TY - GEN
ID - cogprints9209
UR - http://cogprints.org/9209/
A1 - Casares, Ramón
TI - Resolution Machinery
Y1 - 2014/02/24/
N2 - The value of syntax is controversial:
some see syntax as defining us as species,
while for others it just facilitates communication.
To assess syntax
we investigate its relation to problem resolving.
First we define a problem theory from first principles,
and then we translate the theory concepts to mathematics,
obtaining the requirements
that every resolution machine has to implement.
Such a resolution machine will be able to
execute any possible resolution, that is,
any possible way of taking a problem expression
and computing the problem solutions.
Two main requirements are found:
1) syntax is needed to express problems,
that is, separate words are not enough, and
2) the resolution machine has to be as powerful
as lambda calculus is, that is,
it has to be Turing complete.
Noting that every device that can generate
any possible syntax, that is,
any possible syntactically correct sentence
of any possible, natural or artificial, language,
has to be Turing complete,
we conclude that syntax and problem resolving
can use the same components, as, for example,
sentences, functions, and conditionals.
The implication to human evolution is that
syntax and problem resolving should have
co-evolved in humans towards Turing completeness.
AV - public
KW - syntax evolution
KW - problem resolving
KW - Turing completeness
ER -