Monday, January 15, 2007
Real-world semantics is in the eye of the beholder
The notion of semantics in logic can be confusing. I found some good discussions of possible world semantics as based on interpretations, in a book I have on Reserve for my AI courses:
Brachman, R.J. and Levesque, H.J., Knowledge representation and reasoning. Elsevier/Morgan Kaufmann, San Francisco, CA, 2004.
I'll paraphrase their comments on page 20.
The meaning of "hammer" in some interpretation is no more or less than those objects that we consider to be hammers. As far as FOL is concerned, we do not try to say what a hammer is in the way a dictionary might, describing its shape, materials, size, or weight. All we need to say is which objects are and which are not hammers.
On pages 24 and 25, there are further statements to the effect that we can build a system that can be told that Hammer(h1) is true in some user-intended interpretation, so that the system can later come to believe other sentences that are true in that interpretation. "Hammer" is a predicate, and "h1" a term that we create; they have no other existence beyond our creation of them in our system.
I quote their fundamental tenet of knowledge representation:
“Reasoning based on logical consequence is weak, and only allows safe, logically guaranteed conclusions to be drawn. However, by starting with a rich collection of sentences as given premises, including not only facts about particulars of the intended application, but also those expressing connections among the non-logical symbols involved, the set of entailed conclusions becomes a much richer set, closer to the set of sentences true in the intended interpretation. Calculating these entailments thus becomes more like the form of reasoning we would expect of someone who understood the meaning of the terms involved."
Figure 7.6 in the AIMA textbook for the course illustrates some of this from a slightly different perspective.
Brachman, R.J. and Levesque, H.J., Knowledge representation and reasoning. Elsevier/Morgan Kaufmann, San Francisco, CA, 2004.
I'll paraphrase their comments on page 20.
The meaning of "hammer" in some interpretation is no more or less than those objects that we consider to be hammers. As far as FOL is concerned, we do not try to say what a hammer is in the way a dictionary might, describing its shape, materials, size, or weight. All we need to say is which objects are and which are not hammers.
On pages 24 and 25, there are further statements to the effect that we can build a system that can be told that Hammer(h1) is true in some user-intended interpretation, so that the system can later come to believe other sentences that are true in that interpretation. "Hammer" is a predicate, and "h1" a term that we create; they have no other existence beyond our creation of them in our system.
I quote their fundamental tenet of knowledge representation:
“Reasoning based on logical consequence is weak, and only allows safe, logically guaranteed conclusions to be drawn. However, by starting with a rich collection of sentences as given premises, including not only facts about particulars of the intended application, but also those expressing connections among the non-logical symbols involved, the set of entailed conclusions becomes a much richer set, closer to the set of sentences true in the intended interpretation. Calculating these entailments thus becomes more like the form of reasoning we would expect of someone who understood the meaning of the terms involved."
Figure 7.6 in the AIMA textbook for the course illustrates some of this from a slightly different perspective.
Saturday, January 6, 2007
My teaching gateway page
You might have noticed below that all my teaching pages live in a certain section of my webspace. In fact I have a "gateway page" that links to my current courses and others all the way back to 1998 (some on a second page). The course pages vary a lot in depth and quality, depending on how much time I devoted to building them. The gateway is at:
http://www.ccs.neu.edu/home/futrelle/teaching/gateway.html
Otherwise, I'm hard at work finishing off all the major pages for my UG and grad AI courses. First class is the UG one, the afternoon of Monday the 8th of January. Grad one is the following Thursday evening. For whatever reason, these two courses are better organized than any of mine in recent memory. (So if you're not happy, the others were worse ;-).
I've had a bit of luck learning to play Gears of War on my XBOX - enough for me to begin to see what type of artificial intelligence techniques are used in it. One example: When I pick up a weapon, my partner is aware that I now have the weapon and changes his behavior to suit his new knowledge, e.g., suggesting that I use it in a situation in which he is further aware of the fact that I'm being targeted by some nasty foes. There is nothing profound in this; it's not hard to imagine how this could be programmed in. But the accumulation of many such things, including an "understanding" of the physical environment, etc., all adds up to enough complexity and smarts to make it interesting (and to $ales).
http://www.ccs.neu.edu/home/futrelle/teaching/gateway.html
Otherwise, I'm hard at work finishing off all the major pages for my UG and grad AI courses. First class is the UG one, the afternoon of Monday the 8th of January. Grad one is the following Thursday evening. For whatever reason, these two courses are better organized than any of mine in recent memory. (So if you're not happy, the others were worse ;-).
I've had a bit of luck learning to play Gears of War on my XBOX - enough for me to begin to see what type of artificial intelligence techniques are used in it. One example: When I pick up a weapon, my partner is aware that I now have the weapon and changes his behavior to suit his new knowledge, e.g., suggesting that I use it in a situation in which he is further aware of the fact that I'm being targeted by some nasty foes. There is nothing profound in this; it's not hard to imagine how this could be programmed in. But the accumulation of many such things, including an "understanding" of the physical environment, etc., all adds up to enough complexity and smarts to make it interesting (and to $ales).
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