Cactus Language • Overview 3.2
• https://inquiryintoinquiry.com/2025/03/07/cactus-language-overview-3/

Given a body of conceivable propositions we need a way to follow the threads of their indications from their object domain to their values for the mind and a way to follow those same threads back again. Moreover, we need to implement both ways of proceeding in computational form. Thus we need programs for tracing the clues sentences provide from the universe of their objects to the signs of their values and, in turn, from signs to objects. Ultimately, we need to render propositions so functional as indicators of sets and so essential for examining the equality of sets as to give a rule for the practical conceivability of sets. Tackling that task requires us to introduce a number of new definitions and a collection of additional notational devices, to which we now turn.

Resources —

Cactus Language • Overview
• https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Overview

Survey of Animated Logical Graphs
• https://inquiryintoinquiry.com/2024/03/18/survey-of-animated-logical-graphs-7/

Survey of Theme One Program
• https://inquiryintoinquiry.com/2024/02/26/survey-of-theme-one-program-6/

#Peirce #Logic #Semiotics #LogicalGraphs #DifferentialLogic
#AutomataTheory #FormalLanguages #FormalGrammars #GraphTheory

Cactus Language • Overview 3.1
• https://inquiryintoinquiry.com/2025/03/07/cactus-language-overview-3/

In the development of Cactus Language to date the following two species of graphs have been instrumental.

• Painted And Rooted Cacti (PARCAI).
• Painted And Rooted Conifers (PARCOI).

It suffices to begin with the first class of data structures, developing their properties and uses in full, leaving discussion of the latter class to a part of the project where their distinctive features are key to developments at that stage. Partly because the two species are so closely related and partly for the sake of brevity, we'll always use the genus name “PARC” to denote the corresponding cacti.

To provide a computational middle ground between sentences seen as syntactic strings and propositions seen as indicator functions the language designer must not only supply a medium for the expression of propositions but also link the assertion of sentences to a means for inverting the indicator functions, that is, for computing the “fibers” or “inverse images” of the propositions.

#Peirce #Logic #Semiotics #LogicalGraphs #DifferentialLogic
#AutomataTheory #FormalLanguages #FormalGrammars #GraphTheory

Cactus Language • Overview 2
• https://inquiryintoinquiry.com/2025/03/06/cactus-language-overview-2/

In order to facilitate the use of propositions as indicator functions it helps to acquire a flexible notation for referring to propositions in that light, for interpreting sentences in a corresponding role, and for negotiating the requirements of mutual sense between the two domains. If none of the formalisms readily available or in common use meet all the design requirements coming to mind then it is necessary to contemplate the design of a new language especially tailored to the purpose.

In the present application, there is a pressing need to devise a general calculus for composing propositions, computing their values on particular arguments, and inverting their indications to arrive at the sets of things in the universe which are indicated by them.

For computational purposes it is convenient to have a middle ground or an intermediate language for negotiating between the “koine” of sentences regarded as strings of literal characters and the realm of propositions regarded as objects of logical value, even if that makes it necessary to introduce an artificial medium of exchange between the two domains.

If the necessary computations are to be carried out in an organized fashion, and ultimately or partially by familiar classes of machines, then the strings expressing logical propositions are likely to find themselves parsed into tree‑like data structures at some stage of the game. As far as their abstract structures as graphs are concerned, there are several species of graph‑theoretic data structures fitting the task in a reasonably effective and efficient way.

#Peirce #Logic #Semiotics #LogicalGraphs #DifferentialLogic
#FormalLanguages

Cactus Language • Overview 1.2
• https://inquiryintoinquiry.com/2025/03/01/cactus-language-overview-1/

Resource —

For readers interested and intrepid enough to read ahead, here’s an outline of my work in progress on the OEIS Wiki, which I’ll be revising and serializing to my Inquiry blog.

Part 1
• https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Part_1

Cactus Language • Syntax
• https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Part_1#Syntax

Part 2
• https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Part_2

Generalities About Formal Grammars
• https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Part_2#Generalities

Part 3
• https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Part_3

Cactus Language • Stylistics
• https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Part_3#Stylistics

Cactus Language • Mechanics
• https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Part_3#Mechanics

Cactus Language • Semantics
• https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Part_3#Semantics

Stretching Exercises
• https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Part_3#Stretching_Exercises

References
• https://oeis.org/wiki/Cactus_Language_%E2%80%A2_References

Document History
• https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Document_History

#Peirce #Logic #Semiotics #LogicalGraphs #DifferentialLogic
#Automata #FormalLanguages #FormalGrammars #GraphTheory

Cactus Language • Overview 1.1
• https://inquiryintoinquiry.com/2025/03/01/cactus-language-overview-1/

❝Thus, what looks to us like a sphere of scientific knowledge more accurately should be represented as the inside of a highly irregular and spiky object, like a pincushion or porcupine, with very sharp extensions in certain directions, and virtually no knowledge in immediately adjacent areas. If our intellectual gaze could shift slightly, it would alter each quill’s direction, and suddenly our entire reality would change.❞

— Herbert J. Bernstein • “Idols of Modern Science”

The following report describes a calculus for representing propositions as sentences, that is, as syntactically defined sequences of signs, and for working with those sentences in light of their semantically defined contents as logical propositions. In their computational representation the expressions of the calculus parse into a class of graph‑theoretic data structures whose underlying graphs are called “painted cacti”.

Painted cacti are a specialization of what graph‑theorists refer to as “cacti”, which are in turn a generalization of what they call “trees”. The data structures corresponding to painted cacti have especially nice properties, not only useful in computational terms but interesting from a theoretical standpoint. The remainder of the present Overview is devoted to motivating the development of the indicated family of formal languages, going under the generic name of Cactus Language.

#Peirce #Logic #Semiotics #LogicalGraphs #DifferentialLogic
#Automata #FormalLanguages #FormalGrammars #GraphTheory

Charles Sanders Peirce, George Spencer Brown, and Me • 4
• https://inquiryintoinquiry.com/2017/08/06/charles-sanders-peirce-george-spencer-brown-and-me-4/
• https://bsky.app/profile/inquiryintoinquiry.bsky.social/post/3lh5fsszkmk23

Two things impacting my studies of Peirce and Spencer Brown over the years were my parallel studies in mathematics and computer science. In the overlap between those areas came courses in logic, mathematical linguistics, and the theory of formal languages, grammars, and automata.

My intellectual wanderings over a nine‑year undergraduate career would take me through a cycle of majors from math and physics, to communication, psychology, philosophy, and a cross‑cultural liberal arts program, then back to grad school in mathematics.

The puzzles Peirce and Spencer Brown beset my brain with were a big part of what drove me back to math, since I could see I had no chance of resolving them without learning a lot more algebra, logic, and topology than I had learned till then.

#Peirce #Logic #LogicalGraphs #SpencerBrown #LawsOfForm

Charles Sanders Peirce, George Spencer Brown, and Me • 1
• https://inquiryintoinquiry.com/2017/07/20/charles-sanders-peirce-george-spencer-brown-and-me-1/
• https://bsky.app/profile/inquiryintoinquiry.bsky.social/post/3lgxtd6z3nk2t

It’s almost 50 years now since I first encountered the volumes of Peirce’s Collected Papers in the math library at Michigan State, and shortly afterwards a friend called my attention to the entry for Spencer Brown’s Laws of Form in the Whole Earth Catalog and I sent off for it right away.

I would spend the next decade just beginning to figure out what either one of them was talking about in the matter of logical graphs and I would spend another decade after that developing a program, first in Lisp and then in Pascal, converting graph-theoretic data structures formed on their ideas to good purpose in the mechanics of its propositional reasoning engine. I thought it might contribute to a number of ongoing discussions if I could articulate what I think I learned from that experience.

#Peirce #Logic #LogicalGraphs #SpencerBrown #LawsOfForm

Differential Propositional Calculus • 10

Special Classes of Propositions (cont.)

Let’s pause at this point and get a better sense of how our special classes of propositions are structured and how they relate to propositions in general.  We can do this by recruiting our visual imaginations and drawing up a sufficient budget of venn diagrams for each family of propositions.  The case for 3 variables is exemplary enough for a start.

Linear Propositions

The linear propositions, may be written as sums:

One thing to keep in mind about these sums is that the values in are added “modulo 2”, that is, in such a way that

In a universe of discourse based on three boolean variables, the linear propositions take the shapes shown in Figure 8.

At the top is the venn diagram for the linear proposition of rank 3, which may be expressed by any one of the following three forms.

Next are the venn diagrams for the three linear propositions of rank 2, which may be expressed by the following three forms, respectively.

Next are the three linear propositions of rank 1, which are none other than the three basic propositions,

At the bottom is the linear proposition of rank 0, the everywhere false proposition or the constant function, which may be expressed by the form or by a simple

Resources

• Logic Syllabus
• Survey of Differential Logic

cc: Academia.edu • Cybernetics • Structural Modeling • Systems Science
cc: Conceptual Graphs • Laws of Form • Mathstodon • Research Gate

#Amphecks #Animata #BooleanAlgebra #BooleanFunctions #CSPeirce #CactusGraphs #CategoryTheory #Change #Cybernetics #DifferentialAnalyticTuringAutomata #DifferentialCalculus #DifferentialLogic #DiscreteDynamics #EquationalInference #FunctionalLogic #GraphTheory #Hologrammautomaton #IndicatorFunctions #InquiryDrivenSystems #Leibniz #Logic #LogicalGraphs #Mathematics #MinimalNegationOperators #PropositionalCalculus #Time #Topology #Visualization

Differential Propositional Calculus • 8
• https://inquiryintoinquiry.com/2024/12/07/differential-propositional-calculus-8-b/

Formal Development (cont.)

Before moving on, let's unpack some of the assumptions, conventions, and implications involved in the array of concepts and notations introduced above.

A universe of discourse A° = [a₁, …, aₙ] qualified by the logical features a₁, …, aₙ is a set A plus the set of all functions from the space A to the boolean domain B = {0, 1}. There are 2ⁿ elements in A, often pictured as the cells of a venn diagram or the nodes of a hypercube. There are 2^(2ⁿ) possible functions from A to B, accordingly pictured as all the ways of painting the cells of a venn diagram or the nodes of a hypercube with a palette of two colors.

A logical proposition about the elements of A is either true or false of each element in A, while a function f : A → B evaluates to 1 or 0 on each element of A. The analogy between logical propositions and boolean-valued functions is close enough to adopt the latter as models of the former and simply refer to the functions f : A → B as propositions about the elements of A.

Resources —

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

Survey of Differential Logic
• https://inquiryintoinquiry.com/2024/02/25/survey-of-differential-logic-7

#Peirce #Logic #LogicalGraphs #DifferentialLogic #DiscreteDynamicalSystems
#BooleanFunctions #BooleanDifferenceCalculus #CalculusOfLogicalDifferences
#PropositionalCalculus #DifferentialPropositionalCalculus #LogicalDynamics

Differential Propositional Calculus • 7.2
• https://inquiryintoinquiry.com/2024/12/06/differential-propositional-calculus-7-b/

Formal Development (cont.)

Table 7 summarizes the basic notations needed to describe ordinary propositional calculi in a systematic fashion.

Table 7. Propositional Calculus • Basic Notation
• https://inquiryintoinquiry.files.wordpress.com/2020/02/propositional-calculus-basic-notation.png

Resources —

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

Survey of Differential Logic
• https://inquiryintoinquiry.com/2024/02/25/survey-of-differential-logic-7

#Peirce #Logic #LogicalGraphs #DifferentialLogic #DiscreteDynamicalSystems
#BooleanFunctions #BooleanDifferenceCalculus #CalculusOfLogicalDifferences
#PropositionalCalculus #DifferentialPropositionalCalculus #LogicalDynamics

Differential Propositional Calculus • 7.1
• https://inquiryintoinquiry.com/2024/12/06/differential-propositional-calculus-7-b/

Note. Please see the blog post linked above for the proper formats of the notations used below.

Formal Development —

The preceding discussion outlined the ideas leading to the differential extension of propositional logic. The next task is to lay out the concepts and terminology needed to describe various orders of differential propositional calculi.

Elementary Notions —

Logical description of a universe of discourse begins with a collection of logical signs. For simplicity in a first approach we assume the signs are collected in the form of a finite alphabet, ‡A‡ = {“a₁”, …, “aₙ”}. The signs are interpreted as denoting logical features, for example, properties of objects in the universe of discourse or simple propositions about those objects. Corresponding to the alphabet ‡A‡ there is then a set of logical features, †A† = {a₁, …, aₙ}.

A set of logical features †A† = {a₁, …, aₙ} affords a basis for generating an n‑dimensional universe of discourse, written A° = [†A†] = [a₁, …, aₙ]. It is useful to consider a universe of discourse as a categorical object incorporating both the set of points A = <a₁, …, aₙ> and the set of propositions A↑ = {f : A → B} implicit with the ordinary picture of a venn diagram on n features.

Accordingly, the universe of discourse A° may be regarded as an ordered pair (A, A↑) bearing the type (Bⁿ, (Bⁿ → B)), which type designation may be abbreviated as Bⁿ +→ B or even more succinctly as [Bⁿ]. For convenience, the data type of a finite set on n elements may be indicated by either one of the equivalent notations [n] or *n*.

#Peirce #Logic #LogicalGraphs #DifferentialLogic

Differential Propositional Calculus • 6.2
• https://inquiryintoinquiry.com/2024/12/04/differential-propositional-calculus-6-b/

Cactus Calculus (cont.)

The briefest expression for logical truth is the empty word, denoted ε or λ in formal languages, where it forms the identity element for concatenation. It may be given visible expression in textual settings by means of the logically equivalent form (()), or, especially if operating in an algebraic context, by a simple 1. Also when working in an algebraic mode, the plus sign “+” may be used for exclusive disjunction. For example, we have the following paraphrases of algebraic expressions.

• x + y = (x, y)

• x + y + z = ((x, y), z) = (x, (y, z))

It is important to note the last expressions are not equivalent to the triple bracket (x, y, z).

Resources —

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

Survey of Differential Logic
• https://inquiryintoinquiry.com/2024/02/25/survey-of-differential-logic-7

#Peirce #Logic #LogicalGraphs #DifferentialLogic #DiscreteDynamicalSystems
#BooleanFunctions #BooleanDifferenceCalculus #CalculusOfLogicalDifferences
#PropositionalCalculus #DifferentialPropositionalCalculus #LogicalDynamics

Differential Propositional Calculus • 6.1
• https://inquiryintoinquiry.com/2024/12/04/differential-propositional-calculus-6-b/

Cactus Calculus —

Table 6 outlines a syntax for propositional calculus based on two types of logical connectives, both of variable k‑ary scope.

• A bracketed sequence of propositional expressions (e₁, e₂, …, eₖ) is taken to mean exactly one of the propositions e₁, e₂, …, eₖ is false, in other words, their “minimal negation” is true.

• A concatenated sequence of propositional expressions e₁ e₂ … eₖ is taken to mean every one of the propositions e₁, e₂, …, eₖ is true, in other words, their “logical conjunction” is true.

Table 6. Syntax and Semantics of a Calculus for Propositional Logic
• https://inquiryintoinquiry.files.wordpress.com/2022/10/syntax-and-semantics-of-a-calculus-for-propositional-logic-4.0.png

All other propositional connectives may be obtained through combinations of the above two forms. As it happens, the concatenation form is dispensable in light of the bracket form but it is convenient to maintain it as an abbreviation for more complicated bracket expressions. While working with expressions solely in propositional calculus, it is easiest to use plain parentheses for bracket forms. In contexts where parentheses are needed for other purposes “teletype” parentheses (…) or barred parentheses (|…|) may be used for logical operators.

#Peirce #Logic #LogicalGraphs #DifferentialLogic #DiscreteDynamicalSystems
#BooleanFunctions #BooleanDifferenceCalculus #CalculusOfLogicalDifferences
#PropositionalCalculus #DifferentialPropositionalCalculus #LogicalDynamics

Differential Propositional Calculus • 5
• https://inquiryintoinquiry.com/2024/12/03/differential-propositional-calculus-5-b/

Casual Introduction (concl.)

Table 5 exhibits the rules of inference responsible for giving the differential proposition dq its meaning in practice.

Table 5. Differential Inference Rules
• https://inquiryintoinquiry.files.wordpress.com/2020/02/differential-propositional-calculus-e280a2-differential-inference-rules.png

If the feature q is interpreted as applying to an object in the universe of discourse X then the differential feature dq may be taken as an attribute of the same object which tells it is changing “significantly” with respect to the property q — as if the object bore an “escape velocity” with respect to the condition q.

For example, relative to a frame of observation to be made more explicit later on, if q and dq are true at a given moment, it would be reasonable to assume ¬q will be true in the next moment of observation. Taken all together we have the fourfold scheme of inference shown above.

Resources —

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

Survey of Differential Logic
• https://inquiryintoinquiry.com/2024/02/25/survey-of-differential-logic-7

#Peirce #Logic #LogicalGraphs #DifferentialLogic #DiscreteDynamicalSystems
#BooleanFunctions #BooleanDifferenceCalculus #CalculusOfLogicalDifferences
#PropositionalCalculus #DifferentialPropositionalCalculus #LogicalDynamics

Differential Propositional Calculus • 4
• https://inquiryintoinquiry.com/2024/12/02/differential-propositional-calculus-4-b/

Casual Introduction (cont.)

In Figure 3 we saw how the basis of description for the universe of discourse X could be extended to a set of two qualities {q, dq} while the corresponding terms of description could be extended to an alphabet of two symbols {“q”, “dq”}.

Any propositional calculus over two basic propositions allows for the expression of 16 propositions all together. Salient among those propositions in the present setting are the four which single out the individual sample points at the initial moment of observation. Table 4 lists the initial state descriptions, using overlines to express logical negations.

Table 4. Initial State Descriptions
• https://inquiryintoinquiry.files.wordpress.com/2020/02/differential-propositional-calculus-e280a2-initial-state-descriptions.png

Resources —

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

Survey of Differential Logic
• https://inquiryintoinquiry.com/2024/02/25/survey-of-differential-logic-7

#Peirce #Logic #LogicalGraphs #DifferentialLogic #DiscreteDynamicalSystems
#BooleanFunctions #BooleanDifferenceCalculus #CalculusOfLogicalDifferences
#PropositionalCalculus #DifferentialPropositionalCalculus #LogicalDynamics

Differential Propositional Calculus • 3.2
• https://inquiryintoinquiry.com/2024/12/01/differential-propositional-calculus-3-b/

Casual Introduction (cont.)

Figure 1 represents a universe of discourse 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 formal language specifically cut out for discussing X in terms of q. That language is more formally known as the “propositional calculus” with alphabet {“q”}.

In the context marked by X and {q} there are just four distinct pieces of information which can be expressed in the corresponding propositional calculus, namely, the constant proposition False, the negative proposition ¬q, the positive proposition q, and the constant proposition True.

For example, referring to the points in Figure 1, the constant proposition False holds of no points, the negative proposition ¬q holds of a and d, the positive proposition q holds of b and c, and the constant proposition True holds of all points in the sample.

Figure 3 preserves the same universe of discourse and extends the basis of discussion to a set of two qualities, {q, dq}. In corresponding fashion, the initial propositional calculus is extended by means of the enlarged alphabet, {“q”, “dq”}.

Resources —

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

Survey of Differential Logic
• https://inquiryintoinquiry.com/2024/02/25/survey-of-differential-logic-7

#Peirce #Logic #LogicalGraphs #DifferentialLogic #DiscreteDynamicalSystems
#BooleanFunctions #BooleanDifferenceCalculus #CalculusOfLogicalDifferences
#PropositionalCalculus #DifferentialPropositionalCalculus #LogicalDynamics

Differential Propositional Calculus • 3.1
• https://inquiryintoinquiry.com/2024/12/01/differential-propositional-calculus-3-b/

Casual Introduction (cont.)

Figure 3 returns to the situation in Figure 1, but this time interpolates a new quality specifically tailored to account for the relation between Figure 1 and Figure 2.

Figure 3. Back, To The Future
• https://inquiryintoinquiry.files.wordpress.com/2023/11/differential-propositional-calculus-e280a2-figure-3.png

The new quality, dq, is marked as a “differential quality” on account of its absence or presence qualifying the absence or presence of change occurring in another quality. As with any quality, it is represented in the venn diagram by means of a “circle” distinguishing two halves of the universe of discourse, in this case, the portions of X outside and inside the region dQ.

Resources —

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

Survey of Differential Logic
• https://inquiryintoinquiry.com/2024/02/25/survey-of-differential-logic-7

#Peirce #Logic #LogicalGraphs #DifferentialLogic #DiscreteDynamicalSystems
#BooleanFunctions #BooleanDifferenceCalculus #CalculusOfLogicalDifferences
#PropositionalCalculus #DifferentialPropositionalCalculus #LogicalDynamics

Differential Propositional Calculus • 2
• https://inquiryintoinquiry.com/2024/11/30/differential-propositional-calculus-2-b/

Casual Introduction (cont.)

Now consider the situation represented by the venn diagram in Figure 2.

Figure 2. Same Names, Different Habitations
• https://inquiryintoinquiry.files.wordpress.com/2023/11/differential-propositional-calculus-e280a2-figure-2.png

Figure 2 differs from Figure 1 solely in the circumstance that the object c is outside the region Q while the object d is inside the region Q.

Nothing says our encountering the Figures in the above order is other than purely accidental but if we interpret the sequence of frames as a “moving picture” representation of their natural order in a temporal process then it would be natural to suppose a and b have remained as they were with regard to the quality q while c and d have changed their standings in that respect. In particular, c has moved from the region where q is true to the region where q is false while d has moved from the region where q is false to the region where q is true.

Resources —

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

Survey of Differential Logic
• https://inquiryintoinquiry.com/2024/02/25/survey-of-differential-logic-7

#Peirce #Logic #LogicalGraphs #DifferentialLogic #DiscreteDynamicalSystems
#BooleanFunctions #BooleanDifferenceCalculus #CalculusOfLogicalDifferences
#PropositionalCalculus #DifferentialPropositionalCalculus #LogicalDynamics

Differential Propositional Calculus • 1
• https://inquiryintoinquiry.com/2024/11/29/differential-propositional-calculus-1-b/

A “differential propositional calculus” is a propositional calculus extended by a set of terms for describing aspects of change and difference, for example, processes taking place in a universe of discourse or transformations mapping a source universe to a target universe.

Casual Introduction —

Consider the situation represented by the venn diagram in Figure 1.

Figure 1. Local Habitations, And Names
• https://inquiryintoinquiry.files.wordpress.com/2023/11/differential-propositional-calculus-e280a2-figure-1.png

The area of the rectangle represents the universe of discourse X. The universe under discussion may be a population of individuals having various additional properties or it may be a collection of locations occupied by various individuals. The area of the “circle” represents the individuals with the property q or the locations in the corresponding region Q. Four individuals, a, b, c, d, are singled out by name. As it happens, b and c currently reside in region Q while a and d do not.

Resources —

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

Survey of Differential Logic
• https://inquiryintoinquiry.com/2024/02/25/survey-of-differential-logic-7

#Peirce #Logic #LogicalGraphs #DifferentialLogic #DiscreteDynamicalSystems
#BooleanFunctions #BooleanDifferenceCalculus #CalculusOfLogicalDifferences
#PropositionalCalculus #DifferentialPropositionalCalculus #LogicalDynamics

Differential Propositional Calculus • Overview 2
• https://inquiryintoinquiry.com/2024/11/27/differential-propositional-calculus-overview-b/

What follows is the outline of a sketch on differential propositional calculus intended as an intuitive introduction to the larger subject of differential logic, which amounts in turn to my best effort so far at dealing with the ancient and persistent problems of treating diversity and mutability in logical terms.

Note. I'll give just the links to the main topic heads below. Please follow the link at the top of the page for the full outline.

Part 1 —
• https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Part_1

Casual Introduction
• https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Part_1#Casual_Introduction

Cactus Calculus
• https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Part_1#Cactus_Calculus

Part 2 —
• https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Part_2

Formal_Development
• https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Part_2#Formal_Development

Elementary Notions
• https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Part_2#Elementary_Notions

Special Classes of Propositions
• https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Part_2#Special_Classes_of_Propositions

Differential Extensions
• https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Part_2#Differential_Extensions

Appendices —
• https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Appendices

References —
• https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_References

#Peirce #Logic #LogicalGraphs #DifferentialLogic #DiscreteDynamicalSystems
#BooleanFunctions #BooleanDifferenceCalculus #CalculusOfLogicalDifferences
#PropositionalCalculus #DifferentialPropositionalCalculus #LogicalDynamics