Axiomsonly

Axiomsonly is a term used in formal logic and knowledge representation to describe a design stance in which a system’s truths are determined solely by a fixed, explicit set of axioms, with no external inference mechanism to generate new results. In an axiomsonly framework, the developer specifies axiom schemas and their intended interpretation, and proofs or verifications are carried out by applying those axioms and their instances. There is no separate rule engine or deductive system beyond the axioms themselves.

The concept emphasizes transparency and explicitness: all accepted statements are either given as axioms or shown to be direct instances of the axiom set. Proponents use axiomsonly to study the limits of axiomatization, to compare different axiom bases, or to illustrate how far reasoning can proceed when no additional inference rules are employed. The idea is often discussed in contrast to standard deductive systems that combine axioms with general inference rules like modus ponens or resolution.

Origins of the term are informal and it appears mainly in pedagogical discussions and theoretical explorations of axiomatization, rather than as a widely adopted technical framework. As a topic, axiomsonly is used to highlight the trade-offs between minimalism, verifiability, and expressive power in formal systems.

Limitations of an axiomsonly approach are inherent: without a rule-based engine, the expressive power is severely constrained, and many useful mathematical and logical developments cannot be derived. It serves as a theoretical baseline rather than a practical methodology for comprehensive reasoning.

See also: axiomatization, Hilbert systems, deductive systems, automated theorem proving, formal logic.