A logical calculus of the ideas immanent in nervous activity

Inside the paper

The problem

How can the activity of a network of neurons be described precisely enough to reason about what it can do? The authors begin with simplified assumptions about neural firing and fixed connections, rather than a detailed biological simulation.

The idea

They express the firing of neurons as logical statements indexed by time. Networks then become objects whose possible behavior can be analyzed using logical operations and rules for connecting neurons.

How it works

• Each idealized neuron either fires or does not, and fires when enough excitatory inputs arrive unless an inhibitory input prevents it.
• Synaptic delay supplies discrete time steps, so a neuron’s activity can be related to earlier activity in connected neurons.
• Combine excitatory and inhibitory connections to construct networks corresponding to logical combinations of input events.
• Analyze networks with feedback separately, since their present behavior can depend on activity extending into the past.

What it showed

The paper develops correspondences between network behavior and logical expressions under its assumptions. It also discusses how different assumptions about neural details can yield networks with equivalent behavior, sometimes with different timing.

Read it for

Read the assumptions on paper page 118 and the construction examples around pages 121–122 first. The formal proofs and notation in the intervening pages reward a slower second pass; Section IV discusses consequences.

Written in our own words from the paper itself. A draft the editors have not yet reviewed.