Knowledge & Ontology

Knowledge & Ontology 지식표현, 온톨로지

Epistemology • the science of knowledge EPISTEMOLOGY ( Gr. episteme, "knowledge"; logos, "theory"), branch of philosophy concerned with the theory of knowledge. The main problems with which epistemology is concerned are the definition of knowledge and related concepts, the sources and criteria of knowledge, the kinds of knowledge possible and the degree to which each is certain, and the exact relation between the one who knows and the object known. [Infopedia 1996] Agent that reason logically

Knowledge Definitions Knowledge 2 a (1) : the fact or condition of knowing something with familiarity gained through experience or association (2) : acquaintance with or understanding of a science, art, or technique 4 a : the sum of what is known : the body of truth, information, and principles acquired by mankind [Merriam-Webster, 1994] Agent that reason logically

Conventional Programming Knowledge-Based Systems Knowledge in Expert Systems Knowledge + Inference = Intelligent System (Expert System) Algorithms + Data Structures = Programs N. Wirth Agent that reason logically

Knowledge Pyramid Meta-K Knowledge Information Data Noise Agent that reason logically

Types of Knowledge • a priori knowledge • comes before knowledge perceived through senses • considered to be universally true • a posteriori knowledge • knowledge verifiable through the senses • may not always be reliable • procedural knowledge • knowing how to do something • declarative knowledge • knowing that something is true or false • tacit knowledge • knowledge not easily expressed by language Agent that reason logically

Knowledge Base • A set of representations of facts about the world • Knowledge representation language • tell : what has been told to the knowledge base previously • ask : a question and the answer • Inference : what follows from what the KB has been told • Background knowledge : a knowledge base which may initially contained • Sentence : individual representation of a fact Agent that reason logically

Semantic Networks • A semantic network is a simple representation scheme that uses a graph of labeled nodes and labeled, directed arcs to encode knowledge. • Usually used to represent static, taxonomic, concept dictionaries • Semantic networks are typically used with a special set of accessing procedures that perform “reasoning” • e.g., inheritance of values and relationships • Semantic networks were very popular in the ‘60s and ‘70s but are less frequently used today. • Often much less expressive than other KR formalisms • The graphical depiction associated with a semantic network is a significant reason for their popularity. Agent that reason logically

Nodes and Arcs • Arcs define binary relationships that hold between objects denoted by the nodes. mother age Sue john 5 wife age father husband mother(john,sue) age(john,5) wife(sue,max) age(max,34) ... 34 Max age Agent that reason logically

Animal isa hasPart Bird isa Wing Robin isa isa Rusty Red Semantic Networks • The ISA (is-a) or AKO (a-kind-of) relation is often used to link instances to classes, classes to superclasses • Some links (e.g. hasPart) are inherited along ISA paths. • The semantics of a semantic net can be relatively informal or very formal • often defined at the implementation level Agent that reason logically

Reification • Non-binary relationships can be represented by “turning the relationship into an object” • This is an example of what logicians call “reification” • reify v : consider an abstract concept to be real • We might want to represent the generic give event as a relation involving three things: a giver, a recipient and an object, give(john,mary,book32) giver john give recipient object mary book32 Agent that reason logically

Individuals and Classes Genus • Many semantic networks distinguish • nodes representing individuals and those representing classes • the “subclass” relation from the “instance-of” relation Animal instance subclass hasPart Bird subclass Wing Robin instance instance Rusty Red Agent that reason logically

Inference by Inheritance • One of the main kinds of reasoning done in a semantic net is the inheritance of values along the subclass and instance links. • Semantic networks differ in how they handle the case of inheriting multiple different values. • All possible values are inherited, or • Only the “lowest” value or values are inherited Agent that reason logically

Semantix Net Example Abraracourcix Astérix is-boss-of is-boss-of Cétautomatix is-a is-a is-friend-of is-a buys-from Gaul Obélix is-a fights-with is-a AKO Dog Panoramix is-a takes-care-of lives-with Human is-a sells-to barks-at Idéfix Ordralfabetix Agent that reason logically [http://www.asterix.tm.fr]

OAV-Triples • object-attribute-value triplets • can be used to characterize the knowledge in a semantic net • quickly leads to huge tables Agent that reason logically

Multiple inheritance • A node can have any number of superclasses that contain it, enabling a node to inherit properties from multiple “parent” nodes and their ancestors in the network. • These rules are often used to determine inheritance in such “tangled” networks where multiple inheritance is allowed: • If X<A<B and both A and B have property P, then X inherits A’s property. • If X<A and X<B but neither A<B nor B<Z, and A and B have property P with different and inconsistent values, then X does not inherit property P at all. Agent that reason logically

Problems Semantic Nets • expressiveness • no internal structure of nodes • relationships between multiple nodes • no easy way to represent heuristic information • extensions are possible, but cumbersome • best suited for binary relationships • efficiency • may result in large sets of nodes and links • search may lead to combinatorial explosion • especially for queries with negative results • usability • lack of standards for link types • naming of nodes • classes, instances Agent that reason logically

Schemata • suitable for the representation of more complex knowledge • causal relationships between a percept or action and its outcome • “deeper” knowledge than semantic networks • nodes can have an internal structure • for humans often tacit knowledge • related to the notion of records in computer science Agent that reason logically

Concept Schema • abstraction that captures general/typical properties of objects • has the most important properties that one usually associates with an object of that type • may be dependent on task, context, background and capabilities of the user, … • similar to stereotypes • makes reasoning simpler by concentrating on the essential aspects • may still require relationship-specific inference methods Agent that reason logically

Schema Examples • the most frequently used instances of schemata are • frames [Minsky 1975] • scripts [Schank 1977] • frames consist of a group of slots and fillers to define a stereotypical objects • scripts are time-ordered sequences of frames Agent that reason logically

Frame • represents related knowledge about a subject • provides default values for most slots • frames are organized hierarchically • allows the use of inheritance • knowledge is usually organized according to cause and effect relationships • slots can contain all kinds of items • rules, facts, images, video, comments, debugging info, questions, hypotheses, other frames • slots can also have procedural attachments • procedures that are invoked in specific situations involving a particular slot • on creation, modification, removal of the slot value Agent that reason logically

Simple Frame Example Agent that reason logically

Overview of Frame Structure • two basic elements: slots and facets (fillers, values, etc.); • typically have parent and offspring slots • used to establish a property inheritance hierarchy (e.g., specialization-of) • descriptive slots • contain declarative information or data (static knowledge) • procedural attachments • contain functions which can direct the reasoning process (dynamic knowledge) (e.g., "activate a certain rule if a value exceeds a given level") • data-driven, event-driven ( bottom-up reasoning) • expectation-drive or top-down reasoning • pointers to related frames/scripts - can be used to transfer control to a more appropriate frame Agent that reason logically [Rogers 1999]

Slots • each slot contains one or more facets • facets may take the following forms: • values • default • used if there is not other value present • range • what kind of information can appear in the slot • if-added • procedural attachment which specifies an action to be taken when a value in the slot is added or modified (data-driven, event-driven or bottom-up reasoning) • if-needed • procedural attachment which triggers a procedure which goes out to get information which the slot doesn't have (expectation-driven; top-down reasoning) • other • may contain frames, rules, semantic networks, or other types of knowledge [Rogers 1999] Agent that reason logically

Usage of Frames • filling slots in frames • can inherit the value directly • can get a default value • these two are relatively inexpensive • can derive information through the attached procedures (or methods) that also take advantage of current context (slot-specific heuristics) • filling in slots also confirms that frame or script is appropriate for this particular situation Agent that reason logically [Rogers 1999]

Restaurant Frame Example • generic template for restaurants • different types • default values • script for a typical sequence of activities at a restaurant Agent that reason logically [Rogers 1999]

Generic Restaurant Frame Generic RESTAURANT Frame Specialization-of: Business-Establishment Types: range: (Cafeteria, Fast-Food, Seat-Yourself, Wait-To-Be-Seated) default: Seat-Yourself if-needed: IF plastic-orange-counter THEN Fast-Food, IF stack-of-trays THEN Cafeteria, IF wait-for-waitress-sign or reservations-made THEN Wait-To-Be-Seated, OTHERWISE Seat-Yourself. Location: range: an ADDRESS if-needed: (Look at the MENU) Name: if-needed: (Look at the MENU) Food-Style: range: (Burgers, Chinese, American, Seafood, French) default: American if-added: (Update Alternatives of Restaurant) Times-of-Operation: range: a Time-of-Day default: open evenings except Mondays Payment-Form: range: (Cash, CreditCard, Check, Washing-Dishes-Script) Event-Sequence: default: Eat-at-Restaurant Script Alternatives: range: all restaurants with same Foodstyle if-needed: (Find all Restaurants with the same Foodstyle) Agent that reason logically [Rogers 1999]

Restaurant Script EAT-AT-RESTAURANT Script Props: (Restaurant, Money, Food, Menu, Tables, Chairs) Roles: (Hungry-Persons, Wait-Persons, Chef-Persons) Point-of-View: Hungry-Persons Time-of-Occurrence: (Times-of-Operation of Restaurant) Place-of-Occurrence: (Location of Restaurant) Event-Sequence: first: Enter-Restaurant Script then: if (Wait-To-Be-Seated-Sign or Reservations) then Get-Maitre-d's-Attention Script then: Please-Be-Seated Script then: Order-Food-Script then: Eat-Food-Script unless (Long-Wait) when Exit-Restaurant-Angry Script then: if (Food-Quality was better than Palatable) then Compliments-To-The-Chef Script then: Pay-For-It-Script finally: Leave-Restaurant Script Agent that reason logically [Rogers 1999]

Frame Advantages • fairly intuitive for many applications • similar to human knowledge organization • suitable for causal knowledge • easier to understand than logic or rules • very flexible Agent that reason logically

Frame Problems • it is tempting to use frames as definitions of concepts • not appropriate because there may be valid instances of a concept that do not fit the stereotype • exceptions can be used to overcome this • can get very messy • inheritance • not all properties of a class stereotype should be propagated to subclasses • alteration of slots can have unintended consequences in subclasses Agent that reason logically

Agent that reason logically

Representation, Reasoning and Logic • two parts to knowledge representation language: • syntax • describes the possible configurations that can constitute sentences • semantics • determines the facts in the world to which the sentences refer • tells us what the agent believes Agent that reason logically [Rogers 1999]

Reasoning • process of constructing new configurations (sentences) from old ones • proper reasoning ensures that the new configurations represent facts that actually follow from the facts that the old configurations represent • this relationship is called entailment and can be expressed asKB |= alpha • knowledge base KB entails the sentence alpha Agent that reason logically [Rogers 1999]

Logical Knowledge base • The knowledge level :: saying what it knows to KB  “Golden Gates Bridge links San Francisco and Marin Country • The logical level :: the knowledge is encoding into sentences  Links(GGBridge, SF, Marin) • The implementation level :: the level that runs on the agent architecture (data structures to represent knowledge or facts) Agent that reason logically

Knowledge • declarative/procedural • love(john, mary). • can_fly(X) :- bird(X), not(can_fly(X)), !. • learning : general knowledge about the environment given a series of percepts • Commonsense knowledge Agent that reason logically

Figure 6.2 A typical wumpus world Specifying the environment Agent that reason logically

Domain specific knowledge • Domain specific knowledge • In the squares directly adjacent to a pit, the agent will perceive a breeze • Commonsense knowledge • logical reasoning • stench(1,2) & ~setnch(2,1)  ~wumpus(2,2) • wumpus(1,3)  stench(2,1) & stench(2,3) & stench(1,4) Agent that reason logically

1,4 2,4 3,4 4,4 A = Agent B = Breeze G = Glitter, Gold OK = Safe square P = Pit S = Stench V = Visited W = Wumpus 1,4 2,4 3,4 4,4 1,3 2,3 3,3 4,3 1,3 2,3 3,3 4,3 1,2 2,2 3,2 4,2 1,2 2,2 3,2 4,2 P ? OK 1,1 2,1 3,1 4,1 1,1 2,1 3,1 4,1 A V A B OK OK OK OK • Figure 6.3 The first step taken by the agent in the wumpus world. • The initial situation, after percept [None, None, None, None, None]. • After one move, with percept [None, Breeze, None, None, None]. Inference in Wumpus world(I) Agent that reason logically

1,4 2,4 3,4 4,4 A = Agent B = Breeze G = Glitter, Gold OK = Safe square P = Pit S = Stench V = Visited W = Wumpus 1,4 2,4 3,4 4,4 P ? 1,3 2,3 3,3 4,3 1,3 2,3 3,3 4,3 W ! A W! P ? S G B S 1,2 2,2 3,2 4,2 1,2 2,2 3,2 4,2 A V V OK OK OK OK B B 1,1 2,1 3,1 4,1 1,1 2,1 3,1 4,1 V V V V P ! OK OK OK OK • Figure 6.4 Two later stages in the progress of the agent. • After the third move, with percept [Stench, None, None, None, None]. • After the fifth move, with percept [Stench, Breeze, Glitter, None, None]. Inference in Wumpus world(II) Agent that reason logically

Logics • Boolean logic • Symbols represent whole propositions (facts) • Boolean connectives • First-order logic • objects, predicates • connectives, quantifiers Agent that reason logically

Wrong logical reasoning FIRST VILLAGER: We have found a witch. May we burn her? ALL: A witch! Burn her! BEDEVERE: Why do you think she is a witch? SECOND VILLAGER: She turned me into a newt. BEDEVERE: A newt? SECOND VILLAGER (after looking at himself for some time): I got better. ALL: Burn her anyway. BEDEVERE: Quiet! Quiet! There are ways of telling whether she is a witch. BEDEVERE: Tell me … What do you do with witches? ALL: Burn them. BEDEVERE: And what do you burn, apart from witches? FOURTH VILLAGER: … Wood? BEDEVERE: So why do witches burn? SECOND VILLAGER: (pianissimo) Because they’re made of wood? BEDEVERE: Good. ALL: I see. Yes, of course. BEDEVERE: So how can we tell if she is made of wood? FIRST VILLAGER: Make a bridge out of her. BEDEVERE: Ah … but can you not also make bridges out of stone? ALL: Yes, of course … um … er … BEDEVERE: Does wood sink in water? ALL: No, no, it floats. Throw her in the pond. BEDEVERE: Wait. Wait … tell me, what also floats on water? ALL: Bread? No, no no. Apples … gravy … very small rocks … BEDEVERE: No, no no. KING ARTHUR: A duck! (They all turn and look at ARTHUR. BEDEVERE looks up very impressed.) BEDEVERE: Exactly. So … logically … FIRST VILLAGER (beginning to pick up the thread): If she .. Weight the same as a duck … she’s made of wood. BEDEVERE: And therefore? ALL: A witch! Agent that reason logically

Ontological and epistemological commitments • Ontological commitments :: to do with the nature of reality • Propositional logic(true/false), Predicate logic, Temporal logic • Epistemological commitments :: to do with the possible states of knowledge an agent can have using various types of logic • degree of belief • fuzzy logic Agent that reason logically

Commitments Formal languages and their and ontological and epistemological commitments Agent that reason logically

Wumpus world • Initial state ~S1,1 ~B1,1 ~S2,1 B2,1 S1,2 ~B1,2 • Rule R1: ~S1,1 -> ~W1,1 & ~W1,2 & ~W2,1 R2: ~S2,1 -> ~W1,1 & ~W2,1 & ~W2,2 & ~W3,1 R3: ~S1,2 -> ~W1,1 & ~W1,2 & ~W2,2 & ~W1,3 R4: S1,2 -> W1,3 V W1,2 V W2,2 V W1,2 Agent that reason logically

Finding the wumpus • Inference process • Modus ponens : ~S1,1 and R1  ~W1,1 & ~W1,2 & ~W2,1 • And-Elimination ~W1,1 ~W1,2 ~W2,1 • Modus ponens and And-Elimination: ~W2,2 ~W2,1 ~W3,1 • Modus ponens S1,2 and R4  W1,3 V W1,2 V W2,2 V W1,1 Agent that reason logically

Inference process(cont.) • unit resolution ~W1,1 and W1,3 V W1,2 V W2,2 V W1,1  W1,3 V W1,2 V W2,2 • unit resolution ~W2,2 and W1,3 V W1,2 V W2,2  W1,3 V W1,2 • unit resolution ~W1,2 and W1,3 V W1,2  W1,3 Agent that reason logically

Translating knowledge into action • A1,1 & EastA & W2,1 -> ~Forward EastA :: facing east • Propositional logic is not powerful enough to solve the wumpus problem easily Agent that reason logically

First-order logic • A stronger set of ontological commitments • A world in FOL consists of objects, properties, relations, functions • Objects people, houses, number, colors, Bill Clinton • Relations  brother of, bigger than, owns, love • Properties  red, round, bogus, prime • Functions father of, best friend, third inning of Agent that reason logically

First order logics • Objects와 relations • 시간, 사건, 카테고리 등은 고려하지 않음 • 영역에 따라 자유로운 표현이 가능함  ‘king’은 사람의 property도 될 수 있고, 사람과 국가를 연결하는 relation이 될 수도 있다 • 일차술어논리는 잘 알려져 있고, 잘 연구된 수학적 모형임 Agent that reason logically

예 • Constant symbols :: A, B, John, • Predicate symbols :: Round, Brother • Function symbols :: Cosine, FatherOf • Terms :: King John, Richard’s left leg • Atomic sentences :: Brother(Richard,John), Married(FatherOf(Richard), MotherOf(John)) • Complex sentences :: Older(John,30)=>~younger(John,30) Agent that reason logically

Knowledge & Ontology