#logicsyllabus — Public Fediverse posts

Logic Syllabus • Discussion 1
• https://inquiryintoinquiry.com/2023/06/02/logic-syllabus-discussion-1/

Re: Logic Syllabus ( https://inquiryintoinquiry.com/logic-syllabus/ )
Re: Laws of Form ( https://groups.io/g/lawsofform/topic/logic_syllabus/99218507 )
Re: John Mingers ( https://groups.io/g/lawsofform/message/2326 )

JM: ❝In a previous post you mentioned the minimal negation operator. Is there also the converse of this, i.e. an operator which is true when exactly one of its arguments is true? Or is this just XOR?❞

Yes, the “just one true” operator is a very handy tool. We discussed it earlier under the headings of “genus and species relations” or “radio button logic”. Viewed in the form of a venn diagram it describes a partition of the universe of discourse into mutually exclusive and exhaustive regions.

Reading \(\texttt{(} x_1 \texttt{,} \ldots \texttt{,} x_m \texttt{)}\) to mean just one of \(x_1, \ldots, x_m\) is false, the form \(\texttt{((} x_1 \texttt{),} \ldots \texttt{,(} x_m \texttt{))}\) means just one of \(x_1, \ldots, x_m\) is true.

For two logical variables, though, the cases “condense” or “degenerate” and saying “just one true” is the same thing as saying “just one false”.

\[\texttt{((} x_1 \texttt{),(} x_2 \texttt{))} = \texttt{(} x_1 \texttt{,} x_2 \texttt{)} = x_1 + x_2 = \mathrm{xor} (x_1, x_2).\]

There's more information on the following pages.

Minimal Negation Operators
• https://oeis.org/wiki/Minimal_negation_operator

Related Truth Tables
• https://oeis.org/wiki/Minimal_negation_operator#Truth_tables

Genus, Species, Pie Charts, Radio Buttons
• https://inquiryintoinquiry.com/2021/11/10/genus-species-pie-charts-radio-buttons-1/

Related Discussions
• https://inquiryintoinquiry.com/?s=Radio+Buttons

#Logic #LogicSyllabus #BooleanDomain #BooleanFunction #BooleanValuedFunction
#Peirce #LogicalGraph #MinimalNegationOperator #ExclusiveDisjunction #XOR
#CactusLanguage #PropositionalCalculus #RadioButtonLogic #TruthTable

Logic Syllabus • 5
• https://inquiryintoinquiry.com/logic-syllabus/

Related Articles
• https://oeis.org/wiki/Logic_Syllabus#Related_articles

Cactus Language • https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Overview
Futures Of Logical Graphs • https://oeis.org/wiki/Futures_Of_Logical_Graphs
Differential Propositional Calculus • https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Overview
Differential Logic • https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Overview
Differential Logic and Dynamic Systems • https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Overview
Propositions As Types Analogy • https://oeis.org/wiki/Propositions_As_Types_Analogy
Propositional Equation Reasoning Systems • https://oeis.org/wiki/Propositional_Equation_Reasoning_Systems
Prospects for Inquiry Driven Systems • https://oeis.org/wiki/User:Jon_Awbrey/Prospects_for_Inquiry_Driven_Systems
Introduction to Inquiry Driven Systems • https://oeis.org/wiki/Introduction_to_Inquiry_Driven_Systems
Inquiry Driven Systems • Inquiry Into Inquiry • https://oeis.org/wiki/Inquiry_Driven_Systems_%E2%80%A2_Overview

#Logic #LogicSyllabus #CactusLanguage #LogicalGraphs #DifferentialLogic
#DifferentialPropositionalCalculus #DifferentialLogicAndDynamicSystems
#PropositionsAsTypesAnalogy #PropositionalEquationReasoningSystems
#Inquiry #InquiryDrivenSystems #InquiryIntoInquiry #DynamicalSystems

Logic Syllabus • 4
• https://inquiryintoinquiry.com/logic-syllabus/

Relational Concepts
• https://oeis.org/wiki/Logic_Syllabus#Relational_concepts

Continuous Predicate • https://oeis.org/wiki/Continuous_predicate
Hypostatic Abstraction • https://oeis.org/wiki/Hypostatic_abstraction
Logic of Relatives • https://oeis.org/wiki/Logic_of_relatives
Logical Matrix • https://oeis.org/wiki/Logical_matrix
Relation • https://oeis.org/wiki/Relation
Relation Composition • https://oeis.org/wiki/Relation_composition
Relation Construction • https://oeis.org/wiki/Relation_construction
Relation Reduction • https://oeis.org/wiki/Relation_reduction
Relation Theory • https://oeis.org/wiki/Relation_theory
Relative Term • https://oeis.org/wiki/Relative_term
Sign Relation • https://oeis.org/wiki/Sign_relation
Triadic Relation • https://oeis.org/wiki/Triadic_relation

#Logic #LogicSyllabus #ContinuousPredicate #HypostaticAbstraction #LogicOfRelatives
#LogicalMatrix #Relation #RelationComposition #RelationConstruction #RelationReduction
#RelationTheory #RelativeTerm #SignRelation #TriadicRelation

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

Logic Syllabus • 2
• https://inquiryintoinquiry.com/logic-syllabus/

Logical Operators
• https://oeis.org/wiki/Logic_Syllabus#Logical_operators

Logical Negation • https://oeis.org/wiki/Logical_negation
Logical NAND • https://oeis.org/wiki/Logical_NAND
Logical NNOR • https://oeis.org/wiki/Logical_NNOR
Logical Conjunction • https://oeis.org/wiki/Logical_conjunction
Logical Disjunction • https://oeis.org/wiki/Logical_disjunction
Exclusive Disjunction • https://oeis.org/wiki/Exclusive_disjunction
Logical Implication • https://oeis.org/wiki/Logical_implication
Logical Equality • https://oeis.org/wiki/Logical_equality

#Logic #LogicSyllabus #LogicalOperator #LogicalConnective
#Negation #NAND #NNOR #LogicalConjunction #LogicalDisjunction
#ExclusiveDisjunction #XOR #LogicalImplication #LogicalEquality

#LogicSyllabus
• https://inquiryintoinquiry.com/logic-syllabus/

This page serves as a focal node for a collection of related resources.

#Logic #LogicalOperators

#LogicalConjunction #LogicalDisjunction
#ExclusiveDisjunction #LogicalEquality
#LogicalImplication #LogicalNegation
#LogicalNAND #LogicalNNOR

#LogicalConcepts

#Ampheck #SoleSufficientOperator
#BooleanDomain #UniverseOfDiscourse
#LogicalGraph #PropositionalCalculus
#MinimalNegationOperator #TruthTable
#BooleanFunction #BooleanValuedFunction