Logical induction in Python

This repository contains an implementation of a logical inductor in python.

The code was written to support the article [logical induction for software engineers](which has not yet been published). It consists of a python implementation of the logical induction algorithm published by Garrabrant et al in 2018.

I have prioritized simplicity over efficiency.

To run the example code:

$ git clone [email protected]:monasticacademy/logical-induction.git
$ cd logical-induction
$ python examples/two_updates.py

after update 1:
  the sky is blue                          1.000000
  the sky is blue | the sky is green       0.000000

after update 2:
  the sky is green → the world is round    0.000000
  the sky is blue                          0.000000
  the sky is blue | the sky is green       1.000000

Organization of the code

The main interface is the LogicalInductor class in inductor.py:

class LogicalInductor(object):
    ...

    def update(self, observation, trading_algorithm):
        """
        Given: 
         * An observation
         * A trading algorithm
        Return:
         * A belief state
        
        Implements the logical induction algorithm as per 5.4.1 in the paper
        """

The update function takes as input an observation, which is a logical sentence that is to be taken to be true from here on, and a trading algorithm, which is a set of formulas specifying trades to be executed that the logical inductor will set its credences in order to avoid being exploited by.

The representation of logical sentences is implemented in sentence.py and works as follows. The class sentence.Atom represents a claim about the world not further reducible by logical connectives such as AND, OR, NOT. Its constructor takes a string, which can be anything and is only to help humans keep track of what is going on. The other classes in this file implement conjunctions, disjunctions, logical negation, and material implication.

The representation of trading formulas is implemented in formula.py. A trading formula is a simple language for expressing buy/sell trades that a logical inductor must not be exploited by. The classes in this file follow section A.2 from the paper.

The representation of belief states and histories of is in credence.py. A belief state is a map from sentences to credences, and a history of belief states is a list of belief states.

The code in enumerator.py provides various routines for enumerating possible worlds.

The code in example/two_updates.py instantiates a logical inductor and feeds it two observations, printing out the credences it receives in response.