Bill Wadge's Blog

Many years ago Ed Ashcroft and I invented the declarative language Lucid. It’s had an
interesting history.

To begin with, we never intended to design a dataflow language. All we wanted was
a more rigorously structured language which would make it easier to prove assertions
about programs.

I’d moved into computer science after leaving Berkeley and soon became convinced
that this new-fangled “structured programming” was the way to go. In fact I quickly became a real fanatic, convinced that not only did the goto statement have to go, but that even assignment statements caused trouble. My objection to assignments was that they looked like equations but were typically used in a way that defied the logic of equality. For example, early in a program you can have

I = 1

but later you can have

I = J*J+3

which contradicts the first equation. Even worse, you can have

I = I+1

which contradicts itself (because it implies 0=1). No wonder program proving is difficult!

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I don’t know if infinitesimal logic is the best idea I’ve ever had, but it’s definitely the best name.

So here’s the idea: a multivalued logic in which there are truth values that are not nearly as true as ‘standard’ truth, and others that are not nearly as false as ‘standard’ falsity.

An example should help. Suppose  you go to the travel agent and ask if if you can get a flight (1) to Ottawa and (2) in an aisle seat. If the agent says “yes” (meaning true in the standard sense), you’re done. However, if the agent says “no” (meaning false in the standard sense) you don’t know where you stand – maybe there is no flight to Ottawa, or maybe you just can’t get an aisle seat. You can always ask another question, but it would have been more helpful if the agent had given you some indication of the difficulty of flying to Ottawa in an aisle seat.

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