check and trailing turned off when searching for a match.

To try it out, do:

python3 -i tests.py

>>> dtest()

It gives, after digesting a text and then querying it:

   John has (a car).
   Mary has (a bike).
   Mary is (a student).
   John is (a pilot).

('John', 'has', ('a', 'car'))
('Mary', 'has', ('a', 'bike'))
('Mary', 'is', ('a', 'student'))
('John', 'is', ('a', 'pilot'))


Who has (a What)?
--> ('John', 'has', ('a', 'car'))
--> ('Mary', 'has', ('a', 'bike'))

Who is (a pilot)?
--> ('John', 'is', ('a', 'pilot'))

'Mary' is What?
--> ('Mary', 'is', ('a', 'student'))

'John' is (a What)?
--> ('John', 'is', ('a', 'pilot'))

Who is What?
--> ('Mary', 'is', ('a', 'student'))
--> ('John', 'is', ('a', 'pilot'))

Neuro-symbolic tuple database

As an extension to the nested tuple store the neuro-symbolic tuple database uses a machine learning algorithm instead of its indexer.Thus it offers the same interface as the tuple store that it extends. The learner is trained upon loading the database file (from a .nat, .csv or .tsv file) and its inference mechanism is triggered when facts from the database are queried. The stream of tuples returned from the query is then filtered via unification (and possibly, more general integrity constraints, expressed via logic programming constructs).

Example of usage (see more at https://github.com/ptarau/pypro/blob/master/tests.py )

def ndb_test() :
  nd = neural_natlog(file_name="natprogs/dbtc.nat",db_name="natprogs/db.nat")
  print('RULES')
  print(nd)
  print('DB FACTS')
  print(nd.db)
  nd.query("tc Who is_a animal ?")

The output will show the X and y numpy arrays used to fit the sklearn learner and then the logic program's rules and the facts from which the arrays were extracted when the facts were loaded.

X:
 [[1 0 0 0 0 0 0 0 0 0 0 0]
 [0 1 0 0 0 0 0 0 0 0 0 0]
 [0 0 1 0 0 0 0 0 0 0 0 0]
 [0 0 0 1 0 0 0 0 0 0 0 0]
 [0 0 0 0 1 0 0 0 0 0 0 0]
 [0 0 0 0 0 1 0 0 0 0 0 0]
 [0 0 0 0 0 0 1 0 0 0 0 0]
 [0 0 0 0 0 0 0 1 0 0 0 0]
 [0 0 0 0 0 0 0 0 1 0 0 0]
 [0 0 0 0 0 0 0 0 0 1 0 0]
 [0 0 0 0 0 0 0 0 0 0 1 0]
 [0 0 0 0 0 0 0 0 0 0 0 1]]

y:
 [[1 0 1 0 0 0 0 0 0 0]
 [1 1 1 1 1 1 1 1 1 1]
 [1 0 0 0 0 0 0 0 0 0]
 [0 1 0 1 0 0 0 0 0 0]
 [0 1 0 0 0 0 0 0 0 0]
 [0 0 1 1 0 1 0 0 0 0]
 [0 0 0 0 1 0 0 0 0 0]
 [0 0 0 0 1 0 1 0 0 0]
 [0 0 0 0 0 1 1 0 0 1]
 [0 0 0 0 0 0 0 1 1 1]
 [0 0 0 0 0 0 0 1 0 0]
 [0 0 0 0 0 0 0 0 1 0]] 

RULES
(('cat', 'is_a', 'feline'), ())
((0, 'is_a', 1), (('~', 0, 'is', 1),))
(('tc', 0, 1, 2), ((0, 1, 3), ('tc1', 3, 1, 2)))
(('tc1', 0, 1, 0), ())
(('tc1', 0, 1, 2), (('tc', 0, 1, 2),))

DB FACTS
(0, ('tiger', 'is', 'feline'))
(1, ('mouse', 'is', 'rodent'))
(2, ('feline', 'is', 'mammal'))
(3, ('rodent', 'is', 'mammal'))
(4, ('snake', 'is', 'reptile'))
(5, ('mammal', 'is', 'animal'))
(6, ('reptile', 'is', 'animal'))
(7, ('bee', 'is', 'insect'))
(8, ('ant', 'is', 'insect'))
(9, ('insect', 'is', 'animal'))

GOAL PARSED: (('tc', 0, 'is_a', 'animal'),)
ANSWER: ('tc', 'cat', 'is_a', 'animal')
ANSWER: ('tc', 'tiger', 'is_a', 'animal')
ANSWER: ('tc', 'mouse', 'is_a', 'animal')
ANSWER: ('tc', 'feline', 'is_a', 'animal')
ANSWER: ('tc', 'rodent', 'is_a', 'animal')
ANSWER: ('tc', 'snake', 'is_a', 'animal')
ANSWER: ('tc', 'mammal', 'is_a', 'animal')
ANSWER: ('tc', 'reptile', 'is_a', 'animal')
ANSWER: ('tc', 'bee', 'is_a', 'animal')
ANSWER: ('tc', 'ant', 'is_a', 'animal')
ANSWER: ('tc', 'insect', 'is_a', 'animal')