Logics, Formalisms, Languages, and Applications

The purpose of this Zettel is to try and define some of the categories of things we are talking about, here, and maybe help draw boundaries around some of the tags that we’re using to organize them.

I am not a programming language expert, so this is my novice understanding of what we’re talking about. Some of these concepts are pretty clearly distinct from one another, and some overlap heavily.

What is a “Logic”?

A “logic” is a strict way of writing things down, where if the things you write down are true, and you follow the derivation rules, you can generate new statements that you can be confident are also true.

There are a lot of different logics out there, each with their own sets of rules that you can use to generate new knowledge from the knowledge you already have. They are designed for different functions, and some of them are designed specifically for computation, like lambda calculus.

What is a Programming Language?

A programming language is a strict way of writing things down where there is a piece of software that can take that writing and turn it into a set of instructions that will accomplish the things that the language allows for.

So, a programming language is a logic, plus a way of writing that logic so that the computer can read it, and can do the derivations for you. Most popular programming languages implement lambda calculus, and computations get described as functions.

In declarative logic programming, the logic implemented by the programming langauge may be something more like predicate logic, or modal logic, or defeasible logic, and the computations get described as sets of rules, or a set of rules with modes, or a set of rules and exceptions to those rules.

(See the following list for languages that have an entry in this zettelkasten.)

What is a “Formalism”?

A formalism is any strict way of writing things down. A logic is a formalism. A programming languages is a formalism. But if you have a strict way of saying things, and no rules that can be implemented by a computer or a person in order to derive new statements, then your formalism isn’t a logic.

And if it gives you a strict way of writing things down for use in a computer, but there is no way to take what you have written down and generate new information from it, then it is not a programming language.

As an example, LegalRuleML# allows you to write down, in a strictly formalized way, statements of law. But the LegalRuleML standard explicitly states that there is no semantic meaning applied to those statements. You can’t build a LegalRuleML compiler, because there is no logic to implement.

Now, you can take LegalRuleML, and you can convert it into very similar statements in, for example, deontic modal logic. And you can run a deontic modal reasoner on those statements and generate new information. You might also be able to automatically convert from LegalRuleML into that deontic modal langauge, effectively making it possible to execute statements written in LegalRuleML. Now is it a programming language?

Yeah. Because you created a set of rules for taking statements (LegalRuleML) and turning them into new statements (deontic modal logic code). Then you automated them. So you have turned LegalRuleML into a programming langauge.

What is an Application?

Is Microsoft Word an application? Yes. Is it a programming tool? Well, it is analogous to an integrated development environment for writing the XML code that is used to describe word documents. And that XML code can be used to generate new information, for example PDF code that describes the same document. So there is a formalism, and there is a logic, and it automatically generates new information. By the definition above, DOCX, at least, is a programming language, and Microsoft Word is a programming tool.

If that seems intuitively wrong, it may be because of misconceptions we have about programming. Specifically, that it’s supposed to be hard, and it’s supposed to be general purpose.

Not so. And if we let ourselves draw a hard/easy or general/specific distinction between a programming language and an application, and conceive of what we are building as a programming langauge, we give ourselves an excuse for building things that are unnecessarily hard and complicated.

So for our purposes, I think things that are stereotypical programming languages, like ErgoAI / ErgoLite#, and things that are visual tools like Neota Logic#, should be in the same main category: tools.