Differential Logic, Dynamic Systems, Tangent Functors • Discussion 7

Re: Systems ScienceJS

Let’s stand back from the picture and see how the dimensions of syntax, semantics, and pragmatics look from a pragmatic semiotic or sign relational perspective.

O is an object domain, a set of elements under view in a given discussion.  Depending on the application we might be calling it a universe of discourse, a population, a sample space, a state space, or any number of other things.

S and I are sets of signs related to O by means of a triadic relation, L \subseteq O \times S \times I.  If the triadic relation L satisfies a set of conditions set down in a definition of a sign relation then we say L is a sign relation.

Peirce’s best definitions of a sign relation are pretty minimal in what they demand and cover a wide range of cases from barely formed to highly structured.

Let’s move on to the more structured types of sign relations forming our ultimate practical interest.

In a typical case like that, S is a formal language defined by a formal grammar.

Generally speaking, we might think of I as being more loosely defined in its own right but when it comes to formal investigations the so-called interpretant sign domain I will also be a formal language.  Here the cases divide into two broad sorts.

  • (S = I).  We use this case to discuss transitions in time from one sign to the next.
  • (S \ne I).  We use this case to discuss translations from one language to another.

To be continued …


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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