The theory that all propositions can be analysed into simple independent elements of meaning corresponding to elements making up facts about the world. It formed part of the early thought of Wittgenstein and Bertrand Russell.
Starting with the technical side, we have seen that the adoption of predicate logic as the basis of reasoning can lead to logical atomism.
We should note that this is not exactly innocuous; ontologically, it amounts to some sort of logical atomism.
The contrast with Russell, who continued the main line of British empiricism, in terms of what might be called the standard analysis, logical atomism, couldn't be more stark.