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.
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.
In a newly published piece by the Garrison Institute called The Inner Work of System Leadership my co-authors Peter Senge, Radha Ruparell and Hal Hamilton and I explore in depth the connection between inner work and outer change.
Coming 10 years after Peter, Hal and I published the popular leadership piece, The Dawn of System Leadership in Stanford Social Innovation Review, our new article elevates inner work for system leadership and highlights how the inner work of trauma healing is essential for system leaders but often goes unattended to for a myriad of reasons.
Engaging in trauma healing work helps leaders develop more capacity to see, acknowledge, and address historical, intergenerational, and collective trauma that resides in systems and impacts others. Without doing this work, system leaders will find transformational systems change to be elusive, if not impossible.
I invite you to read the new article and I welcome your responses. How important do you think it is for leaders to do their inner work and trauma healing work?
It’s a good piece and will deserve its popularity – but I think it lacks the real grit in the oyster.
Your question begs the question, doesn’t it?
“How important do you think it is for leaders to do their inner work and trauma healing work?” well, yes, put it that way – obviously, VERY important. It reminds me of a phrase I loved from the wave of sensemaking, metarational, new thinking podcasts just before and into COVID: ‘we’ll never create a world of holistic wellbeing from our broken states.
And I’m not against it. Of course it matters. No one wants leaders who are blind to themselves or others.
But that’s not quite the same as the stronger claim being smuggled in: that transforming systems begins with transforming ourselves.
And let me contrast two alternative statements:
‘deeply flawed, traumatised, broken, sometimes immoral people can achieve great good in the world – indeed, great good has never been done any other way’
‘it’s not doing the work on yourself that changes the world, it’s doing the work in the world that changes you’
Similar rhetorical devices, I fancy similar rhetorical power, but rather contrary meaning. I am crafting those sentences only for effect, but/and both feel closer to reality than a prefigurative ideal where better selves produce better systems.
I think the paper is blending very good and strong arguments and slipping in some untested and unchallenged assumptions.
A defensible claim:
‘The way we show up shapes the systems we are trying to change’
quietly becomes:
‘Inner work is essential for transformational systems change’
That leap isn’t evidenced, it’s asserted.
And it matters, because it risks narrowing the field of vision. You end up with a picture of systems change that centres on a fairly specific set of behaviours: openness, empathy, reflection, healing. All good things. But also a very WEIRD, middle-class slice of human possibility.
What drops out is power. Conflict. Dominance. Incentives. Enforcement. Violence. Anger. The fact that systems often work precisely because they constrain behaviour, not because people are aligned or healed.
There’s a long-standing tendency in systems thinking to slide into ‘if we could all just relate better, things would improve’. Sometimes true, especially in the room. But as a theory of change for large-scale systems, it’s thin.
Or more bluntly, as they used to say (about voting): if systems change could change things, it would be illegal.
That’s the gap I think this work is circling. A real and important insight – that inner state and outer system aren’t separate – alongside an underdeveloped account of how change actually happens when interests collide and power is at stake.
If we don’t face that directly, the space gets filled by something else – and, I observe, often a kind of bourgeois conspirituality: psychologically literate, ethically serious, but politically and operationally evasive. Spiritual bypassing, which is a form of complicity.
Inner work matters. But it’s not a substitute for a theory of power, or a method for acting in the world when things get rough. And without that, systems change stays safe, and therefore limited.
I encourage everyone to read the piece – and read it really critically, and to listen as a companion to the two parts of this podcast:
Thu, Mar 26th, 2026 10:30 – 11:45 EET WORKSHOP SCiO Finland All welcome
Date & Time Thu, Mar 26th, 2026 – 10:30 – 11:45 EET
Location This is an online event
Pricing Info Free
Languages spoken English
Access All welcome
We are at a critical juncture where traditional, hierarchical governance systems often struggle to navigate the complexities of the climate emergency and mounting social inequalities.
You are cordially invited to a special webinar launch event hosted by SCiO Finland to explore the findings of a recent systemic co-inquiry: “Understanding and Achieving Systemic Governance: Lessons from Finland”.
Finland is internationally recognised for its innovative “humble governance” and trust-based autonomy, yet these systemic approaches face significant challenges in becoming “sticky” within traditional bureaucratic structures. We will dive into:
Core Principles: Moving from government as a controller to an enabler. Scaling Learning: Why we should focus on scaling capability rather than just fixed solutions. The “Systems Mafia”: The vital role of informal networks in sustaining systemic change. Sustainability: How to institutionalise systemic ideas so they survive political cycles and economic pressures. In this session, authors Ray Ison (Professor Emeritus, The Open University) and Tim Logan (Partner, Good Impact Labs) will outline the key ideas from their research conducted in Finland between 2024 and 2025. The discussion will be moderated by Janne J. Korhonen.
Welcome to this webinar with Professor Emeritus Ray Ison, talking about how we can transform human activity systems towards a more improved human-biosphere agriculture. The webinar is hosted by SLU Global and ELLS . Please register below for zoom-link.
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.
TECHNICAL PAPER| MARCH 06 2026 A VSM governance tool and agricultural paradigm change for climate and ecology Angus Jenkinson
Author & Article Information Kybernetes 1–25. https://doi.org/10.1108/K-06-2025-1586 Article history Share Icon Share Get Permissions Cite Open Menu Purpose This study offers transformation pathways through the intersections of enterprise governance and farming in response to climate and ecological crises (COP21, COP28 et al.). The analysis further proposes Virtuoso as a novel integration capability for the Viable System Model (“VSM”), Stafford Beer’s systemic methodology for enterprise management (Beer, 1985; Jenkinson, 2022). It thereby contrasts farming models and their ways of seeing.
Very happy to share this paper I just published about different farming models and their impact on nature and climate (A VSM governance tool and agricultural paradigm change for climate and ecology). it shows how this relates to ways of seeing the world and managing a company or enterprise. This features the VSM, the viable system model developed by Stafford Beer, whose centennial is this year. It takes a deep look at identity as the guiding star and model.
But what really excites me is its illustration of the immense potential the right kind of farming has. The key to the life and economic health of the farm is soil management and that depends on understanding how to cherish it so that it will support farmer, food, and future.
You see the future is very bleak if farming does not get its act fully together, so I am delighted to showcase genuine best practice in the case study. The featured farm is sequestering around ten times more carbon than it emits
Farming has radically altered the planetary biosphere (Ellis et al., 2010). The IC model is a major contributor to global climate and biodiversity challenges through its degenerative cycle of soil degradation, input dependency, and declining resilience (Montgomery, 2017, 39–40, 80–81). BD demonstrates that economically sound, mitigation and regeneration is possible, exceeding UN COP21 soil organic carbon (“SOC”) targets, a key indicator of climate change (Gantlett, 2021, 2022, 2024, 2025). Virtuoso articulates their contrasting identities and operational logics, revealing latent potential for agriculture and the VSM.
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