Formal Development (cont.)

Before moving on, let’s unpack some of the assumptions, conventions, and implications involved in the array of concepts and notations introduced above.

A universe of discourse qualified by the logical features is a set plus the set of all functions from the space to the boolean domain   There are elements in often pictured as the cells of a venn diagram or the nodes of a hypercube.  There are possible functions from to accordingly pictured as all the ways of painting the cells of a venn diagram or the nodes of a hypercube with a palette of two colors.

A logical proposition about the elements of is either true or false of each element in while a function evaluates to or on each element of   The analogy between logical propositions and boolean-valued functions is close enough to adopt the latter as models of the former and simply refer to the functions as propositions about the elements of

Resources

• Logic Syllabus
• Differential Logic and Dynamic Systems
• Functional Conception of Propositional Calculus
• Qualitative Logic and Quantitative Analogy
• Formal Terms and Flexible Types

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