Knowledge Representation

1. Knowledge Representation • Formalization of facts about the real world • Used for reasoning • Ad-hoc or systematic? • Comprehensiveness • Completeness • Ease of use • Abstraction?

2. Categories • Categories and Objects (like classes in Java) • Can an object be in multiple categories? • How is the category specified? • Strict definition • Natural Kind • Hierarchy of Categories • Single or Multiple Inheritance • Abstract Categories • Abstract vs. Concrete Things

3. Examples • Define a “triangle” • Define a “chair” • Define a “thought”

4. Ways to Categorize an Object • Ideal forms (Plato) • List of properties • Intrinsic vs. Extrinsic • Formal definition (mathematics) • Examples

5. Taxonomic Hierarchy • How to categorize everything possible in an organized manner • Systematize all knowledge • Examples: • Biology (Linnaeus) • Dewey Decimal System • CYC (Lenat)

6. Upper Ontology of the World

7. Purpose • Should be applicable in any special-purpose domain • Should unify different areas of knowledge • Should handle exceptions • Is there one general purpose ontology?

8. Categories (Revisited) • Categories can be: • Disjoint • Exhaustive • Partition (Disjoint & Exhaustive) • Relations between Categories • Subcategory (IsA) • PartOf • Properties • Time, Color, Size, Position

9. Measurements • Properties of Objects • Quantitative or Qualitative (3.51 cm or “short”) • Absolute or Relative • Precise or Fuzzy • Fix or Changable

10. Groups • Structured Group (PartOf) • leg is part of a body • Unstructured Group (BunchOf) • bunch of apples • Count nouns vs. Mass nouns • aamory of aardvarks vs. butter • Example: b ε Butter ^ PartOf(p,b) -> p ε Butter

11. Events • Situational Calculus • Discrete Time Intervals • Predicates augment with additional argument (time) • Event Calculus • Events are objects (instances of event categories) • Events are represented by fluents (propositions) • Fluents may be true at a particular time • Events have properties: Agent, Object, Location

12. Event Calculus • T(f,t) – Fluent f is true at time t • Happens(c,i) – Event e happens over the time interval i • Initiates(e,f,t) – Event e causes fluent f to start to hold at time t • Terminates(e,f,t) – Event e causes fluent f to cease at time t • Clipped(f,i) – Fluent f ceases to be true at some point during time interval i • Restored(f,i) – Fluent f becomes true sometime during time interval i

13. Discrete Events vs. Processes • Discrete events have a definite structure (sub-events) • Processes or liquid events don't – a sub-event is similar to the whole event, i.e., “Flying” • Similar to objects: count vs. mass nouns

14. Time Intervals • Moment vs. Extended Intervals • Set of Relations between Intervals

15. Identity • What does it mean for an object to be the same as itself? • If x and y are identical (are the same thing), must they always be identical? Are they necessarily identical? • What does it mean for an object to be the same, if it changes over time? (Is applet the same as applet+1?) • If an object's parts are entirely replaced over time, as in the Ship of Theseus example, in what way is it the same? (From Wikipedia)

16. Representation • Propositional Logic • Predicate Logic • Some other logic • Semantic Networks • Ad-hoc Representational Schemes

17. Propositional Logic • Incomplete for most uses, but the simplest • Decidable

18. Predicate Calculus • Can represent most things easily • Semi-decidable • Efficient procedures for some tasks • NP-complete in general • Examples: Many from what we've done so far

19. Other Logics • Modal Logic (Belief Systems) • Temporal Logic (Time) • Description Logics (Taxonomic Structure) • Circumscription and Default Logic (Nonmonotonicity) • Informal Reasoning • Naive Physics

20. Peirce: Existential Graphs (1909) Masterman: 100 primitive concepts, 15,000 concepts Wilks: Natural Language system using semantic networks Shapiro: Propositional calculus based semantic network Reference: http://www.jfsowa.com/pubs/semnet.htm Early Work

21. Nodes correspond to word concepts with links to other concepts used to define it. Organized into planes, each plane a graph that defines a single meaning of a word. Links are associative and named, and may be multi-arcs (ors) Use to find relationships between pairs of words through graph search. Quillian's network

22. Simple Semantic Network

23. Four primitive conceptualizations: ACT (actions), PP (objects – picture producers), AA (action modifiers or aiders), PA (picture modifiers or aiders) Fixed set of primitive actions: ATRANS, PTRANS, PROPEL, MOVE, GRASP, INGEST, EXPEL, INGEST, MTRANS, MBUILD, CONC, SPEAK, ATTEND. Schank's Conceptual Dependency

24. Different kind of links (multi-arcs): actor (agent), attribute, object, recipient, donor, direction, instrumental conceptualization, causality, state of change, possessor, part Claim is that all knowledge can be broken down into this primitive concepts. Used to create canonical forms of natural language expressions. Schank (cont'd)

25. Based on Filmore's case structure of verbs. Verbs are the main nodes Have actor, object, instrument, location, and time Captures deep structure of sentence Simmon's Case Based Represent.

26. Semantic Networks

27. Used to incorporate real-world, common-sense default knowledge and to organize large amounts of information. Incorporates expected actions and elements. The actual situation may differ. Scripts have the following components: Entry conditions, Results, Props, Roles, and Scenes. Each element is represented by conceptual dep. Scripts (Schank and Abelson)

28. Amy went out to lunch. She sat at a table and called a waitress, who brought her a menu. She ordered a sandwich. Easy Example

29. John visited his favorite restaurant on the way to the concert. he was pleased by the bill because he liked Mozart. Hard Example

30. Frames are structured entities with named slots and attached values. Values may be procedural (think objects). Frames are related to one another. Example slots: ID, relationship to other frames, description of requirements, procedural information, default information, new instance information. Frames support class inheritance. Frames (Minsky)

31. Two types of nodes: concepts and conceptual relations. Arcs are not labeled – a conceptual relation node appears between two concept nodes instead. Concept nodes may be concrete or abstract objects. Each graph represents a single proposition. A graph may be boxed and used as a node in another graph. Conceptual Graphs (Sowa)

32. Every concept is of a unique individual of a give type. Each concept box is labeled with a type label. (:) A concept could be a specific, but unnamed individual. (#) A name is different from the object (name conceptual relation) A concept may be an unspecified individual (*). There is a type hierarchy. Conceptual Graphs (cont'd)

33. The following rules may be used to modify graphs: An exact copy may be made (copy rule). A generic marker may be replaced by an individual marker (restrict). A type may be replaced by a subtype as long as the subtype is consistent with the referent (restrict). Two graphs may be joined by a common concept (join). Conceptual Graphs: Rules

34. Semantic Networks as Logic • Semantic Networks can be converted into logic • Not necessarily first-order logic • If they reason about beliefs • The claim is that it is easier to manipulate semantic networks • More intuitive • Operations include join, restrict, specialize

35. Belief Systems • Example: • Lois Lane knows that Superman can fly. • Superman is Clark Kent. • Does Lois Lane know that Clark Kent can fly? • How do we represent beliefs and mental states? • How can we reason about beliefs?

36. Modal Logic • Predicate calculus is concerned with a single modality, the modality of truth • Modal logics contain operators that take sentences as objects and can reason about them • Example: KA P means “A knows P” where P is a sentence. • The syntax is the same as predicate calculus except that sentences can be formed with K

37. Modal Logic Semantics • Possible World Semantics • Instead of one universe (world), there are many • Worlds are related by an accessibility relation • w1 is accessible from w0 wrt modal operation KA if everything in w1 is consistent with what A knows in w0. • KA P is true in world w iff P is true in every world accessible from w. • Example: KLois[KClark(Superman=Clark) v KClark(Superman != Clark)].

38. Example

39. Example - Key • Solid Arrows: KSuperman • Dotted Arrows: KLois • R: “The weather for tomorrow is rain.” • I: “Superman's secret identity is Clark Kent.”

40. Believe vs. Know • Know = Belief + Truth

41. Descriptive Logics • Evolved from semantic networks • Retain emphasis on taxonomic structure • Principal inference tasks: • Subsumption: checking if one category is a subset of another by comparing their definitions • Classification: checking whether an object belongs to a category • May also check if category definitions are consistent – membership criteria are logically satisfiable

42. Default Logics • Normally logic is monotonic – the addition of new facts does not invalidate existing facts. • Belief systems may be nonmonotonic. • Example: • Birds can fly. • Squeaky is a bird. • Therefore, Squeaky can fly. • Squeaky is a penguin. • Penguins can't fly.

43. Circumscription • Some predicates are specified to be “as false as possible,” i.e., false for every object except for those that they are know to be true. • Bird(x) and ~Abnormal1(x) -> Flies(X). • Abnormal1 is circumscribed. • Type of model preference logic – a sentence is entailed if it is true in all preferred models.

44. Default Logic • Rules are given in the form: Prerequisite : Justification / Conclusion • Example: Bird(x) : Flies(x) / Flies(x) which means that if Bird(x) is true and Flies(x) is consistent with the KB, then we may derived Flies(x). • An extension of a default theory is the maximum set of consequences of the theory • There can be more than one extension of the theory and they may be inconsistent with one another.

45. Example • Example: • Republicans are not Pacifists. • Quakers are Pacifists. • Richard Nixon was a Republican. • Richard Nixon was a Quaker. • In Circumscription both rules are augmented with Abnormal conditions. There are two preferred models. • In Default Logic, the appropriate Justification must be true. There are two extensions.

46. Truth Maintenance System • A Truth Maintenance Systems (TMS) is a KB where sentences may be retracted as well as established. • If a sentence is retracted it may have a cascading effect on other sentences. • The TMS needs to keep track of which sentences rely on other sentences. • Just because one justification is removed, others may still remain.