Logic Syllabus • 3
• https://inquiryintoinquiry.com/logic-syllabus/

Logical Concepts
• https://oeis.org/wiki/Logic_Syllabus#Logical_concepts

Ampheck • https://oeis.org/wiki/Ampheck
Boolean Domain • https://oeis.org/wiki/Boolean_domain
Boolean Function • https://oeis.org/wiki/Boolean_function
Boolean-Valued Function • https://oeis.org/wiki/Boolean-valued_function
Differential Logic • https://oeis.org/wiki/Differential_logic
Logical Graph • https://oeis.org/wiki/Logical_Graphs
Minimal Negation Operator • https://oeis.org/wiki/Minimal_negation_operator
Multigrade Operator • https://oeis.org/wiki/Multigrade_operator
Parametric Operator • https://oeis.org/wiki/Parametric_operator
Peirce's Law • https://oeis.org/wiki/Peirce%27s_law
Propositional Calculus • https://oeis.org/wiki/Propositional_calculus
Sole Sufficient Operator • https://oeis.org/wiki/Sole_sufficient_operator
Truth Table • https://oeis.org/wiki/Truth_table
Universe of Discourse • https://oeis.org/wiki/Universe_of_discourse
Zeroth Order Logic • https://oeis.org/wiki/Zeroth_order_logic

#Logic #LogicSyllabus #Ampheck #BooleanDomain #BooleanFunction #BooleanValuedFunction
#DifferentialLogic #LogicalGraph #MinimalNegationOperator #MultigradeOperator
#ParametricOperator #PeircesLaw #PropositionalCalculus #SoleSufficientOperator
#TruthTable #UniverseOfDiscourse #ZerothOrderLogic

#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 two values, in other words, #IndicatorFunctions of the form \(f:X\to\mathbb{B},\) #SingularPropositions are those singling out the minimal distinct regions of the universe, represented by single cells of the corresponding #VennDiagram.

Related Subjects —
#Logic #LogicalGraphs #DifferentialLogic
#PropositionalCalculus #BooleanFunctions

#DifferentialPropositionalCalculus • 6.1
• https://inquiryintoinquiry.com/2020/03/02/differential-propositional-calculus-6/

In a #UniverseOfDiscourse based on 3 #BooleanVariables \(p, q, r\) there are \(2^3 = 8\) #PositivePropositions. Their #VennDiagrams are shown in Figure 9.

\(\text{Figure 9. Positive Propositions} : \mathbb{B}^3 \to \mathbb{B}\)
• https://inquiryintoinquiry.files.wordpress.com/2020/03/venn-diagrams-e280a2-p-q-r-e280a2-positive-propositions.jpg

#DifferentialPropositionalCalculus • 5.2
• https://inquiryintoinquiry.com/2020/02/29/differential-propositional-calculus-5/

In a #UniverseOfDiscourse based on 3 #BooleanVariables, \(p, q, r,\) the #LinearPropositions take the shapes shown in Figure 8.

\(\text{Figure 8. Linear Propositions} : \mathbb{B}^3 \to \mathbb{B}\)
• https://inquiryintoinquiry.files.wordpress.com/2020/02/venn-diagrams-e280a2-p-q-r-e280a2-linear-propositions.jpg

Related Subjects —
#Logic #LogicalGraphs #DifferentialLogic
#PropositionalCalculus #BooleanFunctions

#DifferentialPropositionalCalculus • 1.5
https://inquiryintoinquiry.com/2020/02/18/differential-propositional-calculus-1/

Figure 3. Back, To The Future
https://inquiryintoinquiry.files.wordpress.com/2020/02/differential-propositional-calculus-figure-3.jpg

Figure 3 preserves the initial #UniverseOfDiscourse \(X\) and extends the basis of discussion to a set of two qualities \(\{q, \mathrm{d}q\}.\) In corresponding fashion, the initial #PropositionalCalculus is extended by means of the #EnlargedAlphabet \(\{``𝑞", ``d𝑞"\}.\)

#DifferentialPropositionalCalculus • 1.3
https://inquiryintoinquiry.com/2020/02/18/differential-propositional-calculus-1/

Figure 1 represents a #UniverseOfDiscourse \(X\) together with a basis of discussion \(\{q\}\) for expressing propositions about the contents of that universe. Once the quality \(q\) is given a name, say, the symbol \(``q",\) we have the basis for a #FormalLanguage specifically cut out for discussing \(X\) in terms of \(q.\) This language is more formally known as the #PropositionalCalculus with #Alphabet \(\{``q"\}.\)

#DifferentialPropositionalCalculus • Overview
https://inquiryintoinquiry.com/2020/02/16/differential-propositional-calculus-overview/

By way of introduction to #DifferentialLogic, here begins a chapter on #DifferentialPropositionalCalculi, which augment #PropositionalCalculi with terms for describing aspects of change and difference, for example, processes taking place in a #UniverseOfDiscourse or #LogicalTransformations mapping a #SourceUniverse to a #TargetUniverse.

Applications —
#Cybernetics #SystemsTheory
#QualitativeDynamics
#DiscreteDynamics

#DifferentialPropositionalCalculus • 1 (cont.)
https://inquiryintoinquiry.com/2020/02/18/differential-propositional-calculus-1/

Figure 3. Back, To The Future
https://inquiryintoinquiry.files.wordpress.com/2020/02/differential-propositional-calculus-figure-3.jpg

Figure 3 preserves the initial #UniverseOfDiscourse \(X\) and extends the basis of discussion to a set of two qualities, \(\{q, \mathrm{d}q\}.\) In corresponding fashion, the initial #PropositionalCalculus is extended by means of the #EnlargedAlphabet, \(\{``q", ``\mathrm{d}q"\}.\)

#DifferentialPropositionalCalculus • 1 (cont.)
https://inquiryintoinquiry.com/2020/02/18/differential-propositional-calculus-1/

Figure 3. Back, To The Future
https://inquiryintoinquiry.files.wordpress.com/2020/02/differential-propositional-calculus-figure-3.jpg

Figure 3 preserves the initial #UniverseOfDiscourse \(X\) and extends the basis of discussion to a set of two qualities, \(\{q, \mathrm{d}q\}.\) In corresponding fashion, the initial #PropositionalCalculus is extended by means of the #EnlargedAlphabet, \(\{``q", ``\mathrm{d}q".\}\)

#DifferentialPropositionalCalculus • 1 (cont.)
https://inquiryintoinquiry.com/2020/02/18/differential-propositional-calculus-1/

Figure 1 represents a #UniverseOfDiscourse, \(X,\) together with a basis of discussion, \(\{q\},\) for expressing propositions about the contents of that universe. Once the quality \(q\) is given a name, say, the symbol \(``q",\) we have the basis for a #FormalLanguage specifically cut out for discussing \(X\) in terms of \(q.\) This language is more formally known as the #PropositionalCalculus with #Alphabet \(\{``q"\}.\)

#DifferentialPropositionalCalculus • 1 (cont.)
• https://wp.me/p24Ixw-4zs

Figure 1 represents a #UniverseOfDiscourse, \(X,\) together with a basis of discussion, \(\{q\},\) for expressing propositions about the contents of that universe. Once the quality \(q\) is given a name, say, the symbol \(``q",\) we have the basis for a #FormalLanguage specifically cut out for discussing \(X\) in terms of \(q.\) This language is more formally known as the #PropositionalCalculus with #Alphabet \(\{``q"\}.\)

#DifferentialPropositionalCalculus • 1 (cont.)
https://wp.me/p24Ixw-4GT

Figure 1 represents a #UniverseOfDiscourse, \(X,\) together with a basis of discussion, \(\{q\},\) for expressing propositions about the contents of that universe. Once the quality \(q\) is given a name, say, the symbol \(``q",\) we have the basis for a #FormalLanguage specifically cut out for discussing \(X\) in terms of \(q.\) This language is more formally known as the #PropositionalCalculus with #Alphabet \(\{``q"\}.\)

#DifferentialPropositionalCalculus • #Overview

• https://inquiryintoinquiry.com/2020/02/16/differential-propositional-calculus-overview/

By way of introduction to #DifferentialLogic, here begins a chapter on #DifferentialPropositionalCalculi, which augment #PropositionalCalculi with terms for describing aspects of change and difference, for example, processes taking place in a #UniverseOfDiscourse or #LogicalTransformations mapping a #SourceUniverse to a #TargetUniverse.

Applications —
#Cybernetics #SystemsTheory
#QualitativeDynamics
#DiscreteDynamics