Artificial Intelligence
Eric Siegel, Columbia University

Knowledge Representation Rhapsody

Sung to the hypothetical intelligent artifact

Eric Siegel wrote and performed this song when he was a computer science professor at Columbia University, 1997 - 2000.

OUTLINE:   (reverse-chronological music styles)
 Part I    INTRODUCTION         (90s R&B Ballad)
 Part II   MODELS               (rap)
 Part III  PHILOSOPHY           (80s robo-rock)
 Part IV   LOGIC                (disco)
 Part V    TEMPORAL REASONING   (Do-wop)
 Part VI   INFERENCE ALGORITHMS (Classical/operatic)


Part I    INTRODUCTION  (90s R&B Ballad)

You know me well, my friend, in every sense of the word,
'cause there's meaning in your brain, 'specially the semantic third.
But part of your mind's so logical, it's got no friggin' clue.
'Cause I think thought must be heuristic and informal to figure out what to do.

I'm in deep thought to make up my mind: what, when, why?
You're not so clever, if you're looping forever, with intractability.
Socrates wondered, what makes up a mind, sweety-pi?
In a perfect world we'd optimize utility (and simplify ontology).

I'm wondering how to automate my wonderful self --
a wond'rous thought that presupposes my own mental health.
Maybe it's crazy to think thought's so tangible, or that I am a singer.
Either way, if I succeed, my machine will attempt the very same thinger.



Part II   MODELS  (rap)

A model is a formal extrapolation, 
simplifying reality across the nation.
A version of reality in which my knowledge holds true
is a model of my knowledge base, and there may be quite a few.

Entailment only holds if it's true in every such version --
what reality do you live in?  Shprichts-du gut German?
Yes, entailment in terms of models -- natural semanticality.
But that don't "Tell" me how to model nature's causality.

What makes you tick? Y'all kinda unpredictable;
you're fickle, your process is intangible.
Can I tickle your fancy and glean from you the reasons
you emancipate your proclamations irrespective of the season?

What mechanism manifests as your multitude of actions?
You are a beautiful model in disguise with life's real-world complications.
I want to model you, model, you're the Apple of my eye,
and beauty's in the eye of the observing agent, I.

I can only make approximations, but I don't wanna fake it with you.
You told me to "mock this way," so I try to talk the talk the way you do.
Algorithms are young forever, but I am growing very old, 
and I don't wanna hand you that same old line of code. 

I'm a savage enigma of the emotional human type, 
but the devil is in your details and your bit is worse than your byte. 
My microprocessor is functioning at an optimum level; 
My Mail Daemon's Unix, it's not a devil. 

My genetics are a digital instruction set
so I've been perpetually perplexed since the very first day we met.
I feel a magic spark between you and me;
I call it love, but they call it static electricity.

You're syntactic representation is quite a bit eccentric;
you are the very model of a modern major general electric.
You are more than just a model -- your actions are real.
Bit, byte, bat your eye, validate my hypothetical zeal.

You speak the machine language of love, 3PO's little R2. 
You're made by Apple; you're clockwork, orange you? 
[The previous particularly non-funny pun was too painful to pass up.]
I want to model your mind, make a model of modern human kind,
I give you a 99 on the accuracy scale -- I love your binomial bell-curvey tale.
[The previous particularly non-PC pun was too good to pass up.]

I'm biased since you remind me of my mom who made me what I am today;
Nature versus nature?  Eggs all the way!
Don't spurn me, I'm the Ernie to your Bert, I'll burst your bubble;
Big trouble in a little diner where I eat, 
Dinah won't you blow your own horn -- beep beep!
Ya gotta read between the lines of life and find the hidden conceit.
Easter bunny or western shootout, I'm on the lookout for a treat.
Don't mince words -- you're mincemeat, honey; for you my tooth is sweet.


Part III   PHILOSOPHY (80s robo-rock)

Bridge segue:
Some say symbolic manipulation may be too ideal and idea,
but I don't know how else to think about it and 
	how do you know it's not really real?
People guess and people hedge and my computer is on chaos' edge.
Feel my hungry need, it's mealtime, don't seal my lips and your fate -- 
	what is the deal?

Is this the real life; is this just fantasy?
Caught in a landslide, no contact with reality.
Turing Test impersonation; cyclic mimic allegation; 
sexy silicon procreation -- watch your mind's free associations!

Maybe we're just syntax, but perhaps we have a soul.
That's the sole hole in my whole M.O. of controlling brainwork at my console.
Is my mind syntactic logic; reduce the Universe to symbolics?
Either way it doesn't matter; I can't model all details of matter.
So my system's just a model; best be complete 'cause only a lot'll do.

Making ontological assumptions takes a lot of gumption;
Are there universal primitives, such as event versus stative?
I think therefore I love; stupid is as stupid does.
Are these classes hard and sturdy?  There's nothing fuzzy 'bout my Furby.

Can we know about knowledge, R2D2?
Styx and Rolling Stones -- U2, me, too; 
"Know thyself" is my motto; 
thank you very mucho, Mr. Roboto.


Part IV  LOGIC  (disco)

Logic... ooooh, logic...

I've been thinking about thoughts so I know about knowledge.
I have a model of my mind on my mind; I learned it in college.
I decompose my thoughts and I rearrange ideas.
I'm a logically predisposed knowledge engineer.

A symbolic logical system serves an invaluable service:
It captures the epistemological semantics on purpose,
thus representing our mental model on our mind's behalf.
Ergo, ipso facto, a dog's a better pet than a giraffe.

Entailment formalizes what follows in the model with no doubt.
But logic is not concerned with figuring things out;
it leaves those details to what inference puts out.
The implemented inference algorithm finds what entailment's talking about.

Logical systems indulge me with the benefits of formalism,
so I ain't got no reason to not represent my reason with a rhythm.
There's a rhyme to my reason as I'm hacking through the night,
'cause my finger's on the pulse of logic, typing the right bytes.

There's a slew of logics, and you're welcome to make up your own.
They're all made of sentences to state what you know.
A sentence is valid if it's always true.
It's satisfiable in your model if its good enough for you.

I've got a proposition for you, if you don't mind my cognition.
Conjunction junction, what's your boolean function?
AND, OR, NOT, they help a lot to build a boolean expression,
these three operations combine for my propositional logic obsession.

Empower your representation with all the elements you can afford -
this pay's lipservice that the pen is mightier than the sword.
More power to you, in terms of functions and constants, states one's lip.
Now add quantifiers to enumerate; predicates start a new relationship.



Time and time again, I get to planning,
what it will be like when I am spanning,
networks that represent my maximally deducible set of constraints.

Is it too much work, oh oh oh oh?
For this to completely work, uh-oh, Big-O?
No, it's far more efficient 'cause situation calculus is really lame.

I've been passing time modeling temporal relations,
but I didn't understand UNTIL my Mac ran outta RAM.
This temporal relationship revealed its own intractability.


Part VI  INFERENCE (Classical/operatic)

The inference engine that you mentioned - it just won't start,
so I pick your brain, child; your ego is mild, but I'm left in the dark.
Your eerie, twisted grey matter just chatters away --
How the heck does that glob of gook figure out just what to say?

Inference, deduction, and logical application
apply a-priori rules to inputed facts for derivations.
Modus Ponens is the tool by which rules fire
which leads to new conclusions that are true or it's a liar.

I developed a logical proof theory in the previous verse.
But by the time I complete a proof I'll wind up in a herz.
To alleviate the branching factor, generalize Modus Ponens,
and use unification to match things up so you know where to stick your code in.

Now backward and forward chaining inference is sound but not complete,
but resolution kicks proverbial butt 'cause it is really sweet.

In the 70s they got a lot of knowledge engineering grant bucks.
But those were little toy problem -- the Vacuum World really sucks.
Can we emulate a human expert, or are our efforts just symbolic?
Well, you're a meta-expert if you understand these lyrics.
Put your money where your mouth is, 'cause the proof is in the pudding,
and your mouth is the logical place where that pudding should be put in.

Look, I'm trying to be reasonable about tractability,
'cause I know there's a tradeoff between expressiveness and efficiency.
Perhaps I need a theoretician and gifted software engineer.
Well, sing the "Sound of Music," 'cause Al Aho is here!
"On AI, play Al piano?" [a palindrome] You have it backwards, said he.
Strike that; reverse it -- that strikes a chord; on that note, don't skip a beat.
If you spell "it" backwards, you get ti, a drink with jam and bread.
But "fa" is a long long way to run your program, unless you're using your head.

Chorus reprise.

© 1999 Eric V. Siegel