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**Semantics for Thinking Notation** can be constructed from two syntactically valid Thinking Notion *streams of thought* (or, *thinking sequences*).

Deriving the semantics for Boolean Algebra from Thinking Notions is a straightforward affair. We can compare two *thinking sequences* (henceforth, *sequences*) and evaluate them as True or False if they are identical or not.

Using the *Grouping* syntax specified previously, we can also construct the necessary resources for the semantics of Predicate Calculus.

We can also substitute the traditional First Order syntax as needed (by associating constants, variables, and quantifiers with items in a *thinking sequence*).

*Sequences* of *sequences* can also be formed.

This can be used to represent familiar model-theoretic *model classes* or sets of *interpretations*.

Naturally, *sequences* of *sequences* can be used to construct *dimensional* and *higher-dimensional* logics.

##### post: 11/26/2019

##### update: 4/2/2020