axiom-interpretation (math concept)
See also
python declaration class | python inclusion class | python sample
Definition
axiom-interpretation is the inference-rule:
Where:
\(\boldsymbol{\mathcal{A}}\) is an axiom
\(\boldsymbol{P}\) is a propositional formula-statement
In straightforward language, the axiom \(\boldsymbol{\mathcal{A}}\) postulates that \(\boldsymbol{P}\) is true.
Warning
This inference-rule is interpretative, i.e.: it interprets a truth expressed in natural-language (e.g.: an axiom, or a definition) and translates it to a formula-statement. Theory authors must be critically attentive to the semantic accuracy of this interpretation . In effect, punctilious does not verify semantic consistency, it only covers syntactical consistency.
In straightforward language, one may introduce arbitrary statements in a theory with interpretative inference-rules.