Factasia Home Pagecomputing

Overview:

A rather logic oriented selection of topics related to computing.
Artificial Intelligence
There must be a pretty good chance that AI really will happen in the 21st Century. Factasia wants a piece of the action.
formal maths
The logical techniques for fully formal mathematics have been known for a century. Putting them into practice is still a challenge; a software engineering challenge.
Mechanisation of Mathematics
A short story about the mechanisation of mathematics. Its primary purpose is speculation about what could be done, and how, but there's a bit of background material about what has been done.
The Global SuperBrain
A megaproject involving lots of information technology.

Artificial Intelligence
There must be a pretty good chance that AI really will happen in the 21st Century. Factasia wants a piece of the action.
What is Intelligence?
By a way of clarifying the scope of the field and identifying the particular interests of Factasia, we seek a definition of intelligence which is not homo-centric.
Philosophy There are many rich connections between philosophy and AI, particularly between analytic philosophy and logical AI.
The Global Superbrain This extravagent label covers Factasia's interest in the AI project of the (next!) millenium. The world transformed by the evolution of intelligence in cyberspace.
Automation of Deduction Automation of deductive reasoning is the subdomain of AI of greatest interest to Factasia. Crystal clear problems, widespread applications.
Mechanisation of Mathematics Mathematics provides the most complex applications of deductive reasoning and is therefore a testbed for the automation of reasoning. Here we consider the transition from powerful but non-intelligent programs to intelligent mechanised mathematics.
Topography
AI topography
Factasia's architecture for AI places pure logic at the centre of it all.
formal maths
The logical techniques for fully formal mathematics have been known for a century. Putting them into practice is still a challenge; a software engineering challenge.
Background and Motivation
Leibniz dreamed of mechanising reason and mathematics but didn't have the wherewithall. Lots of people still want to do it, and think logic, computers and a bit of graft will do the trick.
Formal Foundations
This whole enterprise depends upon the fact that mathematics can be reduced to logic. So you need to know what a formal logical foundation system is.
Developing Formal Maths
A first goal is to be able to productively develop mathematical theories, in collusion with computers, with all theorems and proofs formal and machine checked.
Applying Formal Maths
A more ambitious (and maybe more profitable) goal is to exploit the formal methods to get computers which are good at applied mathematics.

Mechanisation of Mathematics
A short story about the mechanisation of mathematics. Its primary purpose is speculation about what could be done, and how, but there's a bit of background material about what has been done.

Numeric/Symbolic/Logical
paradigms
The discussion hangs around three paradigms for mathematical software, numeric, symbolic and logical. The first two are already mature, the third is speculative. Each of these paradigms more or less subsumes the previous one, in terms of its capabilities, with a couple of exceptional aspects which we will mention, both connected with rigour.
logical power
When it comes to the logical paradigm, I want to distinguish two levels of capability. I associate these with the terms engineering logic and intelligent logic. The second is what you get if you manage (in this restricted logical domain) to crack the machine intelligence problem. I consider how to do engineering logic in a way which is sympathetic to, but independent of, intelligent logic.

The Global SuperBrain
A megaproject involving lots of information technology.
1. Conceptions
First we look at some of the varied conceptions of the Global Brain elsewhere on the internet.
2. Dimensions
Then we analyse some of the dimensions of variation in these different conceptions of the Global Brain, and begin to position Factasia.
3. Cogitations
Next we have a serious think, integrate the Global SuperBrain into the Factasia philosophical worldview, and identify two quite different superbrain projects for Factasia to run with.
The Holistic Superbrain
The idea of a "control system" is taken from cybernetics and applied on the global scale to the problem of realising a better world.
The Analytic Superbrain
The Global SuperBrain as Hyper-Rational Artificial Intelligence. An intelligent automation of the entire field of a priori knowledge, including mathematics and its applications in science and engineering.

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