A New Kind of Science: The NKS Forum > Pure NKS > Simple Symbolic Systems
Author
Fred Meinberg
Wolfram Science Group

Registered: Sep 2003
Posts: 5

Simple Symbolic Systems

Symbolic systems are rule-based systems of the form
Nest[# /. lhs -> rhs &, init, steps] where the lhs is an expression like e[x_][y_] and the rhs something like
x[x[y]]. Initial conditions (init) are like e[e][e[e[e]e]e[e]

These systems can present considerable complexity, but they are different from Cellular Automata in the sense that they evolve in a largely non-local way.

For symbolic systems, see NKS 102-104 and 896-898, and NKS Open Problems(.pdf), pp. 26-27

The so called SK-combinators invented by SchÃ¶nfinkel are an example of symbolic system with two rules. SK-combinators are capable of universal computation. For details, check NKS 711-714 and 1121-1123.

Last edited by Fred Meinberg on 04-21-2004 at 01:01 AM

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09-29-2003 05:49 PM
Jon Awbrey

Registered: Feb 2004
Posts: 551

Combinatory Logic, Propositions As Types

Fred,

I don't know if you're still around, but I have
some interest in this subject, especially as it
relates to the "propositions as types" (PAT)
analogy and the question of whether there
is a PAT analogy for classical logic.

Jon Awbrey

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02-26-2004 07:58 PM
Fred Meinberg
Wolfram Science Group

Registered: Sep 2003
Posts: 5

Jon,

Symbolic systems generalize combinators (what I did in the NKS SS 2003, and will present at NKS 2004, is basically running one-combinator systems with different rules, different initial conditions, and different evaluation schemes.) So, if combinators are relevant for the PAT question, symbolic systems will be.

Fred Meinberg

Last edited by Fred Meinberg on 06-19-2004 at 12:53 PM

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03-27-2004 08:05 AM

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