Axiomatický

Axiomatický is the Czech adjective meaning related to axioms or based on axioms. In formal disciplines, the term describes an approach in which a theory is developed from a prescribed set of basic propositions, called axioms, which are assumed without proof. The deductive framework then yields theorems through rules of inference.

In mathematics and logic, axiomatization aims to capture a domain with a minimal, independent, and consistent set of axioms. Classic examples include Euclid's elements understood as an axiomatic geometry, and the Peano axioms for natural numbers. An axiomatic system is evaluated by properties such as consistency (no contradictions) and independence (no axiom derivable from the others). The language and symbols of the theory define the scope of statements that can be formulated within the axiomatic framework.

In everyday Czech, axiomatický can describe statements or beliefs that are taken as evident or self-evident, or as a feature of something presented as a priori and not requiring empirical justification. Axiomatically simplistic or dogmatic arguments are sometimes criticized as relying on axiomatické premises rather than proven conclusions. The process of creating an axiomatic framework is called axiomatizace.

Related concepts include axiom, postulate, theorem, proof, and the broader field of axiomatics, which studies the structure and consequences of axiomatic systems.