Epistemic and Inferential Consistency in Knowledge-Based Systems


Wed 12th March 12:30-14:00, Richmond AS03

Ron Chrisley: Epistemic and Inferential Consistency in Knowledge-Based Systems

One way to understand the knowledge-based systems approach to AI is as the attempt to give an artificial agent knowledge (or give it the ability to act like a human that has that knowledge) by putting linguaform representations of that knowledge into the agent’s database (its knowledge base).  The agent can then add to its knowledge base by applying rules of inference to the sentences in it.  An important desideratum for this process is that only true sentences are added (else they cannot be knowledge).  Since typical rules of inference would allow the addition of any sentences, including false ones, to an inconsistent database, care must be taken to ensure that knowledge bases are consistent.  Much effort has been expended on devising tractable ways to do this (e.g., truth maintenance systems, assumption-based truth maintenance systems, partitioned paraconsistent knowledge bases that are locally consistent but may be globally inconsistent, etc.)  I argue that for certain kinds of knowledge representation languages (autoepistemic logics), a further constraint, which I call epistemic consistency, must be met.  I argue for the need to check for epistemic consistency despite the fact that, unlike for consistency simpliciter, failing to meet this constraint is not a logical possibility.  The most basic form of checking that this constraint is met is to ensure that there are no sentences in an agent’s knowledge base that constitute what Sorensen has called an epistemic blindspot for that agent (e.g., “It is raining, but Hal doesn’t know it”, for the agent Hal).  This constraint must be maintained both when initialising the knowledge base, and when applying rules of inference, a fact which requires generalising from Sorensen’s notion of an epistemic blindspot to the concept of epistemic blindspot sets (a move that is independently motivated in applying Sorensen’s surprise examination paradox solution to the strengthened paradox of the toxin).  In addition, and along similar lines, I argue that another form of consistency, which I call inferential consistency, must be maintained.  Inferential consistency does not involve epistemically problematic sentences, but rather epistemically problematic inferences, such as ones concerning the number of inferences one has made.  I consider one way of dealing with such cases, which has the alarming consequence of rendering all rules of inference strictly invalid.  Specifically, I argue that the validity of a rule of inference can only be retained if a semantic restriction (that of excluding reference to the inference process itself) is placed on the sentences over which it can operate.

What is colour?


Fellow Sackler member Jim Parkinson brought to my attention the fact that this year’s Flame Challenge – explaining science to 11-year-olds in less than 300 words – is on the topic “What is Color?”.  I decided to take up the challenge; here’s my entry (299 words!):

The question “what is color?” is tricky.  Understood one way, it hardly needs answering for people with normal vision, who have no problem learning how to use the word “color” and what the names for different colors are: color is just part of the way that things look.   But that answer would be of little use to a blind person, since for them objects don’t “look” any way at all.  Science should try to explain things for everyone, so here’s an explanation of color that works for all people, sighted or blind.
Light is a collection of extremely small particles called photons. A photon might begin its journey at a lamp, bounce off an object (such as a book), and end its journey by being absorbed by one of the cells that line the back wall inside your eye.  Photons wiggle while moving – some wiggle slowly, some quickly.
The color of an object is the mixture of wiggle speeds of photons the object gives off in normal light. 
Sighted people can see an object’s color because the way a photon affects their eye cells depends on its wiggle speed.  For example, if your eye absorbs a slow wiggling photon, you see red; a fast wiggling photon, you see blue. Mixtures of wiggle speeds have a mixture of effects on your eye cells, letting you see a mixture of colors.  Something colored white gives off photons of all wiggle speeds.
If you shine red light on a white ball it looks red, but its actual color is still white because if it were in normal light it would give off photons of all wiggle speeds.  Similarly, a blue book in the dark is still blue because it would still give off fast wiggling photons were it in normal light. 

Comments welcome.