Axiomatic System

An axiomatic system is a formal framework specified in a language (such as first-order logic) which sets out a set of axioms and inference rules that specifies an axiomatic theory.  An axiomatic theory is a body of knowledge (a.k.a. domain of understanding, area of knowledge, universe of discourse).  An axiomatic theory provides the groundwork for deductive reasoning.

A statement (a.k.a. proposition, claim, assertion, belief, idea, fact) is a declarative sentence (e.g. not a question, not a command, not an exclamation).  

An axiom (a.k.a. postulate, assumption) is a self-evident or commonly agreed upon statement that is taken to be true.  An axiom is excepted, it cannot be proven. But no exceptions or counter examples are known to have been found for the accepted axiom.  An axiom is fundamentally accepted as being true per the axiomatic system.

A theorem (a.k.a. proposition, deduction) is a declarative statement that has been proven or can be proven to be true through a structured process of reasoning, based on a set of accepted axioms, inference rules, or other previously proven theorems.

A model is an informative, well-defined, and correct representation of the set of things and relations defined within an axiomatic system. The existence of a concrete model proves the consistency of the axiomatic system. A model is determined to be concrete if the meanings assigned are things and relations from the real world.

I have used this axiomatic system approach to document a Logical Theory Describing Financial Report. You can take the axioms represented in that document and summarize the axioms into a list.  You can create a visualization of that same information.  You can also represent that same information in machine-interpretable form such as XBRL or RDF.

You can get an axiomatic system to perform work.  That work can be collaborative.  Machine work capabilities and human work capabilities can be combined, creating powerful aggregate work capabilities. Lighthouse projects can show the way. Complexity should be embraced.


If you put all the right pieces together in the right way you may be able to create something very useful.  What I want to create is a new approach to financial reporting. That is my axiomatic system.

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