Differential Logic, Dynamic Systems, Tangent Functors • Discussion 6

Re: Systems ScienceJS

A few of my readers are racing well ahead of me, exploring a range of different roads, but I’ll be making a dogged effort to stick to my math-bio-graphical narrative this time around, and try to tell how I came to climb down from logical trees and learned to love logical cacti.

As far as the logical ballpark goes, this is all just classical propositional logic, what my old circle used to call “zeroth order logic”, alluding to its basemental status for every storey built on it.  (But I have since found that others use that term for other things, so usage varies as it usually does.)

When it comes to semantics, the class of formal or mathematical objects residing among the referents of our propositional signs, I’m content for most purposes to say they’re all the same, namely, Boolean functions of abstract type f : \mathbb{B}^k \to \mathbb{B}, where \mathbb{B} = \{ 0, 1 \} and k is a non-negative integer.  Although we’re likely to have other sorts of meanings in mind, this class of models suffices for a ready check on logical consistency and serves us well, especially in practical applications.

The upshot is — I’m aiming for innovation solely in the syntactic sphere, the end being only to discover/invent a better syntax for the same realm of logical objects.

To be continued …

Resources

cc: Structural ModelingOntolog ForumLaws of FormCybernetics

This entry was posted in Amphecks, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamical Systems, Dynamical Systems, Graph Theory, Hill Climbing, Hologrammautomaton, Information Theory, Inquiry Driven Systems, Intelligent Systems, Knowledge Representation, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Systems, Visualization and tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , . Bookmark the permalink.

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