Conceptual dependency & conceptual graphs

Conceptual dependency: canonical meaning

Schank's conceptual dependency (CD) theory aims for a *canonical* semantic representation: sentences that mean the same thing should produce the same internal structure, so understanding becomes matching rather than logical inference. CD claims every verb reduces to one (or a few) of just 11 primitive ACTs. Three you must know:

- ATRANS — transfer of an abstract relationship such as ownership (*give*, *donate*, *sell*). - PTRANS — physical transfer of location (*go*, *move*, *fly to*). - MTRANS — transfer of mental information (*tell*, *read*, *remember*).

So *"give"* and *"donate"* both reduce to ATRANS, and a CD system sees them as identical. The strength is reduced ambiguity and cheap matching; the criticisms are that reduction to primitives is computationally expensive, the 11 primitives are too coarse for subtle distinctions (*push* vs *shove*), and there is no evidence humans actually store meaning this way.

Conceptual graphs: relations as nodes

Sowa's conceptual graphs (CG) fix a weakness of plain semantic nets — that relations hide inside arc *labels*, which makes n-ary relations awkward. A conceptual graph is bipartite: there are concept nodes (objects, drawn as boxes, written type:referent, e.g. dog:emma) and conceptual relation nodes (relations, drawn as ellipses). There are no arc labels — an arc just connects a concept to a relation. An n-ary relation is one relation node with n arcs, so any arity is handled uniformly.

Four canonical formation rules transform graphs: copy, restrict (replace a generic marker with an individual, or a type with a subtype), join (merge two graphs sharing an identical concept node), and simplify (drop a duplicate relation). Restrict and join are *specialisation* operations, and together they implement inheritance. Crucially these rules preserve *meaningfulness*, not truth — they are plausible-reasoning operations, not logical inference.

Worked example & equivalence to logic

Conceptual graphs have exactly the expressive power of predicate calculus. To convert a CG to logic: give each generic concept a unique variable and each individual a unique constant, write each concept node as a unary predicate (dog:emma → dog(emma)), write each relation node as an n-ary predicate over its concept arguments, and existentially quantify the variables. So the CG *[Dog: emma] → (agent) → [Run]* converts to dog(emma) ∧ run(X) ∧ agent(X, emma) — same content, graphical form.