Understanding Intensional vs. Extensional models in AI and Decision Intelligence

In automated and augmented decision making, two types of models stand apart: intensional models, which distill rules from reality, and extensional models, which generate new data by simulating scenarios using techniques like causal AI and digital twins. Intensional models, which can be created through mechanisms like Randomized Controlled Trials, statistical pattern recognition, and machine learning, extract patterns from detailed observations. In contrast, extensional models work in the opposite direction: they create new data from hypothetical worlds by simulating the mechanisms behind them.

The intensional/extensional distinction comes from philosophy and mathematics, which says that a set of objects can be defined extensionally as a list of values, or intensionally as a rule that characterizes those which are “in and out”. Intensional representations are much more compact, but through their compactness they lose information.

Take machine learning, for example, where a model is built from large datasets—like predicting customer behavior based on past sales. An intensional model consists of rules extracted from reality, offering insights rooted in observed patterns (e.g. “customers who spend less than $12 a month are less likely to keep their subscription than those who spend more than $100 a month”). In contrast, consider a supply chain simulation. Here, an extensional model generates data by simulating how products flow through a system, forecasting outcomes based on the mechanisms at play. While one draws from what has happened, the other creates new possibilities by simulating what could happen in novel situations.

The complementary relationship between intensional and extensional models

Intensional models have a key limitation: they rely on historical data. If circumstances shift—new trends emerge or disruptions occur—these models can become outdated, unable to account for changes they haven’t seen before. For example, a model (or even a simple policy) used by a farmer to decide what crop to plant may become obsolete if the average winter temperature changes. But how, exactly, should the model change? If all of the experience that the farmer and his ancestors used to create a model or policy is now obsolete, then so is the model or policy.

As a general rule, intensional models are brittle to changes in external conditions in this way.

Extensional models, however, are different. By simulating systems and their underlying mechanisms, they can explore scenarios that have never happened. This ability to model the unknown makes extensional models crucial when facing uncertainty, where relying on the past is no longer enough. I described extensional digital twins and their relationship to DI in this recent article.

While extensional models excel at generating data for new scenarios, they come with their own challenge: the sheer volume of data they produce. This flood of information can be overwhelming. That’s where intensional models come back into play. By summarizing and distilling this vast data into manageable insights, intensional models provide piecewise components that can be used within extensional models. Intensional methods can also be used to capture rules and patterns from simulation-generated data, thereby identifying systematic emergent patterns.

Together, these two approaches give us the best of both worlds: the ability to simulate new possibilities while retaining the power to extract meaningful, actionable patterns in novel situations.

The meaning of “Decision Intelligence” has changed through the years: from extensional only to a combination of intensional and extensional

In 2008, after nearly two decades of delivering applied machine learning through intensional models, and interviewing decision makers as a technology analyst, I came to a surprising realization. Despite their applicability, analytic and AI models weren’t being used on any widespread basis by decision makers. Through dozens of interviews described in this report, and as articulated in more detail in in this one, Mark Zangari and I discovered that decision makers were doing extensional simulations “in their heads”, imagining the impact of their actions on the outcomes they cared about. When careful reasoning was called for, decision makers were essentially running mental simulations of extensional models.

This cognitive mismatch: decision makers thinking about actions and outcomes extensionally, while data scientists were delivering intensional models with missing actions and outcomes–explained a lot about why data and ML was being systematically underutilized by non-technical experts.

Around 2012, Mark and I decided to rename our emerging formulation “Decision Intelligence” instead of “Decision Engineering”. As you can read in those early reports, and as articulated in my first Decision Intelligence book and extended in The Decision Intelligence Handbook with my colleague N.E Malcolm, the heart of the original DI formulation was the extensional modeling approach we captured in our causal decision diagram (CDD)—a framework that filled an important gap, linking actions to outcomes through a complex systems diagram. It also included a process for eliciting these diagrams from nontechnical decision makers—an exercise made more “natural” since our diagrams were designed to match—as much as possible—the “mental simulation” that decision makers were already performing.

In the years that followed, we realized that causal decision diagrams could integrate intensional models—like machine learning, randomized control trials, and other patterns derived from historical data—into their framework. When making decisions, people often rely on their knowledge of similar past situations, drawing on patterns they can articulate. But with machine learning, we can also uncover patterns that may be harder for humans to recognize or explain. Decision intelligence, therefore, embraces a “kitchen sink” kind of approach, combining multiple types of models. It allows us to leverage the backward-facing power of intensional models while harnessing the flexibility of extensional models. This fusion enables us to create adaptable frameworks capable of addressing complex, ever-changing situations where traditional training data may not exist, and machine learning alone would fall short.

But lately, the situation has been getting a bit muddy.

The term “decision intelligence” originally referred in our work only to action-to-outcome extensional models. However, the DI name “left the lab”: many vendors started using the term “decision intelligence” to describe intensional approaches as well, like decision trees and machine learning. Fast forward to today, and now decision intelligence for many simply means using data, AI, and various technologies to support decision making. The Gartner group says that it’s an increasingly widely-used term, but that it is often not reflective of fundamentally new approaches.

Today, a critical distinction is often overlooked: decision intelligence can refer to either classification and conclusions in an intensional model, or—as we originally intended—it can mean using extensional models to map out causal structures from actions to outcomes, following our original formulation that we continue to deliver to customers today.

Keeping intensional and extensional benefits distinct

So where do we stand today? This broader use of the term “decision intelligence” has helped to bring attention to our work and expanded its reach. The newer definition, which encompasses data, business intelligence, and other technologies, does fit into the larger action-to-outcome puzzle of decision models.

However, we must not lose sight of the key distinction: within decision intelligence, there are two fundamentally different types of models—those that capture patterns from past data and those that generate new empirical data through simulation. Both are critical, both are powerful, and both are exciting. It’s essential to keep them distinct to maximize the synergies between them, and data / AI professionals need to understand their differing roles in supporting their customers.