• Maybe RJ meant "Theoretical Ko terms"?
• Or is this related to Solving Go on small Boards? ("Solving Go" seems to recur in RJ's quest.)

In general, my definition of terms approach to Go theory is mathematical, except for the annotation, which often uses sentences of English language so that non-mathematicians get also their chance to understand and so that the research work for myself can proceed much faster. In principle, the English language annotation of definitions could be substituted by maths-formula-like annotation. E.g., even the axioms of the Japanese 2003 Rules could be replaced by definitions if one uses the analogy of John Conway's On Number and Games approach to define numbers by supersets on the empty set, which is the major axiom for his theory. As also Olmsted and Heine had recognized, rules are just imprecise definitions. Mathematically precise rules should be expressed as sets of definitions. When defining go terms formally, I use the definition upon definition approach. Sometimes, when being a bit "efficient", I still use some rules. E.g., I use the Default Restriction Rules as part of the ko intersection definition. If you wanted it more precise, you could simply spell out each rule more carefully as a definition relying on more fundamental definitions. OTOH, there is little wrong with also using "rules" in mathematics, except that it is not so obvious where to find a good description of used axioms. Most maths favours definitions rather than rules.

For some go terms, conceptually more than definitions is used: also propositions (aka theorems or lemmas) and their proofs. You can see such, e.g., in my Types of Basic Ko paper or in my pass fights research, where I first define what particular kinds of pass fights are, then proved for classes of positions that such pass fights do not occur. From a view of conceptual maths tools, defining "ko" is simpler though: Propositions are not needed. Definitions (or definitions and rules) suffice. This purity might disappoint some maths students who always get to see also propositions and their proofs. It is an advantage for go players though because they do not run into the difficulty of having to understand formal proofs.

Some might have been a bit sceptical because the maths of go rules and go terms is somehow different from most other maths. It is a new field of mathematics, one might say. Not conceptually though - when one really searches for other maths topics, one can also find related kinds of studies like, e.g., a specific type of logic that focuses around strategic decision making in the force / prevent sense. By topic, go rules / go terms study is a new field of maths. Olmsted had defined Go by relying on set theory. Others referred to graph theory. For defining go rules, both are an overkill though. My conceptual approach to start afresh directly from axioms (or even only one axiom: the empty set) is much simpler. One does not need to understand other maths theories like full-fledged set theory or graph theory. This may let it look different from school maths and more similar to English language - but the kind of working is mathemetical (except that one might always use a yet stricter and more symbolic annotation instead of words of the English language).