#singularpropositions — Public Fediverse posts

#DifferentialPropositionalCalculus • 7.3
• https://inquiryintoinquiry.com/2020/03/05/differential-propositional-calculus-7/

Figure 10. #VennDiagrams for #SingularPropositions on 3 Variables
• https://inquiryintoinquiry.files.wordpress.com/2020/03/venn-diagrams-e280a2-p-q-r-e280a2-singular-propositions.jpg

Rank 3. The cell \(pqr.\)

Rank 2. The 3 cells \(pr\texttt{(}q\texttt{)}, qr\texttt{(}p\texttt{)}, pq\texttt{(}r\texttt{)}.\)

Rank 1. The 3 cells \(q\texttt{(}p\texttt{)(}r\texttt{)}, p\texttt{(}q\texttt{)(}r\texttt{)}, r\texttt{(}p\texttt{)(}q\texttt{)}.\)

Rank 0. The cell \(\texttt{(}p\texttt{)(}q\texttt{)(}r\texttt{)}.\)

#Logic

#DifferentialPropositionalCalculus • 7.2
• https://inquiryintoinquiry.com/2020/03/05/differential-propositional-calculus-7/

In a #UniverseOfDiscourse based on 3 #BooleanVariables \(p,q,r\) there are \(2^3=8\) #SingularPropositions. Their #VennDiagrams are shown in Figure 10.

\(\text{Figure 10. Singular Propositions} : \mathbb{B}^3 \to\mathbb{B}\)
• https://inquiryintoinquiry.files.wordpress.com/2020/03/venn-diagrams-e280a2-p-q-r-e280a2-singular-propositions.jpg

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

#DifferentialPropositionalCalculus • 7.1
• https://inquiryintoinquiry.com/2020/03/05/differential-propositional-calculus-7/

The #SingularPropositions \(\{\mathbf{x}:\mathbb{B}^n\to\mathbb{B}\}=(\mathbb{B}^n\xrightarrow{s}\mathbb{B})\) may be written as products:

\[\prod_{i=1}^n e_i~=~e_1 \cdot\ldots\cdot e_n~\text{where}~\left\{\begin{matrix}e_i=a_i\\ \text{or}\\ e_i=\texttt{(}a_i\texttt{)}\end{matrix}\right\}~\text{for}~i=1~\text{to}~n.\]

#Logic #LogicalGraphs #DifferentialLogic
#PropositionalCalculus #BooleanFunctions
#MinimalNegationOperators

#DifferentialPropositionalCalculus • 7
• https://inquiryintoinquiry.com/2020/03/05/differential-propositional-calculus-7/

In our #Model of #Propositions as #Mappings of a #UniverseOfDiscourse to a set of 2 values, in other words, #IndicatorFunctions of the form \(f:X\to\mathbb{B},\) #SingularPropositions are those singling out the #MinimalDistinctRegions of the universe, represented by single cells of the corresponding #VennDiagram.

#Logic #LogicalGraphs #DifferentialLogic
#PropositionalCalculus #BooleanFunctions
#ModelTheory #ProofTheory #Semiotics

#DifferentialPropositionalCalculus • 7
• https://inquiryintoinquiry.com/2020/03/05/differential-propositional-calculus-7/

In our #Model of #Propositions as #Mappings of a #UniverseOfDiscourse to a set of 2 values, in other words, #IndicatorFunctions of the form \(f:X\to\mathbb{B},\) #SingularPropositions are those singling out the #MinimalDistinctRegions of the universe, represented by single cells of the corresponding #VennDiagram.

#Logic #LogicalGraphs #DifferentialLogic
#PropositionalCalculus #BooleanFunctions
#ModelTheory #ProofTheory #Semiotics

#DifferentialPropositionalCalculus • 7
• https://inquiryintoinquiry.com/2020/03/05/differential-propositional-calculus-7/

In our #Model of #Propositions as #Mappings of a #UniverseOfDiscourse to a set of 2 values, in other words, #IndicatorFunctions of the form \(f:X\to\mathbb{B},\) #SingularPropositions are those singling out the #MinimalDistinctRegions of the universe, represented by single cells of the corresponding #VennDiagram.

#Logic #LogicalGraphs #DifferentialLogic
#PropositionalCalculus #BooleanFunctions
#ModelTheory #ProofTheory #Semiotics