#DifferentialPropositionalCalculus • 4.10
• https://inquiryintoinquiry.com/2020/02/25/differential-propositional-calculus-4/

The #BasicPropositions \(a_i : \mathbb{B}^n \to \mathbb{B}\) are both linear and positive. So those two families of propositions, the linear & the positive, may be viewed as two different ways of generalizing the class of basic propositions.

Related Subjects —

#CoordinatePropositions #SimplePropositions
#LinearPropositions #SingularPropositions

#Logic #LogicalGraphs #DifferentialLogic
#PropositionalCalculus #BooleanFunctions

#DifferentialPropositionalCalculus • 4.9
• https://inquiryintoinquiry.com/2020/02/25/differential-propositional-calculus-4/

In each family the rank \(k\) ranges from \(0\) to \(n\) and counts the number of positive appearances of #CoordinatePropositions \(a_1, \ldots, a_n\) in the resulting expression. For example, when \(n=3\) the #LinearProposition of rank \(0\) is \(0,\) the #PositiveProposition of rank \(0\) is \(1,\) and the #SingularProposition of rank \(0\) is \(\texttt{(}a_1\texttt{)} \texttt{(}a_2\texttt{)} \texttt{(}a_3\texttt{)}.\)

#Logic

#DifferentialPropositionalCalculus • 4.3
• https://inquiryintoinquiry.com/2020/02/25/differential-propositional-calculus-4/

The full set of propositions \(f : A \to \mathbb{B}\) contains a number of smaller classes deserving of special attention.

A #BasicProposition in the universe of discourse \([a_1, \ldots, a_n]\) is one of the propositions in the set \(\{a_1, \ldots, a_n\}.\) There are of course exactly \(n\) of these. Depending on the context, #BasicPropositions may also be called #CoordinatePropositions or #SimplePropositions.

#LogicalGraphs