AI · Knowledge, reasoning, and planning

10 · Knowledge Representation

Knowledge representation organizes concepts, objects, events, and defaults so a system can draw useful conclusions while respecting exceptions.

Structure knowledge for inference

10.1 Ontological Engineering

An ontology specifies categories, relations, and constraints for a domain. Its vocabulary and level of detail should support the questions a system must answer.

10.2 Categories and Objects

Categories group individuals and support inheritance: a robin is a bird, so properties of birds may apply to it. Taxonomies and part–whole relations capture different kinds of structure.

10.3 Events

Event representations describe actions and changes over time, including participants, time, and resulting states. They help reason about what was true before and after an event.

10.4 Mental Objects and Modal Logic

Beliefs, knowledge, and other attitudes can be represented as relations between agents and propositions. Modal operators distinguish what is true from what an agent believes or knows.

10.5 Reasoning Systems for Categories

Description-logic systems classify concepts and individuals using formal definitions, subsumption, and consistency checking.

10.6 Reasoning with Default Information

Defaults are normally true but defeasible. An exception such as “penguins do not fly” can override the inherited bird default without making the knowledge base inconsistent.

Key terms and inheritance trace

Ontology: a domain vocabulary plus formal relationships and constraints. Subclass links a narrower category to a broader one; instance links an individual to a category. Default is a defeasible “normally” rule, unlike a strict implication. Unknown means the encoded facts do not decide the question—not that its negation is true.

For Pip, follow Penguin → Bird → Animal. The generic bird default tentatively suggests flying, but the more specific penguin exception blocks that conclusion. For Bela the model contains no bird/flying rule, so it correctly reports unknown rather than assuming either answer.

Categories, part–whole links, events, and beliefs model different relations: “is-a” is not “part-of,” an event records change and participants, and a belief is attributed to an agent rather than asserted as objective fact.

Interactive inheritance

Defaults meet exceptions

All birds normally fly. Penguins are birds, but the explicit exception blocks that default.

Choose an individual

Category path

Conclusion about Fly(x)

Demo lookup and complexity

The selected key (“robin,” “penguin,” or “bat”) directly retrieves a prewritten example record containing its path, conclusion, and explanation. The displayed chain is explanatory data; this demo does not traverse a general taxonomy or resolve arbitrary competing defaults.

Let C be the number of records. Time: O(1) average per selection/update using JavaScript object-key lookup (then a constant number of text/style updates). Auxiliary space: O(1) per update; the fixed example records and rendered labels occupy O(C) input/UI space. Here C = 3. A general inheritance engine would need bounds based on its graph and rules; these constant-time claims do not describe one.