Theme One Program • Exposition 7

Mathematical Structure and Logical Interpretation

The main things to take away from the previous post are the following two ideas, one syntactic and one semantic.

  • The compositional structures of cactus graphs and cactus expressions are constructed from two kinds of connective operations.
  • There are two ways of mapping these compositional structures into the compositional structures of propositional sentences.

The two kinds of connective operations are described as follows.

  • The node connective joins a number of component cacti C_1, \ldots, C_k to a node:

Node Connective

  • The lobe connective joins a number of component cacti C_1, \ldots, C_k to a lobe:

Lobe Connective

The two ways of mapping cactus structures to logical meanings are summarized in Table 3, which compares the entitative and existential interpretations of the basic cactus structures, in effect, the graphical constants and connectives.

\text{Table 3. Logical Interpretations of Cactus Structures}
Logical Interpretations of Cactus Structures


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This entry was posted in Algorithms, Animata, Artificial Intelligence, Boolean Functions, C.S. Peirce, Cactus Graphs, Cognition, Computation, Constraint Satisfaction Problems, Data Structures, Differential Logic, Equational Inference, Formal Languages, Graph Theory, Inquiry Driven Systems, Laws of Form, Learning Theory, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Semiotics, Spencer Brown, Visualization and tagged , , , , , , , , , , , , , , , , , , , , , , , , , , . Bookmark the permalink.

1 Response to Theme One Program • Exposition 7

  1. Pingback: Survey of Theme One Program • 4 | Inquiry Into Inquiry

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