Proof-Systems

Yesterday I explored how proof trees and machine learning can work together. Today, let’s get practical: how do you actually build these hybrid declarative systems? Back in 2012, I built a proof of concept for medical software that tracked drug interactions, advised on dosage, and provided decision support that human doctors could review. It was a glimpse into what’s now becoming mainstream. Here’s how I’d build it now. The Four-Layer Architecture Think of a hybrid declarative system like a brain with specialized regions that collaborate: ...

In my previous article, I explored proof trees: how declarative languages like Prolog break down questions into smaller steps until they can be answered with known facts. It’s structured, logical, and explainable. But it also has a weakness: proof trees need perfect information. If a fact is missing or noisy, the tree collapses. Machine learning has the opposite strengths and weaknesses. ML thrives in messy environments (images, speech, incomplete data), but its reasoning is often a black box. You get an answer, but not much of a “why.” ...

Most programming feels like giving detailed instructions to a very literal assistant. You write if-else conditions, call functions in sequence, and manage state step by step. This is imperative programming — you tell the computer exactly how to solve your problem. By contrast, declarative programming is about stating what you want rather than how to do it. It’s like the difference between giving turn-by-turn directions versus simply stating your destination and letting the GPS choose the route. ...