Knowledge Representation I I

1. Gerstner Laboratory for Intelligent Decision Making and Control Knowledge Representation II Michal Pěchouček

2. Conceptual Graphs • network knowledge representation schema • rooted in association theory of meaning • very much used in the problem of natural language processing Conceptual Graph is complete bipartite oriented graph, where each node is either a concept or a relation between two concepts, there is one or two edges each going to concepts, and each concept may represent another conceptual graph colour dog brown

3. part of agent object monkey scratch ear instrument part of paw Conceptual Graphs A monkey scratches its ear with a pawn

4. Conceptual Graphs • each concept has got its type and an instance general concept – a concept with a wildcard instance specific concept – a concept with a concrete instance • there exsists a hierarchy of types subtype: • concept w is specialisation of concept v iftype(v)>type(w) or instance(w)::type(v) colour dog:*X brown colour dog:Emma brown animal dog cat

5. Conceptual Graphs • canonic conceptual graph is sensible representation of knowledge that can be but does not necessary need to be true • canonic formation rules formalise rules of inference between two graph for while preserving canonicity • copy – identical cloning of a graph • restriction – substituting a concept in a graph with its specialisation • join – joining two graphs via shared concept • simplification – deleting identical relations

6. Restriction of Concepts agent object person person eat pie pie pie pie pie pie pie agent object girl eat pie pie pie pie pie pie pie agent object person:Sue eat pie pie pie pie pie pie pie agent object girl:Sue eat pie pie pie pie pie pie pie

7. Joining Concepts agent object person girl:Sue eat pie pie pie pie pie pie pie agent manner person girl:Sue eat pie pie pie fast pie pie pie agent object pie pie pie pie pie pie pie eat person manner fast agent

8. Simplification of Concepts agent object pie pie pie pie pie pie pie person eat manner fast agent object pie pie pie pie pie pie pie agent person eat manner fast

9. Conceptual Graphs • FOPL transformation to CG • for each node  predicate • general concept variable, specific concept  atomtype:instance type(instance) • relation n-ary predicat relation(in1, in2, …, inn) with arguments conncecting neighbouring concepts • CG is existencionally quantified conjunction of these predicates  X (dog(emma)  color(emma,X)  brown(X)) colour dog:Emma brown

10. Frames • instance of structured representation (schemes) • static data-structure representing stereotyped situation • predecessor of object-oriented systems • default slots • daemons – procedural attachment (infoseek) hotelchair special of:chair legs:four use:sitting hotelroom special of:room location:hotel contains: hotel chair hotel phone hotel bed hotelphone special of:phone use: calling room service billing: through room hotelbed superclass:bed use:sleeping size:king part:mattress frame mattress superclass:cushion firmness:firm

11. Scripts • Schank’s formalisation of stereotyped sequence of events in a particular context • knowledge base representation in terms of the situations that the system is supposed to understand • a restaurant script

12. Modal Logic • While propositional logic will allow us to make statements about object it does not allow us to make statements about the statements John is at home I know that John is at home • Modal logic augments predicate calculus with • ℒoperatorsaying that the statement is necessary true • ℳoperatorsaying that the statement is possibly true ℒ(location(John, home))

13. Modal Logic Semantics • ℒoperator • necessary true, agent knows, true in all times, obligatory • ℳoperator • possible true, agent beliefs, true sometimes, permissible • Possible Worlds Semantics • the logical true is different in different worlds • the worlds are mutually accessible via accessibility relation ℒ() is true in w if is true in allwiaccessible from w ℳ() is true in wif is true in at least one wiaccessible from w card playing example

14. Temporal Logic • Linear with explicit time representation • now(), true_in(,t), occurs(,i), (t1 < t2), start(I,t), end(I,t) • Linear without time representation • φ, XPF (Ftrue) (GF). • Branching time logic • represents all possible courses of action, branches in future • E, A- EA example: in t0EFx is true in t0AF(xy) is true

15. Temporal Logic Limitations • Duration of actions • different speed of action at different situations • Effects occurrence (do not need to be immediate) • Concurrency, Parallel Computation (different formalisms) • Qualification Problem • how to make sound inference about the future without considering everything in the past • Ramification Problem • how to formalise everything that changes after an action occurs • Frame Problem • how to formalise what does not change after an action

16. Non-Monotonic Logic • Unlike in classical logic, a new fact deduced from an already existing theory of facts may contradict with the theory lives(Bob,Europe) fact X: lives(X,Europe) ℳlives(X,Prague) rule ℳlives(Bob,Prague) deduced fact lives(Bob,London) acquired fact • There are Truth Maintenance Systems that maintains proof (justification) of each fact that is deduced within the theory. If an inconsistent hypothesis is found, the dependent course of reasoning is detected and removed (reformulated).