Reflective Interpretive Frameworks • Incident 1

Posted on March 26, 2026 by Jon Awbrey

Re: William Waites • The Agent That Doesn’t Know Itself

WW:  ❝Why Has Nobody Done This?❞

People who study C.S. Peirce would say reflective reasoning requires triadic relations at core and there is work being done on that.  One of the challenges is clarifying the role of triadic relations in category theory and raising them into higher relief as fundamental operations.

  • Note.  I was looking for a word to describe a random encounter with something that jogs one’s memory of a recurring theme — incident plays into the reflection theme and looked worth trying for now.

Resources

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

Posted in Arithmetization, C.S. Peirce, Gödel Numbers, Higher Order Sign Relations, Inquiry Driven Systems, Inquiry Into Inquiry, Logic, Mathematics, Quotation, Recursion, Reflection, Reflective Interpretive Frameworks, Semiotics, Sign Relations, Triadic Relations, Use and Mention, Visualization | Tagged , , , , , , , , , , , , , , , , | 1 Comment

Differential Logic • Discussion 17

Posted on March 18, 2026 by Jon Awbrey

Re: Differential Logic • The Logic of Change and Difference
Re: Systems Science Working Group • Paola Di Maio

PDM:
Subject: Differential Logic —
A point of contact with AI Knowledge Representation

Dear Jon,

Thank you for keeping the bell tolling — your framing of differential logic as the logic of variation arrives at a propitious moment.

For the past year I have been working at the intersection of knowledge representation, non‑logical reasoning, and AI systems, partly through the W3C AI Knowledge Representation Community Group (which I chair) and partly through independent research.  One of the persistent problems we encounter is that classical propositional and first order logic, however powerful for static state description, cannot represent the dynamics of reasoning systems — what changes, how fast, under what perturbation.

Your formulation cuts right to it:  ordinary propositional calculus describes positions in logical space; differential propositional calculus describes movement through it.  The analogy to Leibniz–Newton augmenting Descartes marks a categorical shift.

This connects directly to work I have been developing on what I call the five‑corners framework, extending Nagarjuna’s “catuskoti” (the four‑cornered logic:  true, false, both, neither — with Graham Priest’s fifth corner as refusal of the frame) toward a relational and co‑evolutionary account of knowledge.  The catuskoti gives us positions;  your differential extension gives us the calculus of transitions between them.  The five corners are attractors;  differential logic describes the manifold on which the system moves.

I am attaching a recent research note —

  • “Beyond Formal Logic:  Non‑Logical Forms of Valid Reasoning and Their Implications for AI Knowledge Representation”.  Online.

It documents three classes of reasoning that produce valid outcomes yet resist formalization in FOL:  embodied ecological reasoning, somatic‑intuitive reasoning, and transrational insight.

I suspect your differential extension of propositional calculus may offer formal traction on at least the first two, precisely because it can represent how a reasoning agent’s truth‑value assignments shift as context changes.

I also noticed your reference to neural network activation states and competition constraints in relation to the boundary operator.

This is terrain I am actively exploring in connection with oscillatory network models and a citizen science project on anomalous luminous phenomena (where the signal is change, not static state).  I may have to write a paper on that.

Jotted down some thoughts —

With collegial regards,

Paola Di Maio
Chair, W3C AI Knowledge Representation Community Group
Research Lead, Center for Systems, Knowledge Representation and Neuroscience, Ronin Institute

Dear Paola,

Many thanks for your kind reply and comments.

I was getting ready to devote a blog post (or two or three) by way of responding to your very substantial comments and I see you addressed the Systems Science Working Group but your post did not make it through to the web interface.  Did you intend to post it there?  It would help if I had a list link in my response if you did so.  Otherwise, if it’s okay with you, I could just quote the whole of your remarks on my blog.  Please let me know what you prefer.

Regards,
Jon

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cc: Research Gate • Structural Modeling • Systems Science • Syscoi

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Change, Cybernetics, Differential Calculus, Differential Logic, Discrete Dynamics, Equational Inference, Functional Logic, Gradient Descent, Graph Theory, Inquiry Driven Systems, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Propositional Calculus, Time, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Differential Logic • The Logic of Change and Difference

Posted on March 14, 2026 by Jon Awbrey

Differential logic is the logic of variation — the logic of change and difference.

Differential logic is the component of logic whose object is the description of variation — the aspects of change, difference, distribution, and diversity — in universes of discourse subject to logical description.  A definition as broad as that naturally incorporates any study of variation by way of mathematical models, but differential logic is especially charged with the qualitative aspects of variation pervading or preceding quantitative models.

To the extent a logical inquiry makes use of a formal system, its differential component treats the use of a differential logical calculus — a formal system with the expressive capacity to describe change and diversity in logical universes of discourse.

A simple case of a differential logical calculus is furnished by a differential propositional calculus, a formalism which augments ordinary propositional calculus in the same way the differential calculus of Leibniz and Newton augments the analytic geometry of Descartes.

Resources

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Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Change, Cybernetics, Differential Calculus, Differential Logic, Discrete Dynamics, Equational Inference, Functional Logic, Gradient Descent, Graph Theory, Inquiry Driven Systems, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Propositional Calculus, Time, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , | 4 Comments

Differential Logic • 18

Posted on March 6, 2026 by Jon Awbrey

Tangent and Remainder Maps

If we follow the classical line which singles out linear functions as ideals of simplicity then we may complete the analytic series of the proposition f = pq : X \to \mathbb{B} in the following way.

The next venn diagram shows the differential proposition \mathrm{d}f = \mathrm{d}(pq) : \mathrm{E}X \to \mathbb{B} we get by extracting the linear approximation to the difference map \mathrm{D}f = \mathrm{D}(pq) : \mathrm{E}X \to \mathbb{B} at each cell or point of the universe X.  What results is the logical analogue of what would ordinarily be called the differential of pq but since the adjective differential is being attached to just about everything in sight the alternative name tangent map is commonly used for \mathrm{d}f whenever it’s necessary to single it out.

Tangent Map d(pq) : EX → B
\text{Tangent Map}~ \mathrm{d}(pq) : \mathrm{E}X \to \mathbb{B}

To be clear about what’s being indicated here, it’s a visual way of summarizing the following data.

\begin{array}{rcccccc} \mathrm{d}(pq) & = & p & \cdot & q & \cdot & \texttt{(} \mathrm{d}p \texttt{,} \mathrm{d}q \texttt{)} \\[4pt] & + & p & \cdot & \texttt{(} q \texttt{)} & \cdot & \mathrm{d}q \\[4pt] & + & \texttt{(} p \texttt{)} & \cdot & q & \cdot & \mathrm{d}p \\[4pt] & + & \texttt{(} p \texttt{)} & \cdot & \texttt{(} q \texttt{)} & \cdot & 0 \end{array}

To understand the extended interpretations, that is, the conjunctions of basic and differential features which are being indicated here, it may help to note the following equivalences.

\begin{matrix} \texttt{(} \mathrm{d}p \texttt{,} \mathrm{d}q \texttt{)} & = & \texttt{~} \mathrm{d}p \texttt{~} \texttt{(} \mathrm{d}q \texttt{)} & + & \texttt{(} \mathrm{d}p \texttt{)} \texttt{~} \mathrm{d}q \texttt{~} \\[4pt] dp & = & \texttt{~} \mathrm{d}p \texttt{~} \texttt{~} \mathrm{d}q \texttt{~} & + & \texttt{~} \mathrm{d}p \texttt{~} \texttt{(} \mathrm{d}q \texttt{)} \\[4pt] \mathrm{d}q & = & \texttt{~} \mathrm{d}p \texttt{~} \texttt{~} \mathrm{d}q \texttt{~} & + & \texttt{(} \mathrm{d}p \texttt{)} \texttt{~} \mathrm{d}q \texttt{~} \end{matrix}

Capping the analysis of the proposition pq in terms of succeeding orders of linear propositions, the final venn diagram of the series shows the remainder map \mathrm{r}(pq) : \mathrm{E}X \to \mathbb{B}, which happens to be linear in pairs of variables.

Remainder r(pq) : EX → B
\text{Remainder}~ \mathrm{r}(pq) : \mathrm{E}X \to \mathbb{B}

Reading the arrows off the map produces the following data.

\begin{array}{rcccccc} \mathrm{r}(pq) & = & p & \cdot & q & \cdot & \mathrm{d}p ~ \mathrm{d}q \\[4pt] & + & p & \cdot & \texttt{(} q \texttt{)} & \cdot & \mathrm{d}p ~ \mathrm{d}q \\[4pt] & + & \texttt{(} p \texttt{)} & \cdot & q & \cdot & \mathrm{d}p ~ \mathrm{d}q \\[4pt] & + & \texttt{(} p \texttt{)} & \cdot & \texttt{(} q \texttt{)} & \cdot & \mathrm{d}p ~ \mathrm{d}q \end{array}

In short, \mathrm{r}(pq) is a constant field, having the value \mathrm{d}p~\mathrm{d}q at each cell.

Resources

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cc: Research Gate • Structural Modeling • Systems Science • Syscoi

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Change, Cybernetics, Differential Calculus, Differential Logic, Discrete Dynamics, Equational Inference, Functional Logic, Gradient Descent, Graph Theory, Inquiry Driven Systems, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Propositional Calculus, Time, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , | 3 Comments

Differential Logic • 17

Posted on March 5, 2026 by Jon Awbrey

Enlargement and Difference Maps

Continuing with the example pq : X \to \mathbb{B}, the following venn diagram shows the enlargement or shift map \mathrm{E}(pq) : \mathrm{E}X \to \mathbb{B} in the same style of field picture we drew for the tacit extension \boldsymbol\varepsilon (pq) : \mathrm{E}X \to \mathbb{B}.

Enlargement E(pq) : EX → B
\text{Enlargement}~ \mathrm{E}(pq) : \mathrm{E}X \to \mathbb{B}

\begin{array}{rcccccc} \mathrm{E}(pq) & = & p & \cdot & q & \cdot & \texttt{(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)} \\[4pt] & + & p & \cdot & \texttt{(} q \texttt{)} & \cdot & \texttt{(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~} \\[4pt] & + & \texttt{(} p \texttt{)} & \cdot & q & \cdot & \texttt{~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)} \\[4pt] & + & \texttt{(} p \texttt{)} & \cdot & \texttt{(} q \texttt{)} & \cdot & \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~} \end{array}

A very important conceptual transition has just occurred here, almost tacitly, as it were.  Generally speaking, having a set of mathematical objects of compatible types, in this case the two differential fields \boldsymbol\varepsilon f and \mathrm{E}f, both of the type \mathrm{E}X \to \mathbb{B}, is very useful, because it allows us to consider those fields as integral mathematical objects which can be operated on and combined in the ways we usually associate with algebras.

In the present case one notices the tacit extension \boldsymbol\varepsilon f and the enlargement \mathrm{E}f are in a sense dual to each other.  The tacit extension \boldsymbol\varepsilon f indicates all the arrows out of the region where f is true and the enlargement \mathrm{E}f indicates all the arrows into the region where f is true.  The only arc they have in common is the no‑change loop \texttt{(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)} at pq.  If we add the two sets of arcs in mod 2 fashion then the loop of multiplicity 2 zeroes out, leaving the 6 arrows of \mathrm{D}(pq) = \boldsymbol\varepsilon(pq) + \mathrm{E}(pq) shown in the following venn diagram.

Differential D(pq) : EX → B
\text{Difference}~ \mathrm{D}(pq) : \mathrm{E}X \to \mathbb{B}

\begin{array}{rcccccc} \mathrm{D}(pq) & = & p & \cdot & q & \cdot & \texttt{((} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{))} \\[4pt] & + & p & \cdot & \texttt{(} q \texttt{)} & \cdot & \texttt{~(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~~} \\[4pt] & + & \texttt{(} p \texttt{)} & \cdot & q & \cdot & \texttt{~~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)~} \\[4pt] & + & \texttt{(} p \texttt{)} & \cdot & \texttt{(}q \texttt{)} & \cdot & \texttt{~~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~~} \end{array}

Resources

cc: Academia.edu • Cybernetics • Laws of Form • Mathstodon (1) (2)
cc: Research Gate • Structural Modeling • Systems Science • Syscoi

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Change, Cybernetics, Differential Calculus, Differential Logic, Discrete Dynamics, Equational Inference, Functional Logic, Gradient Descent, Graph Theory, Inquiry Driven Systems, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Propositional Calculus, Time, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , | 3 Comments

Differential Logic • 16

Posted on March 4, 2026 by Jon Awbrey

Propositions and Tacit Extensions

Now that we’ve introduced the field picture as an aid to visualizing propositions and their analytic series, a pleasing way to picture the relationship of a proposition f : X \to \mathbb{B} to its enlargement or shift map \mathrm{E}f : \mathrm{E}X \to \mathbb{B} and its difference map \mathrm{D}f : \mathrm{E}X \to \mathbb{B} can now be drawn.

To illustrate the possibilities, let’s return to the differential analysis of the conjunctive proposition f(p, q) = pq and give its development a slightly different twist at the appropriate point.

The proposition pq : X \to \mathbb{B} is shown again in the venn diagram below.  In the field picture it may be seen as a scalar field — analogous to a potential hill in physics but in logic amounting to a potential plateau — where the shaded region indicates an elevation of 1 and the unshaded region indicates an elevation of 0.

Proposition pq : X → B
\text{Proposition}~ pq : X \to \mathbb{B}

Given a proposition f : X \to \mathbb{B}, the tacit extension of f to \mathrm{E}X is denoted \boldsymbol\varepsilon f : \mathrm{E}X \to \mathbb{B} and defined by the equation \boldsymbol\varepsilon f = f, so it’s really just the same proposition residing in a bigger universe.  Tacit extensions formalize the intuitive idea that a function on a given set of variables can be extended to a function on a superset of those variables in such a way that the new function obeys the same constraints on the old variables, with a “don’t care” condition on the new variables.

The tacit extension of the scalar field pq : X \to \mathbb{B} to the differential field \boldsymbol\varepsilon (pq) : \mathrm{E}X \to \mathbb{B} is shown in the following venn diagram.

Tacit Extension ε(pq) : EX → B
\text{Tacit Extension}~ \boldsymbol\varepsilon (pq) : \mathrm{E}X \to \mathbb{B}

\begin{array}{rcccccc} \boldsymbol\varepsilon (pq) & = & p & \cdot & q & \cdot & \texttt{(} \mathrm{d}p \texttt{)} \texttt{(} \mathrm{d}q \texttt{)} \\[4pt] & + & p & \cdot & q & \cdot & \texttt{(} \mathrm{d}p \texttt{)} \texttt{~} \mathrm{d}q \texttt{~} \\[4pt] & + & p & \cdot & q & \cdot & \texttt{~} \mathrm{d}p \texttt{~} \texttt{(} \mathrm{d}q \texttt{)} \\[4pt] & + & p & \cdot & q & \cdot & \texttt{~} \mathrm{d}p \texttt{~} \texttt{~} \mathrm{d}q \texttt{~} \end{array}

Resources

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Differential Logic • 15

Posted on March 2, 2026 by Jon Awbrey

Differential Fields

The structure of a differential field may be described as follows.  With each point of X there is associated an object of the following type:  a proposition about changes in X, that is, a proposition g : \mathrm{d}X \to \mathbb{B}.  In that frame of reference, if {X^\bullet} is the universe generated by the set of coordinate propositions \{ p, q \} then \mathrm{d}X^\bullet is the differential universe generated by the set of differential propositions \{ \mathrm{d}p, \mathrm{d}q \}.  The differential propositions \mathrm{d}p and \mathrm{d}q may thus be interpreted as indicating ``\text{change in}~ p" and ``\text{change in}~ q", respectively.

A differential operator \mathrm{W}, of the first order type we are currently considering, takes a proposition f : X \to \mathbb{B} and gives back a differential proposition \mathrm{W}f : \mathrm{E}X \to \mathbb{B}.  In the field view of the scene, we see the proposition f : X \to \mathbb{B} as a scalar field and we see the differential proposition \mathrm{W}f : \mathrm{E}X \to \mathbb{B} as a vector field, specifically, a field of propositions about contemplated changes in X.

The field of changes produced by \mathrm{E} on pq is shown in the following venn diagram.

Enlargement E(pq) : EX → B
\text{Enlargement}~ \mathrm{E}(pq) : \mathrm{E}X \to \mathbb{B}

\begin{array}{rcccccc} \mathrm{E}(pq) & = & p & \cdot & q & \cdot & \texttt{(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)} \\[4pt] & + & p & \cdot & \texttt{(} q \texttt{)} & \cdot & \texttt{(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~} \\[4pt] & + & \texttt{(} p \texttt{)} & \cdot & q & \cdot & \texttt{~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)} \\[4pt] & + & \texttt{(} p \texttt{)} & \cdot & \texttt{(} q \texttt{)} & \cdot & \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~} \end{array}

The differential field \mathrm{E}(pq) specifies the changes which need to be made from each point of X in order to reach one of the models of the proposition pq, that is, in order to satisfy the proposition pq.

The field of changes produced by \mathrm{D} on pq is shown in the following venn diagram.

Differential D(pq) : EX → B
\text{Difference}~ \mathrm{D}(pq) : \mathrm{E}X \to \mathbb{B}

\begin{array}{rcccccc} \mathrm{D}(pq) & = & p & \cdot & q & \cdot & \texttt{((} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{))} \\[4pt] & + & p & \cdot & \texttt{(} q \texttt{)} & \cdot & \texttt{~(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~~} \\[4pt] & + & \texttt{(} p \texttt{)} & \cdot & q & \cdot & \texttt{~~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)~} \\[4pt] & + & \texttt{(} p \texttt{)} & \cdot & \texttt{(}q \texttt{)} & \cdot & \texttt{~~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~~} \end{array}

The differential field \mathrm{D}(pq) specifies the changes which need to be made from each point of X in order to feel a change in the felt value of the field pq.

Resources

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cc: Research Gate • Structural Modeling • Systems Science • Syscoi

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Differential Logic • 14

Posted on February 28, 2026 by Jon Awbrey

Field Picture

Let us summarize the outlook on differential logic we’ve reached so far.  We’ve been considering a class of operators on universes of discourse, each of which takes us from considering one universe of discourse X^\bullet to considering a larger universe of discourse \mathrm{E}X^\bullet.  An operator \mathrm{W} of that general type, namely, \mathrm{W} : X^\bullet \to \mathrm{E}X^\bullet, acts on each proposition f : X \to \mathbb{B} of the source universe {X^\bullet} to produce a proposition \mathrm{W}f : \mathrm{E}X \to \mathbb{B} of the target universe \mathrm{E}X^\bullet.

The operators we’ve examined so far are the enlargement or shift operator \mathrm{E} : X^\bullet \to \mathrm{E}X^\bullet and the difference operator \mathrm{D} : X^\bullet \to \mathrm{E}X^\bullet.  The operators \mathrm{E} and \mathrm{D} act on propositions in X^\bullet, that is, propositions of the form f : X \to \mathbb{B} which amount to propositions about the subject matter of X, and they produce propositions of the form \mathrm{E}f, \mathrm{D}f : \mathrm{E}X \to \mathbb{B} which amount to propositions about specified collections of changes conceivably occurring in X.

At this point we find ourselves in need of visual representations, suitable arrays of concrete pictures to anchor our more earthy intuitions and help us keep our wits about us as we venture into ever more rarefied airs of abstraction.

One good picture comes to us by way of the field concept.  Given a space X, a field of a specified type Y over X is formed by associating with each point of X an object of type Y.  If that sounds like the same thing as a function from X to the space of things of type Y — it is nothing but — and yet it does seem helpful to vary the mental images and take advantage of the figures of speech most naturally springing to mind under the emblem of the field idea.

In the field picture a proposition f : X \to \mathbb{B} becomes a scalar field, that is, a field of values in \mathbb{B}.

For example, consider the logical conjunction pq : X \to \mathbb{B} shown in the following venn diagram.

Conjunction pq : X → B
\text{Conjunction}~ pq : X \to \mathbb{B}

Each of the operators \mathrm{E}, \mathrm{D} : X^\bullet \to \mathrm{E}X^\bullet takes us from considering propositions f : X \to \mathbb{B}, here viewed as scalar fields over X, to considering the corresponding differential fields over X, analogous to what in real analysis are usually called vector fields over X.

Resources

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Differential Logic • 13

Posted on February 27, 2026 by Jon Awbrey

Transforms Expanded over Ordinary and Differential Variables

Two views of how the difference operator \mathrm{D} acts on the set of sixteen functions f : \mathbb{B} \times \mathbb{B} \to \mathbb{B} are shown below.  Table A5 shows the expansion of \mathrm{D}f over the set \{ p, q \} of ordinary variables and Table A6 shows the expansion of \mathrm{D}f over the set \{ \mathrm{d}p, \mathrm{d}q \} of differential variables.

Difference Map Expanded over Ordinary Variables

\text{Table A5.}~ \mathrm{D}f ~\text{Expanded over Ordinary Variables}~ \{ p, q \}

Df Expanded over Ordinary Variables {p, q}

Difference Map Expanded over Differential Variables

\text{Table A6.}~ \mathrm{D}f ~\text{Expanded over Differential Variables}~ \{ \mathrm{d}p, \mathrm{d}q \}

Df Expanded over Differential Variables {dp, dq}

Resources

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Differential Logic • 12

Posted on February 26, 2026 by Jon Awbrey

Transforms Expanded over Ordinary and Differential Variables

A first view of how the shift operator \mathrm{E} acts on the set of sixteen functions f : \mathbb{B} \times \mathbb{B} \to \mathbb{B} was provided by Table A3 in the previous post, expanding the expressions of \mathrm{E}f over the set \{ p, q \} of ordinary variables.

A complementary view of the same material is provided by Table 4 below, this time expanding the expressions of \mathrm{E}f over the set \{ \mathrm{d}p, \mathrm{d}q \} of differential variables.

Enlargement Map Expanded over Differential Variables

\text{Table A4.}~ \mathrm{E}f ~\text{Expanded over Differential Variables}~ \{ \mathrm{d}p, \mathrm{d}q \}

Ef Expanded over Differential Variables {dp, dq}

Resources

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cc: Research Gate • Structural Modeling • Systems Science • Syscoi

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Change, Cybernetics, Differential Calculus, Differential Logic, Discrete Dynamics, Equational Inference, Functional Logic, Gradient Descent, Graph Theory, Inquiry Driven Systems, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Propositional Calculus, Time, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , | 2 Comments