XBRL-based structured digital financial reporting - Blog: Digital Financial Reporting (using XBRL)

Different domains such as philosophy, computer science, and knowledge engineering use different terminology to describe and discuss logic which can be quite confusing and make these things harder to understand. Below are the common fundamental terms that I came up with based on what others are using in an attempt to come up with a best practices summary of this terminology.

Logic is a set of principles that forms a framework for correct reasoning. Logic is a process of deducing information correctly. Logic is about the correct methods that can be used to prove a statement is true or false. Logic tells us exactly what is meant. Logic allows systems to be proven. Using logic information can be created that is understandable both to humans and to machines.

A logical system or formal system is a set of terms, relations, assertions, and a world view that is proven to be consistent, valid, complete, sound, and fully expressed. An ontology-like thing can define a logical system. A financial report is a type of logical system.
A model, or conceptual model or conceptualization, describes a possible world. There exists some set of all possible models that can be used to describe real worlds that could exist.
A logical statement is a sentence that carries information that is either true or false. Terms, relations and assertions are all forms of statements which provide information about a logical system. A statement, a statement of fact, and a fact mean the same thing. Questions, commands, and opinions are not logical statements. All statements have a truth value with respect to some model.
Axioms, theorems, and restrictions are all types of assertions.
An axiom is a type of statement that describes self-evident logical statements related to a logical system that no one would argue with.
A theorem is a type of statement that is a logical deduction which can be proven by constructing a chain of reasoning by applying axioms or other theorems in the form of IF…THEN statements.
A restriction is a constraint or limit usually mandated by some sort of authority.
A rule is a synonym for assertion with respect to some model of the real world that could possibly exist (i.e. you cannot create rules that are true in worlds that can never exist).
A conditional statement is a type of statement that has an IF…THEN type format. Look at a statement as being a piece of information that is either correct or incorrect.
Logical entailment, or logical consequent, is when a logical statement follows from another statement or set of statements. Synonyms for logical entailment include logical inference or logical deduction. Accountants sometimes use the term impute. The rules of inference provide a system in which we can produce new information (statements) from known information (statements).
The connectors AND, OR, and NOT are used to combined statements to create compound statements.

Logic gates are building blocks of a digital system. Terms, relations, and assertions of some logical system can be determined to be logically consistent or inconsistent with some logical system.

Professional accountants have an innate understanding of logic. Having a bit more formal understanding will help professional accountants thrive in the digital age and what is being called the fourth industrial revolution.