In my life, I have spent many hundreds of hours defining new languages, logics, and even maths in an attempt to get something which would allow me to perform specific untractable problems. My common focus was on making systems which could be executed by computer, with a few very notable exceptions.
It is not overstatement to say I have made literally hundreds of new almost-languages, almost-logics, and/or almost-maths. But these are invariably incomplete, largely because I'm not nearly as smart as I think I am.
Two things fascinate me when it comes to these things, and most of my systems deal with either one, the other, or both. The first thing which fascinates me is patterns. Pattern recognition on any meaningful level is almost impossible for anything which isn't a biological brain. It's probably almost impossible for a biological brain, too, but we just through a lot of firepower at it. Many times, I've tried to come up with a language which either contains or explains patterns such that it is, in itself, the pattern recognition system. No luck as of yet.
The other thing which fascinates me is logical fallacies. There are some really bizarre tidbits out there - chinks in the armor of math and logic which reveal that the whole thing is just crazy-glued together. The easiest example would be simple paradox, something like "this sentence is false". I'm not sure if anyone has come up with a useful system in which such things can be said without causing logical fault. I've never seen one outside of my own extremely limited attempts.
My early attempts were what I call "linear" attempts. They were unable to reference "backwards", including themselves. While this did eliminate most of the paradoxes, it was totally unsuitable for... well, anything. Unfortunately, later attempts to make nonlinear systems have been largely unsuccessful. My only successes on this front have been related to forced uncertainty and partitioning. Which are moderately interesting - I might go into them at some point, especially partitioning - but they don't really allow for useful pattern recognition. They also have many of the same logic holes that common languages and maths do, although they solve certain problems and allow for some pretty interesting computer-driven analysis.
My most recent attempt is the self-modifying logic set, which is really just an upgraded version of the uncertainty ideas I had. It occurred to me as I was writing self-modifying PHP that there was no real reason to keep statements set in stone - the only reason we think like that is because of the prevalence of the written word. Assuming I don't come back and change this paragraph, it will always be the same, regardless of who reads it. But that's not really the case, and that's not really something that needs to be kept.
For example, if I say "nuns are evil", people will interpret that in many different ways, depending on their various religious ideals and what they think of me. The language doesn't matter at all. I could say "la nunna es loco", or whatever it actually is in whatever language I'm butchering, and I would get largely the same response, albeit from a whole bunch of people whose commentary I can't understand.
Originally, I just assumed that was a glitch in the actual grammatical rules inherent in romance languages. Having looked into many decidedly unromantic languages, all their grammatical rules allow for the exact same flaws. Obviously, if no language, logic, or math has as of yet varied even a SMIDGE as to which kinds of flaws it allows, it's a bit unlikely I can create something which solves these problems working from the same basis.
What I want is a language PROCESSING algorithm - something like the strip of fat in our heads that is telling you that I'm talking about brains when I say "the strip of fat in our heads".
Unfortunately, I've been there, too. If you wish to picture that field in your head, it looks a lot like a popular sporting event right after the home team wins the big game. Well, it looks like that if you also light the stadium on FIRE.
There's literally thousands of brilliant people - and tens of thousands of not-so-brilliant people - working on that problem. Some call themselves computer scientists, some call themselves "cog sci", some call themselves space cowboys. They all share one thing: a deep frustration at their continued abject failure.
Which, I'm sure you'll agree, does not bode well for our hero's chances should he enter such a place.
Meh. Onward! Fat will fry!