Monday, January 18, 2010

Inference engines and automated reasoning

An inference engine is a computer program that reasons, using some form of knowledge representation.

This can be done with propositional logic or first-order logic, assuming each proposition is completely unambiguous and is either 100% true or 100% false. These simplistic engines are fun little exercises in programming but in real-world situations, reasoning usually needs to consider ambiguities and uncertainties. Instead of simply being true or false, propositions may be likely or unlikely, or their likelihood may be something to be tested or determined. Some elements of some propositions may be poorly defined.

In the unambiguous binary case, it's typical to express rules for generating new propositions as if-then rules with variables in them. We call these production rules because they are used to produce new propositions.
If X is a man, then X is mortal.
Given the statement "Socrates is a man", we
  • match the statement to the rule's IF clause
  • take note of all variable assignments: X=Socrates
  • plug assignments into the THEN clause: "Socrates is mortal"
Obviously this isn't rocket science, but even without handling uncertainty, it will still be useful if scaled to very large numbers of propositions, as in the semantic web.

How to handle uncertainty? This can be done by representing knowledge as a Bayesian network, a directed graph where the edges represent the influences and dependencies between random variables. There is a good tutorial about these online. Here's an example from the Wikipedia article where the probability of rain is an independent variable, and the sprinkler system is usually off if it's raining, and the grass can get wet from either rain or the sprinkler.

There are at least two open-source inference engines that work with Bayesian networks. One is SMILE, another is the OpenBayes library for the Python language. OpenBayes allows you to update the state of your knowledge with a new observation.
Suppose now that you know that the sprinkler is on and that it is not cloudy, and you wonder what's the probability of the grass being wet : Pr(w|s=1,c=0). This is called evidence...
and then perform inference in the same way... The grass is much more likely to be wet because the sprinkler is on!
Here is a list of many more Bayesian network libraries, and another list. There is also a nice tutorial on Learning Bayesian Networks from Data, the process of taking a bunch of data and automatically discovering the Bayesian network that might have produced it. Another Bayesian reasoning system is BLOG.
Bayesian logic (BLOG) is a first-order probabilistic modeling language under development at MIT and UC Berkeley. It is designed for making inferences about real-world objects that underlie some observed data: for instance, tracking multiple people in a video sequence, or identifying repeated mentions of people and organizations in a set of text documents. BLOG makes it (relatively) easy to represent uncertainty about the number of underlying objects and the mapping between objects and observations.
Are production rule systems and Bayesian network systems mutually compatible? I don't yet know. Do Bayesian networks adequately represent all important forms of uncertainty or vagueness that one might encounter in working with real-world data? I don't know that either. Are there other paradigms I should be checking out? Probably.

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