#basicpropositions — Public Fediverse posts

#DifferentialPropositionalCalculus • 5.5
• https://inquiryintoinquiry.com/2020/02/29/differential-propositional-calculus-5/

The third row of Figure 8 shows #VennDiagrams for the 3 #LinearPropositions of rank 1, which are none other than the 3 #BasicPropositions, \(p, q, r.\)

For example —

\(\text{Figure 8.3. Venn Diagram for}~p\)
• https://inquiryintoinquiry.files.wordpress.com/2020/02/venn-diagram-e280a2-p-q-r-e280a2-p.jpg

Related Subjects —
#Logic #LogicalGraphs #DifferentialLogic
#PropositionalCalculus #BooleanFunctions
#CactusSyntax #MinimalNegationOperators
#DiscreteDynamics #QualitativeDynamics

#DifferentialPropositionalCalculus • 4.11
• https://inquiryintoinquiry.com/2020/02/25/differential-propositional-calculus-4/

Linearity, Positivity, Singularity are relative to the basis \(\mathcal{A}.\) #SingularPropositions on one basis do not remain so if new features are added to the basis. #BasisChanges even within the same pairwise options \(\{a_i\}\cup\{\texttt{(}a_i\texttt{)}\}\) change the sets of #LinearPropositions and #PositivePropositions. Both are fixed by the choice of #BasicPropositions which amounts to taking a cell as origin.

#Logic

#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