A SEMANTIC NET (or ASSOCIATIVE NET) represents knowledge as a GRAPH: NODES represent objects, concepts, events or situations ARCS (labelled, directed) represent the RELATIONSHIPS between them Originally proposed by Quillian (1968) as a model of human associative memory, which is why the emphasis is on retrieval by following links rather than on logical inference. THE ESSENTIAL IDEA: knowledge is in the CONNECTIONS. A concept's meaning is given by its position in the network — what it is a kind of, what its parts are, what it can do — rather than by an internal definition. THE STANDARD ARC TYPES, and the distinction that matters most: isa class inclusion: one class is a subclass of another Bird isa Animal instance_of class membership: an individual belongs to a class Tweety instance_of Bird has_part part-whole (partonomy) Bird has_part Wing property arcs any attribute: colour, size, ability Tweety colour Yellow ISA VERSUS INSTANCE_OF IS EXAMINED CONSTANTLY, and confusing them is a genuine modelling error: isa is a relation between two CLASSES and it is TRANSITIVE — Sparrow isa Bird, Bird isa Animal, therefore Sparrow isa Animal. instance_of relates an INDIVIDUAL to a CLASS and it is NOT transitive — Tweety instance_of Bird and Bird isa Animal gives Tweety instance_of Animal (which is inheritance working), but Tweety is not an instance of "the class of classes". A TEST: if you can meaningfully say "a member of it", it is a class and takes isa; if it is a particular thing with a name, it is an individual and takes instance_of. A WORKED NETWORK: Animal ▲ isa │ Bird ──has_part──▶ Wing ▲ │ ┌───────┴────────┐ │ number isa isa ▼ Sparrow Penguin 2 ▲ ▲ instance_of instance_of │ │ Tweety Pingu │ colour ──▶ Yellow plus property arcs at the class level: Bird can_fly ──▶ True Penguin can_fly ──▶ False ← an OVERRIDE Bird covering ──▶ Feathers ANSWERING QUERIES BY TRAVERSAL: Q: Can Tweety fly? Tweety has no can_fly arc → follow instance_of to Sparrow → no can_fly → follow isa to Bird → can_fly = True. ANSWER: yes, INFERRED in three hops. Q: Can Pingu fly? Pingu → instance_of Penguin → can_fly = False FOUND HERE, so the search stops before reaching Bird. ANSWER: no. THE MORE SPECIFIC VALUE WINS, which is how exceptions are handled — and it depends entirely on the search stopping at the first value found. Q: How many wings does Pingu have? Pingu → Penguin → Bird → has_part Wing, number 2. ANSWER: 2, inherited across a part-whole arc. THE INFERENCE MECHANISM IS THEREFORE JUST GRAPH TRAVERSAL — which is the source of both the appeal and the limitations.

TWO EXTENSIONS that address real gaps. 1. PARTITIONED SEMANTIC NETS (Hendrix) THE PROBLEM: a plain net cannot express quantification or scope. "Every dog bit a postman" — is it one postman or one per dog? A net has no way to say. THE SOLUTION: divide the network into SPACES (partitions), with a node for each space and arcs indicating which statements lie inside which. A universally quantified statement becomes a general statement node (a GS node) whose `form` arc points to a partition containing the quantified relation, with ∀ and ∃ arcs naming the variables. WHY IT MATTERS: it restores the ability to express what first-order logic expresses, at the cost of the diagram becoming considerably harder to read — which is a fair summary of the whole expressiveness trade-off. 2. CONCEPTUAL DEPENDENCY and CONCEPTUAL GRAPHS Schank's CONCEPTUAL DEPENDENCY represents sentences by a small set of PRIMITIVE ACTS, so that sentences with the same meaning get the same representation regardless of wording. the primitives include ATRANS (transfer of an abstract relationship, e.g. give), PTRANS (transfer of physical location, e.g. go), PROPEL, MOVE, INGEST, MTRANS (transfer of mental information, e.g. tell), MBUILD, ATTEND, SPEAK, GRASP, EXPEL WORKED: "John gave Mary a book" and "Mary received a book from John" both become an ATRANS with actor John, object book, recipient Mary, donor John. CANONICAL FORM MEANS PARAPHRASES BECOME IDENTICAL, which is exactly what a question-answering system needs. ✘ the primitive set is contentious — is there really a fixed small basis for all action? — and complex sentences produce unwieldy structures. THE LIMITATIONS OF SEMANTIC NETS — the examinable list: 1. NO STANDARD MEANING FOR THE LINKS. `isa` means class inclusion to one author and class membership to another, and nothing in the notation enforces either. TWO NETS DRAWN BY TWO PEOPLE MAY NOT BE COMPARABLE. 2. CANNOT EXPRESS NEGATION, DISJUNCTION OR QUANTIFICATION natively. "Tweety is not a penguin" — there is no arc for "not" "Either Ram or Sita will attend" — no arc for "or" "Every student has a supervisor" — needs partitioning THIS IS THE DECISIVE LIMITATION: it is a representational inadequacy in the sense of the earlier topic, and it is why logic is needed. 3. THE EXCEPTION PROBLEM. Inheritance with overrides is convenient and NON-MONOTONIC, so it has no clean logical semantics — and the Nixon diamond (conflicting inherited defaults) has no syntactic resolution. 4. INFERENCE IS LIMITED TO TRAVERSAL. There is no general inference procedure, so what can be concluded depends on what links happen to exist rather than on what follows logically. 5. NO WAY TO REPRESENT KNOWLEDGE ABOUT THE NET ITSELF — certainty, provenance, or the time at which something was true — without ad-hoc additions. 6. COMBINATORIAL GROWTH. Representing a moderately complex domain produces a graph too large to draw and hard to maintain, and there is no modularity mechanism. THE HONEST ASSESSMENT: semantic nets are excellent at TAXONOMIC and RELATIONAL knowledge, and poor at everything else. That is not a small niche — taxonomies are enormously useful — but a system needing negation, disjunction or quantification must use logic.

SEMANTIC NETS AND LOGIC ARE NOT RIVALS SO MUCH AS DIFFERENT NOTATIONS FOR OVERLAPPING CONTENT. Most of a semantic net translates directly into first-order logic: NET LOGIC ───────────────────────────────────────────────────────────── Tweety instance_of Bird Bird(Tweety) Sparrow isa Bird ∀x Sparrow(x) → Bird(x) Bird has_part Wing ∀x Bird(x) → ∃y Wing(y) ∧ part_of(y, x) Tweety colour Yellow colour(Tweety, Yellow) ───────────────────────────────────────────────────────────── WHAT THE NET ADDS: an INDEXING STRUCTURE. Finding everything related to Tweety is following its arcs, whereas in a flat logical database it means scanning every sentence for the term. THAT IS THE INFERENTIAL EFFICIENCY PROPERTY from the first KR topic, and it is the real contribution — the net is a data structure for logic as much as an alternative to it. WHAT THE NET LOSES: negation, disjunction, and quantifier scope, as above. AND ONE THING THE NET MAKES EASY THAT LOGIC MAKES AWKWARD: DEFAULTS WITH OVERRIDES. `Penguin can_fly False` overriding `Bird can_fly True` is a one-arc edit in a net, and requires non-monotonic machinery in logic. WHERE THIS STRUCTURE IS ACTUALLY USED TODAY: KNOWLEDGE GRAPHS search-engine entity graphs, Wikidata; facts as (subject, predicate, object) triples, which IS a semantic net WORDNET a lexical database of English organised by synonymy, hypernymy (isa) and meronymy (has_part) — used throughout natural language processing ONTOLOGIES RDF and OWL, with formal semantics added precisely to fix limitation 1 PRODUCT TAXONOMIES every online catalogue's category tree BIOMEDICAL the Gene Ontology, SNOMED CT — among TERMINOLOGIES the largest deployed knowledge structures anywhere THE HISTORICAL LESSON WORTH DRAWING: the original semantic net's fatal weakness was the absence of agreed link semantics, and the modern successors fixed exactly that. RDF specifies that a triple is a triple; OWL specifies what `subClassOf` means and what a reasoner may conclude from it. THE STRUCTURE SURVIVED; WHAT WAS ADDED WAS A DEFINITION OF WHAT THE ARCS MEAN. A WORKED SCALE COMPARISON, to make the point that this is not a historical curiosity: the 8-node bird example above 8 nodes, ~12 arcs WordNet ~117,000 synsets Wikidata over 100,000,000 items → the same node-and-arc idea, at nine orders of magnitude difference in scale, which is only possible because the arc semantics are fixed and the structure is machine- readable rather than drawn.