antlerboy - Benjamin P Taylor 11:20 am on February 23, 2026

Systems Thinking: Unraveling Conway’s Law – Francois Trudel in the Systems Thinking Network group on LinkedIn

As I just posted in that group:

Systems Thinking network is weird and wild again!

Blimey. I just went through and approved a massive backlog of posts – all of us administrators of this group (speaking for myself anyway) are a bit benevolently negligent.

It feels a bit as though we are back to ‘the good (?) old days’ of lots of wide-ranging stuff being posted here – perhaps fewer discussions, but I feel a change in the LinkedIn algorithm and it seems more of this kind of natural content is back.

what can it mean?!

François Trudel

Senior Software Engineer | Technical Leader.

February 16, 2026

Systems Thinking: Unraveling Conway’s Law

François Trudel
Senior Software Engineer | Technical Leader.

February 16, 2026
(8) Systems Thinking: Unraveling Conway’s Law | LinkedIn

https://www.linkedin.com/pulse/systems-thinking-unraveling-conways-law-fran%25C3%25A7ois-trudel-qe7le/?trackingId=J%2BH%2BaaIeCtb%2FYB6xpLGtYA%3D%3D

antlerboy - Benjamin P Taylor 11:14 am on February 23, 2026

Launch of a new 𝐄𝐱𝐞𝐜𝐮𝐭𝐢𝐯𝐞 𝐃𝐁𝐀 (𝐋𝐞𝐚𝐝𝐞𝐫𝐬𝐡𝐢𝐩, 𝐒𝐮𝐬𝐭𝐚𝐢𝐧𝐚𝐛𝐢𝐥𝐢𝐭𝐲 𝐚𝐧𝐝 𝐒𝐲𝐬𝐭𝐞𝐦𝐢𝐜 𝐓𝐫𝐚𝐧𝐬𝐟𝐨𝐫𝐦𝐚𝐭𝐢𝐨𝐧) at Kemmy Business School, University of Limerick, Ireland.

Posted by Catriona Burke in the Systems Thinking Network group on LinkedIn

https://www.linkedin.com/feed/update/urn:li:activity:7431729420882632704/?utm_source=share&utm_medium=member_desktop&rcm=ACoAAAGCu-gBqvreuMwCuzuEH5SCA4-Fww8NZ9A

Senior leaders today operate at the intersection of 𝐦𝐮𝐥𝐭𝐢𝐩𝐥𝐞, 𝐢𝐧𝐭𝐞𝐫𝐚𝐜𝐭𝐢𝐧𝐠 𝐜𝐫𝐢𝐬𝐞𝐬: 𝐜𝐥𝐢𝐦𝐚𝐭𝐞 𝐭𝐫𝐚𝐧𝐬𝐢𝐭𝐢𝐨𝐧, 𝐠𝐞𝐨𝐩𝐨𝐥𝐢𝐭𝐢𝐜𝐚𝐥 𝐢𝐧𝐬𝐭𝐚𝐛𝐢𝐥𝐢𝐭𝐲, 𝐭𝐞𝐜𝐡𝐧𝐨𝐥𝐨𝐠𝐢𝐜𝐚𝐥 𝐝𝐢𝐬𝐫𝐮𝐩𝐭𝐢𝐨𝐧, 𝐢𝐧𝐬𝐭𝐢𝐭𝐮𝐭𝐢𝐨𝐧𝐚𝐥 𝐟𝐫𝐚𝐠𝐢𝐥𝐢𝐭𝐲 𝐚𝐧𝐝 𝐚𝐜𝐜𝐞𝐥𝐞𝐫𝐚𝐭𝐢𝐧𝐠 𝐬𝐨𝐜𝐢𝐚𝐥 𝐞𝐱𝐩𝐞𝐜𝐭𝐚𝐭𝐢𝐨𝐧𝐬. These conditions are systemic, contested, emergent and deeply embedded. Optimisation approaches and linear, reductionist logic have extremely limited contributions to make in these contexts.

Following increasing calls globally for an alternative paradigm, after several years of design, consultation and engagement with leading international scholarship and practice, I am pleased, as Academic Director, to announce the launch of a new 𝐄𝐱𝐞𝐜𝐮𝐭𝐢𝐯𝐞 𝐃𝐁𝐀 (𝐋𝐞𝐚𝐝𝐞𝐫𝐬𝐡𝐢𝐩, 𝐒𝐮𝐬𝐭𝐚𝐢𝐧𝐚𝐛𝐢𝐥𝐢𝐭𝐲 𝐚𝐧𝐝 𝐒𝐲𝐬𝐭𝐞𝐦𝐢𝐜 𝐓𝐫𝐚𝐧𝐬𝐟𝐨𝐫𝐦𝐚𝐭𝐢𝐨𝐧) at Kemmy Business School, University of Limerick, Ireland.

This programme is built on a different premise: that 𝐥𝐞𝐚𝐝𝐞𝐫𝐬𝐡𝐢𝐩 in the 21st century 𝐫𝐞𝐪𝐮𝐢𝐫𝐞𝐬 𝐭𝐡𝐞 𝐜𝐚𝐩𝐚𝐜𝐢𝐭𝐲 𝐭𝐨 𝐧𝐚𝐯𝐢𝐠𝐚𝐭𝐞, 𝐢𝐧𝐭𝐞𝐫𝐯𝐞𝐧𝐞 𝐢𝐧, 𝐚𝐧𝐝 𝐫𝐞𝐬𝐡𝐚𝐩𝐞 𝐜𝐨𝐦𝐩𝐥𝐞𝐱 𝐬𝐲𝐬𝐭𝐞𝐦𝐬. 𝐒𝐲𝐬𝐭𝐞𝐦𝐬 𝐭𝐡𝐢𝐧𝐤𝐢𝐧𝐠 𝐭𝐡𝐞𝐫𝐞𝐟𝐨𝐫𝐞 𝐬𝐢𝐭𝐬 𝐚𝐭 𝐭𝐡𝐞 𝐜𝐨𝐫𝐞 𝐨𝐟 𝐭𝐡𝐞 𝐩𝐫𝐨𝐠𝐫𝐚𝐦𝐦𝐞’𝐬 𝐢𝐧𝐭𝐞𝐥𝐥𝐞𝐜𝐭𝐮𝐚𝐥 𝐚𝐫𝐜𝐡𝐢𝐭𝐞𝐜𝐭𝐮𝐫𝐞.

The design furthermore brings into deliberate relationship four elements:
• The senior leader as practitioner-scholar, operating with real authority and responsibility
• A high-stakes complex phenomenon embedded in the leader’s context
• Cutting-edge knowledge frontiers spanning disciplines and epistemologies
• Advanced research mastery enabling rigorous, reflexive, transdisciplinary inquiry

Together, these enable the creation of knowledge that is simultaneously academically robust, practically consequential, and societally relevant.
━━━━━━━━━━━━━━━━━━
🎓 Programme Structure for Senior Leaders
━━━━━━━━━━━━━━━━━━
🏛️ Immersive residencies – Intensive week-long sessions per taught semester (4 in total)
🌍 Leadership Summits – Dialogue with global thought leaders and peers (3 in total)
🤝 A global learning ecosystem – Sustained intellectual and practical support
🌐 Research focus – A complex organisational or societal phenomenon privileging actionable knowledge and real world impact
👥 Cohort – Exclusively experienced senior leaders across sectors

It is a doctorate designed for leaders who 𝐢𝐧𝐭𝐞𝐧𝐝 𝐭𝐨 𝐬𝐡𝐚𝐩𝐞 𝐭𝐡𝐞 𝐟𝐮𝐭𝐮𝐫𝐞, not merely adapt to it. We welcome enquiries from senior leaders prepared to undertake demanding intellectual work in pursuit of 𝐦𝐞𝐚𝐧𝐢𝐧𝐠𝐟𝐮𝐥 𝐨𝐫𝐠𝐚𝐧𝐢𝐬𝐚𝐭𝐢𝐨𝐧𝐚𝐥 𝐚𝐧𝐝 𝐬𝐨𝐜𝐢𝐞𝐭𝐚𝐥 𝐢𝐦𝐩𝐚𝐜𝐭.

📄 Programme brochure: https://bit.ly/4axBjpb
📩 𝐃𝐢𝐫𝐞𝐜𝐭 𝐞𝐧𝐪𝐮𝐢𝐫𝐢𝐞𝐬: 𝐜𝐚𝐭𝐫𝐢𝐨𝐧𝐚.𝐛𝐮𝐫𝐤𝐞@𝐮𝐥.𝐢𝐞
Post | Feed | LinkedIn

https://www.linkedin.com/feed/update/urn:li:activity:7431729420882632704/?utm_source=share&utm_medium=member_desktop&rcm=ACoAAAGCu-gBqvreuMwCuzuEH5SCA4-Fww8NZ9A

antlerboy - Benjamin P Taylor 8:10 am on February 23, 2026

Is China a cybernetics-systems miracale or nightmare? Shared by Örsan Şenalp in The Ecology of Systems Thinking group on Facebook

https://www.facebook.com/groups/ecologyofsystemsthinking/?multi_permalinks=25925964837055982&notif_id=1771795392605445&notif_t=group_activity&ref=notif

DYLAN LEVI KING OCTOBER 17, 2022 ARTICLES
The Genealogy of Chinese Cybernetics
The Genealogy of Chinese Cybernetics

https://www.palladiummag.com/2022/10/17/the-genealogy-of-chinese-cybernetics/?fbclid=IwY2xjawQJMKNleHRuA2FlbQIxMQBicmlkETJhVlFEbmdGNTVxSzdiYnRmc3J0YwZhcHBfaWQQMjIyMDM5MTc4ODIwMDg5MgABHiIOb-sh28JR-0Q3saUWCoEg6bohw-W5mLvhbSoaciKDJqH7CtPJlLWk1-5z_aem_48Gxk0x0gEAI7jnZbAYBDA

The Critical Legacy of Chinese Cybernetics

https://www.combinationsmag.com/the-critical-legacy-of-chinese-cybernetics/?fbclid=IwY2xjawQJMKVleHRuA2FlbQIxMABicmlkETJhVlFEbmdGNTVxSzdiYnRmc3J0YwZhcHBfaWQQMjIyMDM5MTc4ODIwMDg5MgABHpxybfDgakKcgMIk0zcSYF0Q5Q7AdCjelfJf-_fxSvFDAlzDAba5KmxAm58E_aem_m3WQedDtm970BXhJtO6-2g

Five Moments in the History of Chinese Cybernetics

https://thereader.mitpress.mit.edu/five-moments-in-the-history-of-chinese-cybernetics/?fbclid=IwY2xjawQJMKZleHRuA2FlbQIxMABicmlkETJhVlFEbmdGNTVxSzdiYnRmc3J0YwZhcHBfaWQQMjIyMDM5MTc4ODIwMDg5MgABHqdWCBdDrsGS1D2QQcjXzbLzlEfRWnKdYJiZN30Td6fWbgR7vTbmoeSavCov_aem_wS3wYoRBlTwRfUPlXS6wqw

Jon Awbrey 11:20 am on February 21, 2026
Tags: Amphecks ( 25 ), Animata ( 27 ), Boolean Algebra ( 25 ), Boolean Functions ( 26 ), C.S. Peirce ( 56 ), Cactus Graphs ( 26 ), Change ( 22 ), cybernetics ( 35 ), Differential Calculus ( 22 ), Differential Logic ( 26 ), Discrete Dynamics ( 22 ), Equational Inference ( 24 ), Functional Logic ( 23 ), Gradient Descent ( 21 ), Graph Theory ( 28 ), Inquiry Driven Systems ( 33 ), logic ( 58 ), Logical Graphs ( 27 ), Mathematics ( 56 ), Minimal Negation Operators ( 26 ), Propositional Calculus ( 26 ), Time ( 21 ), Visualization ( 38 )

Differential Logic • 9

Propositional Forms on Two Variables

Table A2 arranges the propositional forms on two variables according to another plan, sorting propositions with similar shapes into seven subclasses. Thereby hangs many a tale, to be told in time.

$\text{Table A2. Propositional Forms on Two Variables}$

Resources

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

#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

antlerboy - Benjamin P Taylor 6:01 am on February 21, 2026

When Does a System Exist? The Myth of the Given System – Jose, 2026

In today’s post, I want to look at a question that seems almost too simple to ask: when does a system exist? For this I will be drawing on ideas from…
When Does a System Exist? The Myth of the Given System:

Dr. Steffen Roth 9:48 am on February 20, 2026

Event | Wolfson Tool Factory in Cambridge (April 2026)

Event | Wolfson Tool Factory

Barbara Schmidt-Abbey 7:36 pm on February 19, 2026

European Evaluation Society (EES): Call for Proposals open for 16th biennial conference: Evaluation for Vibrant Democracies (16-30 October 2026), Lille, France

This may be of interest to those working at the intersection of ‘systems’ and ‘evaluation’ and/or public policy: the Call for Abstracts for hashtag#EES2026 is now open: https://lnkd.in/dNieqnzz
Submissions are accepted until 31 March 2026. The conference takes place in Lille (France), 26-30 October 2026.

Do consider submitting an abstract to share relevant work with the evaluation community gathering there.

Since 2025, EES has been a member organisation in the IFSR, and relevant contributions from the ‘systems’ field to the conference are very welcome and desired! One of the main themes of the conference is “Systemic Learning: Complex societal challenges demand more than isolated interventions. Therefore, this conference will allow us to explore system-level approaches that drive transformational change, and how evaluators can navigate complexity while maintaining accountability and learning, which is critical to healthy democracies.”

Several accepted strands may align with your proposals, including one from EES’ Thematic Working Group on ‘systems approaches in evaluation’.

More information also here.

Go to ‘Call B’ to submit proposals.

It would be great to see many participants joining from the systems community, for further cross-fertilization between these two meta- and transdisciplines, who can mutually benefit from learning from and with each other, and join forces.

hashtag#EES

hashtag#EESTWG8

hashtag#systemicevaluation

antlerboy - Benjamin P Taylor 3:14 pm on February 19, 2026

Unlocking the Real OODA Loop: Cybernetics, AI, and Epstein’s Hidden Connections – No Way Out -The OODA Loop and Flow Podcast

No Way Out -The OODA Loop and Flow Podcast

Unlocking the Real OODA Loop: Cybernetics, AI, and Epstein’s Hidden Connections – YouTube

audio link

https://nowayout.buzzsprout.com/2109174/episodes/18709202-unlocking-the-real-ooda-loop-cybernetics-ai-and-epstein-s-hidden-connections

Jon Awbrey 3:45 pm on February 18, 2026
Tags: Amphecks ( 25 ), Animata ( 27 ), Boolean Algebra ( 25 ), Boolean Functions ( 26 ), C.S. Peirce ( 56 ), Cactus Graphs ( 26 ), Change ( 22 ), cybernetics ( 35 ), Differential Calculus ( 22 ), Differential Logic ( 26 ), Discrete Dynamics ( 22 ), Equational Inference ( 24 ), Functional Logic ( 23 ), Gradient Descent ( 21 ), Graph Theory ( 28 ), Inquiry Driven Systems ( 33 ), logic ( 58 ), Logical Graphs ( 27 ), Mathematics ( 56 ), Minimal Negation Operators ( 26 ), Propositional Calculus ( 26 ), Time ( 21 ), Visualization ( 38 )

Differential Logic • 8

Propositional Forms on Two Variables

To broaden our experience with simple examples, let’s examine the sixteen functions of concrete type $P \times Q \to \mathbb{B}$ and abstract type $\mathbb{B} \times \mathbb{B} \to \mathbb{B}.$ Our inquiry into the differential aspects of logical conjunction will pay dividends as we study the actions of $\mathrm{E}$ and $\mathrm{D}$ on this family of forms.

Table A1 arranges the propositional forms on two variables in a convenient order, giving equivalent expressions for each boolean function in several systems of notation.

$\text{Table A1. Propositional Forms on Two Variables}$

Resources

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

antlerboy - Benjamin P Taylor 5:15 am on February 17, 2026

Problematique Dialogue + Conversation as Process and Connection | Systems Thinking Ontario | 20260209

February 16, 2026 daviding

Problematique Dialogue + Conversation as Process and Connection | Systems Thinking Ontario | 20260209
February 16, 2026 daviding
Problematique Dialogue + Conversation as Process and Connection |… – Coevolving Innovations

Problematique Dialogue + Conversation as Process and Connection | Systems Thinking Ontario | 20260209

antlerboy - Benjamin P Taylor 4:06 am on February 17, 2026

Harish’s Notebook: When the Map Becomes More Coherent Than the Territory – Jose (2026)

When the Map Becomes More Coherent Than the Territory:

antlerboy - Benjamin P Taylor 3:09 am on February 17, 2026

a new home for Krishan Mathis’ Viability Canvas at Tautai Salon

VSM and Viablity Canvas
now at https://salon.tautai.net/
VSM and Viablity Canvas

https://companion.tautai.net/docs/vsm-viability-canvas

antlerboy - Benjamin P Taylor 3:56 pm on February 16, 2026

NEEDED: SYSTEMS THINKING IN PUBLIC AFFAIRS – Conway (2024)

h/t Ivo Velitchkov

Introduction

What is systems thinking? The answer depends on whom you ask. Here are two commonperspectives from which you will get two different answers. Engineering. Here, systems thinking is what you need to build a system whose requirements go beyond current practice. Example: all stages in a plan to evolve into a national energy distribution system for low-emission transportation. Metapolitics (a neologism analogous to metamathematics). Here, systems thinking is what you need (1)to understand the ambient social systems in which we all have unconsciously long been embedded, and (2)to use that understanding to attempt to bring these systems into alignment with current needs, given some disruptive change such as newtechnology or increased scale. Example: modifying the global economy in response to climate change.

This essay is based on the Metapolitics perspective. In two Examples I explore perverse behavior patterns of two ambient social systems, a newoneandanolder one: 1. mass radicalization, disinformation, and other perverse social consequences secondary to new technologies that facilitate intensive everyone-to-everyone communication (for example, “social networking”), and 2. environmental destruction secondary to a compulsion to grow arising from the financing structures of public corporations. Analysis of both of these behavior patterns reveals a common element: Emergent behaviors, not anticipated in classical thinking, arise from highly intraconnected or coupled networks. This failure of classical thought leads to The Big Lesson I wish to communicate in this essay: THINK NETWORKSFIRST, ACTORS SECOND. Here is the importance of this lesson: Effective interventions will arise from altering interactions within networks. You cannot even see these interactions unless you focus on the network. This essay offers two examples that contradict the conventional understanding of Network Effects. We are living inside something we don’t understand.

Click to access ty.pdf

antlerboy - Benjamin P Taylor 6:22 pm on February 15, 2026

Peter Tuddenham on LinkedIn – mapping Claude’s eight conversation surfaces through the lens of Gordon Pask’s conversation theory

Peter writes:

“I’ve spent 40 years applying cybernetic frameworks to real organisations — from the U.S. Army War College to UNESCO to distributed educator networks spanning 18,000 participants. Recently, I’ve been working intensively with Claude (Anthropic’s AI), and something struck me: every interface Claude offers is a different kind of conversation, with different affordances and different costs.
So I wrote a practitioner’s guide mapping Claude’s eight conversation surfaces through the lens of Gordon Pask’s Conversation Theory (1975, 1976).
The core insight: every time you switch from chat to Claude Code, or from a Project to an Artifact, you’re not just changing tools — you’re changing the structure of the conversation itself. And that structure determines what kind of knowing is possible.
The guide introduces what I call the “re-education tax” — the real cost of re-establishing shared understanding when you switch surfaces or start fresh sessions. If you’ve ever felt frustrated explaining context to an AI again after switching tools, you’ve been paying this tax without naming it.”
(2) Post | LinkedIn

https://www.linkedin.com/posts/peterdtuddenham_claude-conversation-surfaces-a-practitioners-ugcPost-7425557491205246978-MB9C/?utm_source=share&utm_medium=member_desktop&rcm=ACoAAACuq-oBecVFDW6PCf3lkoG-peMeuLBeoho

Jon Awbrey 5:15 pm on February 15, 2026
Tags: Amphecks ( 25 ), Animata ( 27 ), Boolean Algebra ( 25 ), Boolean Functions ( 26 ), C.S. Peirce ( 56 ), Cactus Graphs ( 26 ), Change ( 22 ), cybernetics ( 35 ), Differential Calculus ( 22 ), Differential Logic ( 26 ), Discrete Dynamics ( 22 ), Equational Inference ( 24 ), Functional Logic ( 23 ), Gradient Descent ( 21 ), Graph Theory ( 28 ), Inquiry Driven Systems ( 33 ), logic ( 58 ), Logical Graphs ( 27 ), Mathematics ( 56 ), Minimal Negation Operators ( 26 ), Propositional Calculus ( 26 ), Time ( 21 ), Visualization ( 38 )

Differential Logic • 7

Differential Expansions of Propositions

Panoptic View • Enlargement Maps

The enlargement or shift operator $\mathrm{E}$ exhibits a wealth of interesting and useful properties in its own right, so it pays to examine a few of the more salient features playing out on the surface of our initial example, $f(p, q) = pq.$

A suitably generic definition of the extended universe of discourse is afforded by the following set‑up.

$\begin{array}{cccl} \text{Let} & X & = & X_1 \times \ldots \times X_k. \\[6pt] \text{Let} & \mathrm{d}X & = & \mathrm{d}X_1 \times \ldots \times \mathrm{d}X_k. \\[6pt] \text{Then} & \mathrm{E}X & = & X \times \mathrm{d}X \\[6pt] & & = & X_1 \times \ldots \times X_k ~\times~ \mathrm{d}X_1 \times \ldots \times \mathrm{d}X_k \end{array}$

For a proposition of the form $f : X_1 \times \ldots \times X_k \to \mathbb{B},$ the (first order) enlargement of $f$ is the proposition $\mathrm{E}f : \mathrm{E}X \to \mathbb{B}$ defined by the following equation.

$\mathrm{E}f(x_1, \ldots, x_k, \mathrm{d}x_1, \ldots, \mathrm{d}x_k) ~=~ f(x_1 + \mathrm{d}x_1, \ldots, x_k + \mathrm{d}x_k) ~=~ f(\texttt{(} x_1 \texttt{,} \mathrm{d}x_1 \texttt{)}, \ldots, \texttt{(} x_k \texttt{,} \mathrm{d}x_k \texttt{)})$

The differential variables $\mathrm{d}x_j$ are boolean variables of the same type as the ordinary variables $x_j.$ Although it is conventional to distinguish the (first order) differential variables with the operational prefix $``\mathrm{d}",$ that way of notating differential variables is entirely optional. It is their existence in particular relations to the initial variables, not their names, which defines them as differential variables.

In the example of logical conjunction, $f(p, q) = pq,$ the enlargement $\mathrm{E}f$ is formulated as follows.

$\begin{matrix} \mathrm{E}f(p, q, \mathrm{d}p, \mathrm{d}q) & = & (p + \mathrm{d}p)(q + \mathrm{d}q) & = & \texttt{(} p \texttt{,} \mathrm{d}p \texttt{)(} q \texttt{,} \mathrm{d}q \texttt{)} \end{matrix}$

Given that the above expression uses nothing more than the boolean ring operations of addition and multiplication, it is permissible to “multiply things out” in the usual manner to arrive at the following result.

$\begin{matrix} \mathrm{E}f(p, q, \mathrm{d}p, \mathrm{d}q) & = & p~q & + & p~\mathrm{d}q & + & q~\mathrm{d}p & + & \mathrm{d}p~\mathrm{d}q \end{matrix}$

To understand what the enlarged or shifted proposition means in logical terms, it serves to go back and analyze the above expression for $\mathrm{E}f$ in the same way we did for $\mathrm{D}f.$ To that end, the value of $\mathrm{E}f_x$ at each $x \in X$ may be computed in graphical fashion as shown below.

Collating the data of that analysis yields a boolean expansion or disjunctive normal form (DNF) equivalent to the enlarged proposition $\mathrm{E}f.$

$\begin{matrix} \mathrm{E}f & = & pq \cdot \mathrm{E}f_{pq} & + & p(q) \cdot \mathrm{E}f_{p(q)} & + & (p)q \cdot \mathrm{E}f_{(p)q} & + & (p)(q) \cdot \mathrm{E}f_{(p)(q)} \end{matrix}$

Here is a summary of the result, illustrated by means of a digraph picture, where the “no change” element $\texttt{(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)}$ is drawn as a loop at the point $p~q.$

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

We may understand the enlarged proposition $\mathrm{E}f$ as telling us all the ways of reaching a model of the proposition $f$ from the points of the universe $X.$