Creating a Deductive Apparatus using XBRL

A model-based financial report created using the Seattle Method or the forthcoming Standard Business Report Model (SBRM) is a deductive apparatus.

A deductive apparatus (a.k.a. formal system, axiomatic system, formal theory) is a formally specified, well-formed, and completely described system that is understandable by both humans and by machines.  A deductive apparatus is a tool.  That tool helps the user of that system to draw correct conclusions using that system. A deductive apparatus is a problem solving system.

A well-formed system is a system that adheres to specific rules, standards, or conventions. This ensures consistency, predictability, and interoperability.

Effective automation (i.e. human-task performance), such as algorithmic regulation, can be achieved using a well-formed and completely described deductive apparatus. Such a deductive apparatus consists of a particular set of axioms, a set of inference rules that enable derivation of theorems from the provided set of axioms, and a set of assertions that any axiom or theorem within the formal system must not contradict. These axioms, inference rules, derived theorems, and  assertions provide formal provability (formal proof, formal verifiability) within the specific provided boundaries of the well-formed system per incompleteness theorems and refutation proofs.

To be clear; consistency, predictability, and interoperability relate to information within the system to the extent that rules exist that can be systematically provided to prove that specific system.  No system can provide a guarantee that every conceivable rule (i.e. even those rules not provided) or prove the system is absolutely correct within every possible context (i.e. within every possible other external systems). There are limits. But with care, useful deductive apparatus can be effectively created and used successfully to automate tasks and practical, useful model-based financial reports can be created.

My PROOF and SUPER PROOF are examples of the capabilities of a deductive apparatus specified by the Seattle Method.  A more full set of capabilities can be seen in the Showcase of Reports.

Auditchain's Luca is an existing cloud-based software application that enables the creation of such a deductive apparatus. Auditchain Pacioli is a SWI-Prolog based engine that can prove that a deductive apparatus is well-formed syntactically and semantically and properly functioning. XBRL is a global standard technical format for creating and exchanging such a deductive apparatus.

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