Functional Logic • Inquiry and Analogy • Preliminaries
• https://inquiryintoinquiry.com/2023/06/20/functional-logic-inquiry-and-analogy-preliminaries-2/

Functional Logic • Inquiry and Analogy
• https://oeis.org/wiki/Functional_Logic_%E2%80%A2_Inquiry_and_Analogy

This report discusses C.S. Peirce's treatment of analogy, placing it in relation to his overall theory of inquiry. We begin by introducing three basic types of reasoning Peirce adopted from classical logic. In Peirce's analysis both inquiry and analogy are complex programs of logical inference which develop through stages of these three types, though normally in different orders.

Note on notation. The discussion to follow uses logical conjunctions, expressed in the form of concatenated tuples \(e_1 \ldots e_k,\) and minimal negation operations, expressed in the form of bracketed tuples \(\texttt{(} e_1 \texttt{,} \ldots \texttt{,} e_k \texttt{)},\) as the principal expression-forming operations of a calculus for boolean-valued functions, that is, for propositions. The expressions of this calculus parse into data structures whose underlying graphs are called “cacti” by graph theorists. Hence the name “cactus language” for this dialect of propositional calculus.

Resources —

Logic Syllabus
• https://oeis.org/wiki/Logic_Syllabus

Boolean Function
• https://oeis.org/wiki/Boolean_function

Boolean-Valued Function
• https://oeis.org/wiki/Boolean-valued_function

Logical Conjunction
• https://oeis.org/wiki/Logical_conjunction

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

#Peirce #Logic #Abduction #Deduction #Induction #Analogy #Inquiry
#BooleanFunction #LogicalConjunction #MinimalNegationOperator
#LogicalGraph #CactusLanguage #PropositionalCalculus

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

#DifferentialPropositionalCalculus • 6.2
• https://inquiryintoinquiry.com/2020/03/02/differential-propositional-calculus-6/

Figure 9. #VennDiagrams for #PositivePropositions on 3 Variables
• https://inquiryintoinquiry.files.wordpress.com/2020/03/venn-diagrams-e280a2-p-q-r-e280a2-positive-propositions.jpg

Rank 3 (Top). The #BooleanProduct or #LogicalConjunction \(pqr.\)

Rank 2. The 3 #BooleanProducts \(pr, qr, pq.\)

Rank 1. The 3 #BasicPropositions \(q, p, r.\)

Rank 0 (Bottom). The #ConstantFunction \(1 : \mathbb{B}^3 \to \mathbb{B}\) or the #ConstantProposition expressed in #CactusSyntax by the form \(\texttt{((}~\texttt{))}.\)

#Logic

#DifferentialPropositionalCalculus • 2.2
• https://inquiryintoinquiry.com/2020/02/22/differential-propositional-calculus-2/

Table 6 outlines a #Syntax for #PropositionalCalculus based on two types of #LogicalConnectives, both of variable \(k\)-ary scope.
• https://inquiryintoinquiry.files.wordpress.com/2020/02/syntax-and-semantics-of-a-calculus-for-propositional-logic.png

In the second type of connective a concatenation of propositional expressions in the form \(e_1 ~ e_2 ~ \ldots ~ e_{k-1} ~ e_k\) indicates all the propositions \(e_1, e_2, \ldots, e_{k-1}, e_k\) are true, in other words, their #LogicalConjunction is true.