(7) The (Logic) Truth is out
there,
Mauldner: in front of your eyes! ;-)
Remember
“Carnaugh maps”, and other methods of “Boolean minimisation” for designing more
efficient Digital Circuitry? Well, “Multiple Form
Logic™” appears to get similar results with much less effort. How
much? Well, this episode (of X-files?) needs further investigation.
However, by running the program, it is easy to see at
once, some visible benefits. (It is hard to deny you’re facing an elephant, when you see him!)
Some of my most hilarious memories from “Computer Science
Education” are those rainy (Essex, UK) days when we were taught Logic and
I asked for our lecturers' permission to demonstrate quite shorter proofs of the same formulae. I would
transliterate them first into Multiple Form Logic™, simplify them in a
couple of lines, and then translate them back into Propositional Logic.
(Some lecturers loved it; others hated it).
It has now
become possible for you to do the same thing automatically, by using
this program, which is public domain, intended
for general distribution through the Internet.
Use it freely, to impress your lecturers, if you are a student learning Logic.
Use it to change opinions, about good old Propositional
Calculus: - It is an old seedy house full of
junk, in need of renovation!
(8) What about Predicate Calculus?
It still remains to be seen, if the
methods of “Multiple Form Logic™” reduce
the computational effort required for Predicate Calculus, equally well.
In my old hand-written notes (recently re-discovered inside some old
dossiers) it appears that about fifteen years ago I had managed to model Predicate Calculus in Multiple Form
Logic™, by making the assumption that Predication is a specialised form of Implication or
Generalisation, i.e. P(x) was interpreted as “x -> P” (together with
certain other formal assumptions). I am in the process of checking
through the validity of these old notes, now, and will keep readers informed, after this material is checked thoroughly. Back in 1983/84, I embarked on a self-educational
journey about the Foundations of Logic and Predicate Calculus. Later on,
my attention shifted to automatic theorem
proving, while Axiomatic Logic slowly became a secondary issue.
I realised that if we bring Predicates and Existential Quantifiers inside Multiple Form Logic™, to create practical theorem proving software, such
extensions can cause some difficulties: It was like bringing “real” Existential
or Universal Quantifiers, as built-in predicates, inside a PROLOG
compiler. (Most Prolog compilers are not made this way, for reasons of
efficiency). Meanwhile, I could not find a set of Predicate Calculus
Axioms which could be consistent with “everything else” (in the Universe, which
is... 42, ;-) etc.) So in 1992 I stopped this (profit-less) quest and started
doing (to earn a living) something else: dictionary software development. At that time, I believed we could
apply Multiple Forms to boost up the speed of Logic Inferences in PROLOG compilers.
I still believe this, even though an e-friend (Dave Keenan) has spent years trying to apply
"Boundary Logic" to "self-designing logic circuits", with
no apparent success in the end, despite overwhelming evidence to the contrary.
I am not sure what will happen when we "model" things like Prolog Unifications in Multiple Form Logic™, but have a strong
feeling that only good things can
happen. After all, a full-blown Predicate Logic in light
Multiple-Form clothing, was my favourite
recursive dream, unfulfilled due to other duties for a long
time! It's time to make the dream come true.
<soapbox: ON>
Meanwhile, my old notes (literally thousands) remain
buried in dusty old dossiers. Unlike
dolphins, we (humans) misuse Reason and Logic,
to destroy each other’s minds or (e.g.) to mystify further our
(already mystified) Alien Babies, ex-Atlanteans etc., ;-) who become the grown-up Students of Earthling-Science.
However, Logic I.M.H.O. is not just about "true" and
"false". It’s about the Mind's ability for remarkable feats,
as constellations of Multiple Forms… “...drawn in
a world where initially boundaries can be drawn in any way we please, and where
the universe - at this phase - seems like sifting sand beneath our feet"
(quoting George Spencer-Brown, from "Laws of Form").
<soapbox:
OFF>
next
section 
So, where
does the "efficiency" of Multiple Forms come from?
previous
section 
How to
download and run the Prolog Theorem-Proving Program