Comments for Anima Ex Machina

Comment on On single and shortest axioms for Boolean logic by John Halleck

John Halleck — Thu, 29 Dec 2011 20:29:03 +0000

Opps… a English reference for Tarski’s claim is:

Alfred Tarski [1956] Logic, Semantics, Metamathematics, Papers from
1923 to 1938 (Translated by J. H. Woodger), Clarendon Press / Oxford UP,
Oxford UK 1956. (A second revised edition has been issued by J. Corcoran
(ed.), at Hackett Pub. Co., Indianapolis IN, in 19832 .)

Comment on On single and shortest axioms for Boolean logic by John Halleck

John Halleck — Thu, 29 Dec 2011 20:24:49 +0000

If you have an interest in single axioms for systems, you might be interested in Tarsi’s 1930 result, which is that if you have a logic defined by axioms, the rule of Modus Ponens, and the rule of Uniform Substitution, then is MUST have a single axiom basis if it can prove two specific theorems he gave.

Giving names to the theorems for discussion:
I: Cpp p -> p
K: CpCqp p -> (q -> p)
C: CCpCqrCqCpr (p -> (q -> r)) -> (q -> (p -> r))
D: CpCqCCpCqrr p -> (q -> ((p -> (q -> r)) -> r))
E: CpCqCCpCqrCsr p -> (q -> ((p -> (q -> r)) -> (s -> r)))
C*: CpCqCCpCqrr p -> (q -> ((p -> (q -> r)) -> r))

Tarski proved the theorems K + D and the theorems K + E insured the existence of a single axiom for the system.

Since then the provability of the following pairs proved the existence of a single axiom for the system.

K+C, K+C*, I+E

Comment on Towards a Web of One… by Frida

Frida — Sat, 26 Nov 2011 06:11:20 +0000

Muy interesante TED Talk. Qué curioso que en mi clase pasada tocábamos este problema. Desde mi perspectiva lo que debemos fomentar es un uso crítico de Internet y de las redes sociales. Los problemas continúan siendo los mismos, la tecnología mejora, pero necesitamos educarnos para su mejor empleo.

Comment on Is Faster Smarter? IBM’s Watson Search Engine Approach to Beat Humans by anima ex machina

anima ex machina — Fri, 15 Jul 2011 13:24:05 +0000

@Hector
the link to video is broken (FF v5, MAC OSX) ** is now fixed **

nota :
i like the name of this site !

cheers from France

Sebastien

Comment on Compression-based Investigation of Cellular Automata, A Phase Transition Coefficient and a Conjecture Related to Universal Computation by Hector Zenil

Hector Zenil — Thu, 14 Jul 2011 13:43:34 +0000

It would. If you capture the change of behavior by taking pictures of the system for long enough, you would see that the transition coefficient will make the derivative to fall into the new class.