DL axioms

Body-of-Water (BoW) patterns, τ-mappings, self-restrictions

Unlike pure DL notation alone, the TAoKE mirror follows naming conventions: class names and most object properties start with a capital letter. The Body of Water (BoW) axiom set (Excel source by T. Hoppe, 2021, on taoke.de) is expressed in DL, then converted by reification for triple storage. Intermediate nodes use readable ids such as ≡estuary.Sea, ≡BoW_connects_min_2_seas, ≡BoW_pond_or_pond-origin.Ice_Age.

A mapping τ maps an internal id to the DL term, e.g. τ(≡BoW_inside_salt_water_and_no_estuary.ocean) expands to a conjunction of BoW, inlandopen.inland, saltfreshtype.Saltwater, and ¬ Estuary.Ocean (canonical expansion on taoke.de).

The canonical page lists twelve illustrative axioms (backwaters, mountain streams, rivers, canals, crater lakes, salt lakes, ponds from ice-age origin, etc.), mixing role cardinality, data properties (width, flow, drainage), and concept union/intersection. For example: a backwater may require little flow and a single river connection; a sea canal may connect exactly two seas; a salt lake is inland salt water without an estuary into an ocean in the source formulation.

Poetic summary from [Rudo2011] on taoke.de: DL is “variable-free” yet quantified—aligned with the same lecture notes used in DL related work for SROIQ.

The lateral-channel axiom uses ⊓ ∃◊Connection.Self to exclude flows that connect to a different flow than themselves. Other self examples: PersonCommittingSuicide ≡ ∃kills.Self, Narcissist ≡ ∃loves.Self or ∃◊isLoverOf.Self — same pattern as on the related-work page.

For OWL concrete syntax and tooling, see [AlHe2020]; deriver.app rules can express analogous checks when you materialise role paths in session variables.