KM The Knowledge Machine A knowledge representation and

KM: The Knowledge Machine A knowledge representation and reasoning system

What is KM? • A Knowledge Representation Language (KRL) – (like KIF, or Cyc. L, or …) – an interpreter sitting on top of Lisp – expressive – formal semantics • A Reasoning Engine – backward chaining – automatic classification – reasoning with actions (simulation) – defaults (inheritance with overrides) • Mature • Free

What Do You Do with KM? • Create Knowledge Bases – descriptions of things in the world • objects, events, properties, relationships – descriptions of the rules that allow us to reason about things in the world • Ask Questions about Knowledge – what are the facts? – what can be inferred from the inferences from facts? • Run Simulations in the World Described in the KB – what would be the state of objects if certain events took place?

Representing Knowledge • What are the kinds of things in the world? – Event, Object, Artifact, Device, Computer, … • What are the real individual things of each kind? – Party. At. My. House. This. Saturday, The. PCIn. My. Office • What properties hold for all individuals of some kind? – all events occur at some place and time – most computers have hard drives • What properties hold for specific individuals? – this lecture is at 3: 30 pm, your favorite color is green • How do kinds of things relate to each other? – all Computers are Devices, all People have a Mother • How do individuals relate to each other? – Thomas’ father is Bob, Texas is part of the USA

An Informal Knowledge Base • Classes – Event, Object, Artifact, Device, Computer, Person, Place, Hard-Drive are Classes – every Event e occurs at a time-of-occ t and place-of-occ p – The superclass of Computer is Device – every Person p 1 has a mother p 2 – most Computers c have a part h that is a Hard-Drive • Instances – Party. At. My. House. This. Saturday is an instance of Event – The. PCIn. My. Office is an instance of Computer – This. Lecture is an instance of Event with time-of-occ 3: 30 pm – You is an instance of Person with favorite-color green – Thomas is an instance of Person with father Bob (a Person) – Texas is an instance of Place with is-part-of USA (a Place)

KM for Representing Knowledge • English – The. PCIn. My. Office is an instance of Computer – the superclass of Computer is Device ? Is The. PCIn. My. Office a Device? • FOPC – Computer(The. PCIn. My. Office) – x Computer(x) Device(x) ? Device(The. PCIn. My. Office) • KM – (The. PCIn. My. Office has (instance-of (Computer)) ) – (Computer has (superclasses (Device)) ) ? (The. PCIn. My. Office isa Device) (t)

This Tutorial • Overview of the KM language and inference – based on a detailed script of using KM – the examples are “toy” • Not a tutorial in how to do knowledge representation! • KM Manuals give the full reference* – how to download and run KM – details of the syntax – logical semantics for the expressions • Tutorial works best if you ask lots of questions!! * http: //www. cs. utexas. edu/~mfkb/km. html

Interaction with KM • Interaction with KM: read-eval-print – User gives KM an expression (assertion/query) – KM • “reads” the expression given by the user • evaluates it and • prints the result KM> 123 (123) KM> (1 + 1) (2) KM> (the count of Monte. Cristo) (Edmond) KM> _

Expressions in KM • The basic expressions in KM are – assertions • facts and rules about the world – queries • expressions whose evaluation searches the facts and rules KM> (*Shiner has (instance-of (Cat))) (*Shiner) KM> (*Shiner has (brother (*Kashmir))) (*Shiner) KM> (the brother of *Shiner) (*Kashmir) KM> (the instance-of of *Kashmir) (Cat) How does it know? The ‘*’ has no special meaning in KM; We use it as a handy visual indicator to distinguish instances and classes

Knowledge Bases in KM • KM expressions can be loaded from a file into KM • More KM expressions can be evaluated by the interpreter, possibly modifying the loaded KB • The modified KB can be saved from the KM environment into a file KM> (load-kb "a-family. km") Loading a-family. km. . . a-family. km loaded! KM> (the father of *Thomas) (*Bob) KM> (the mother of *Thomas) (*Betty. Jo) KM> (*Bryen has (father (*Thomas))) (*Bryen) KM> (the grandmother of *Bryen) (*Betty. Jo) KM> (save-kb "a-family 2. km") a-family 2. km saved!

Instances • Recall: – an instance denotes some object in the world – a class is a collection of instances 1 • An instance (individual) evaluates to itself ; ; ; --- instances --- ‘; ’ = comment to end of line ; ; ; "Fred" KM> *Fred (*Fred) ; ; ; "1" KM> 1 (1) ; ; ; "1 + 1" KM> (1 + 1) (2) 1 or, more precisely, a class has a collection of instances associated with it (the class’s extension)

“Creating instances” (existential quantification) • We can “create” (assert the existence of) an instance of a particular class – Logic: x. <classname>(x) (e. g. x. Cat(x)) – KM: (a <classname>) ; ; ; "A cat. " KM> (a Cat) (_Cat 0) ; _Cat 0 is a Skolem individual denoting that cat ; ; ; "A black cat with a head and a tail. " KM> (a Cat with (color (*Black)) (parts ((a Head) (a Tail))) ) An (_Cat 1) KM> (showme _Cat 1) (_Cat 1 has (instance-of (Cat)) (color (*Black)) (parts ((a Head) (a Tail)))) (_Cat 1) Guaranteed unique and fresh! instance together with all the knowledge attached to that instance is called a “Frame”

Slots • Slots relate instances together • Two ways to specify slots: – on existing instances • (<instance> has (<slot> (<value>))) – directly on new instances when created • (a <classname> with (<slot> (<value>))) KM> (a Car) (_Car 3) KM> (_Car 3 has (color (*Silver))) (_Car 3) KM> (showme _Car 3) (_Car 3 has (instance-of (Car)) (color (*Silver))) Slot KM> (a Car with (color (*Silver))) (_Car 4) KM> (showme _Car 4) (_Car 4 has (instance-of (Car)) (color (*Silver))) Frame Value

Slots • Slots can relate instances together • Slots are themselves frames – can specify properties of the slot on these frames ; ; ; --- slot declarations (optional) --; ; ; "'age' is a slot relating physical objects (Physobj) to Numbers. ; ; ; A physical object has at most one age. " KM> (age has (instance-of (Slot)) Frame (domain (Physobj)) (range (Number)) (inverse (is-age-of)) ; name of the inverse slot (cardinality (N-to-1))) ; one age per thing Slot Value

Superclasses • Slots can also give information about classes • The syntax is the same as for instances – (<class> has (<slot> (<value>))) KM> (Car has (superclasses (Vehicle)) (subclasses (Hybrid-Car Station-Wagon Sports-Car)) (instances (_Car 3 _Car 4))) (Car) KM> (the subclasses of Vehicle) (Car)

The Taxonomy (Inheritance Hierarchy) • Classes can themselves be subclasses of (multiple) other classes • (taxonomy) shows the entire taxonomy KM> (*Fred has (instance-of (Person))) KM> (Person has (superclasses (Physobj))) KM> (Physobj has (superclasses (Thing))) ; ; ; "Show me the concept taxonomy. " KM> (taxonomy) Thing Number Physobj Car Cat House Person I *Fred I *Joe …. etc…. . Thing Physobj Car Person Number ….

Instance Frames and Simple Queries • Frames describe objects in the world – list its properties, and relationships to other objects • Queries: Form is (the <slot> of <object>) – an “access path” ; ; ; "Fred is a person. " KM> (*Fred has (instance-of (Person))) ; ; ; "Fred's age is 32. " KM> (*Fred has (age (32))) ; ; ; "Show me the frame representing Fred. " KM> (showme *Fred) (*Fred has (instance-of (Person)) (age (32))) ; ; ; "What is the age of Fred? " KM> (the age of *Fred) Frame (32) Value Slot (identifier)

Slot Inverses • KM keeps track of inverse relations also X→r→Y Y→r-1→X ; ; ; "Fred owns a car. " KM> (*Fred has (owns ((a Car)))) ; ; ; "What does Fred own? " KM> (the owns of *Fred) (_Car 1) ; (Skolem _Car 1 created, denoting that car) ; ; ; "Show me the frame representing that last car. " KM> (showme (thelast Car)) (_Car 1 has (instance-of (Car)) (owns-of (*Fred))) ; note the inverse slot (default name is "<slot>-of")

Embedded Units and Access Paths • Frames can be embedded within frames • An access path may be embedded in an access path ; ; ; --- embedded units --; ; ; "Joe is a person, and owns a red car. " KM> (*Joe has (instance-of (Person)) (owns ((a Car with (color (*Red)))))) ; ; ; --- access paths --; ; ; "What are the color(s) of the thing(s) which Joe owns? " KM> (the color of (the owns of *Joe)) evaluates to a Frame (*Red) KM> (the owns of *Joe) ( ) KM> (the color of ) (*Red)

Embedded Units and Access Paths (cont) • An access path will select all values on a slot. • (the <slot> of <instance>) • To select a subset – give a class name in the query • (the <class> <slot> of <instance>) – add a filter (“generate and test”), discussed later • (allof (the <slot> of <instance>) where <filter-condition>) ; ; ; "Joe is a person, and owns a car and a teddy bear. " KM> (*Joe has (instance-of (Person)) (owns ((a Car) (a Teddy-Bear)))) ; ; ; "What does Joe own? " KM> (the owns of *Joe) (_Car 1 _Teddy-Bear 2) ; ; ; "What vehicles does Joe own? " KM> (the Vehicle owns of *Joe)) (_Car 1)

Class Frames and Inheritance • Can state properties for all members of a class – (every <classname> has (<slot> (<value>))) • Each instance of that class acquires (inherits) those properties ; ; ; "People are physical objects" (property of the class) KM> (Person has (superclasses (Physobj))) ; ; ; "Every person lives in a house. " (property of class members) KM> (every Person has (lives-in ((a House)))) ; ; ; "Every house has a door and a roof. " KM> (every House has (parts ((a Door) (a Roof)))) ; ; ; "What does Joe live in? " KM> (the lives-in of *Joe) (_House 3) ; ; ; "What are the parts of the thing which Joe lives in? " KM> (the parts of (the lives-in of *Joe)) (_Door 4 _Roof 5)

Self • Within a class frame, Self refers to the instance inheriting the information. ; ; ; "Every person likes him/herself" KM> (every Person has (likes (Self))) (Person) KM> (the likes of *Fred) (*Fred) KM> (the likes of *Joe) (*Joe) ; ; ; "Every person likes their favorite color(s). " KM> (every Person has (likes ((the favorite-color of Self)))) (Person) ; ; ; "Fred's favorite color is blue. " KM> (*Fred has (instance-of (Person)) (favorite-color (*Blue))) (*Fred) KM> (the likes of *Fred) (*Fred *Blue) KM> (the Color likes of *Fred) (*Blue)

Exercises ; ; "All professors have (at least) one car which is old, is ; ; their favorite color, and was made in Sweden. " (Professor has (superclasses (Person))) (every Professor has (owns ( (a Car with (age (*Old)) (color ((the favorite-color of Self))) (made-by ((a Manufacturer with (location (*Sweden))))) 1. Write the KM queries to find: - the car that a professor owns - the age of a professor’s car - the location of the manufacturer of the professor’s car 2. Create a KM frame describing the concept of a Car (the Car class): (every Car has. . . )

Answers to Exercises 1 a. (the 1 b. (the 1 c. (the Car owns of (a Professor)) age of (the Car owns of (a Professor))) location of (the made-by of (the Car owns of (a Professor)))) 2. For example. . . (every Car has (color (age (made-by (parts ((a ((a (a (a Color))) Age-Value))) Manufacturer))) Chassis) Engine) Fuel-Tank with (supplies ((the Engine parts of Self)))))))

Exercise (Electrophoresis has (superclasses (Process))) (every Electrophoresis has (sample ((a Chemical))) (equipment ((a Separation-unit) (a Syringe))) (subevents ( (a Remove with (object ((the sample of Self))) (location ((the delivery-medium of (the sample of Self))))) (a Insert with (object ((the sample of Self))) (destination ((the Separation-unit equipment of Self))) (equipment ((the Syringe equipment of Self))))))) (Albumin has (superclasses (Chemical))) (every Albumin has (delivery-medium ((a Bottle))) (storage-medium ((a Fridge)))) 3. What is the result of the query: KM> (the location of (the Remove subevents of (a Electrophoresis with (sample ((a Albumin))))))

Answers to Exercises 3. _Bottle 8 (i. e. , a Skolem instance of Bottle). (the location of (the Remove subevents of (a Electrophoresis with (sample ((a Albumin))))))

Answers to Exercises 3. _Bottle 8 (i. e. , a Skolem instance of Bottle). (the location of (the Remove subevents of (a Electrophoresis with (sample ((a Albumin)))))) KM> (a Electrophoresis with (sample ((a Albumin)))) (_Electrophoresis 5)

Answers to Exercises 3. _Bottle 8 (i. e. , a Skolem instance of Bottle). (the location of (the Remove subevents of (a Electrophoresis with (sample ((a Albumin)))))) (the location of (the Remove subevents of _Electrophoresis 5))

Answers to Exercises 3. _Bottle 8 (i. e. , a Skolem instance of Bottle). (the location of (the Remove subevents of (a Electrophoresis with (sample ((a Albumin)))))) KM> (showme _Electrophresis 5) (_Electrophoresis 5 has (the location of (instance-of (Electrophoresis)) (the Remove subevents of _Electrophoresis 5)) (sample ((a Albumin))) (subevents ((a Remove) (a Insert))))

Answers to Exercises 3. _Bottle 8 (i. e. , a Skolem instance of Bottle). (the location of (the Remove subevents of (a Electrophoresis with (sample ((a Albumin)))))) (the location of (the Remove subevents of _Electrophoresis 5)) (the location of _Remove 6)

Answers to Exercises 3. _Bottle 8 (i. e. , a Skolem instance of Bottle). (the location of (the Remove subevents of (a Electrophoresis with (sample ((a Albumin)))))) KM> (showme _Remove 6) (_Remove 6 has (the location of (instance-of (Remove)) (the Remove subevents of _Electrophoresis 5)) (object ((the sample of _Electrophoresis 5))) (location ((the delivery-medium of (the sample of _Electrophoresis 5)))) (the location of _Remove 6) (subevents-of (_Electrophoresis 5)))

Answers to Exercises 3. _Bottle 8 (i. e. , a Skolem instance of Bottle). (the location of (the Remove subevents of (a Electrophoresis with (sample ((a Albumin)))))) (the location of (the Remove subevents of _Electrophoresis 5)) (the location of _Remove 6) (the delivery-medium of (the sample of _Electrophoresis 5))

Answers to Exercises 3. _Bottle 8 (i. e. , a Skolem instance of Bottle). (the location of (the Remove subevents of (a Electrophoresis with (sample ((a Albumin)))))) KM> (showme _Electrophresis 5) (_Electrophoresis 5 has (the location of (instance-of (Electrophoresis)) (the Remove subevents of _Electrophoresis 5)) (sample ((a Albumin))) (subevents (_Remove 6 (the location of _Remove 6) (a Insert)))) (the delivery-medium of (the sample of _Electrophoresis 5))

Answers to Exercises 3. _Bottle 8 (i. e. , a Skolem instance of Bottle). (the location of (the Remove subevents of (a Electrophoresis with (sample ((a Albumin)))))) (the location of (the Remove subevents of _Electrophoresis 5)) (the location of _Remove 6) (the delivery-medium of (the sample of _Electrophoresis 5)) (the delivery-medium of _Albumin 7)

Answers to Exercises 3. _Bottle 8 (i. e. , a Skolem instance of Bottle). (the location of (the Remove subevents of (a Electrophoresis with (sample ((a Albumin)))))) KM> (showme _Alubmin 7) (_Albumin 7 has (the location of (instance-of (Albumin)) (the Remove subevents of _Electrophoresis 5)) (sample-of (_Electrophoresis 5)) (delivery-medium ((a Bottle))) (the location of _Remove 6) (storage-medium ((a Fridge)))) (the delivery-medium of (the sample of _Electrophoresis 5)) (the delivery-medium of _Albumin 7)

Answers to Exercises 3. _Bottle 8 (i. e. , a Skolem instance of Bottle). (the location of (the Remove subevents of (a Electrophoresis with (sample ((a Albumin)))))) (the location of (the Remove subevents of _Electrophoresis 5)) (the location of _Remove 6) (the delivery-medium of (the sample of _Electrophoresis 5)) (the delivery-medium of _Albumin 7) (a Bottle)

Answers to Exercises 3. _Bottle 8 (i. e. , a Skolem instance of Bottle). (the location of (the Remove subevents of (a Electrophoresis with (sample ((a Albumin)))))) (the location of (the Remove subevents of _Electrophoresis 5)) (the location of _Remove 6) (the delivery-medium of (the sample of _Electrophoresis 5)) (the delivery-medium of _Albumin 7) (a Bottle) _Bottle 8

Simple Data Types • KM has numbers, integers, strings, booleans KM> (3. 1 isa Number) (t) KM> (3 isa Integer) (t) KM> (3. 1 isa Integer) NIL KM> (t = (not NIL)) (t) KM> (f = NIL) NIL KM> ("apocope" isa String) (t) KM> (99 = 100 +/- 2) (t) KM> (99 = 100 +/- 1 %) (t) KM> (4. 99999 = 5. 00000) (t) mind the gap x = y if [x equals y +/- (0. 0001 or 0. 01% of max(x, y), whichever is smaller (so 0. 0001 ≠ 0. 0002))]

Rules • The expression for a slot-value may be a rule • The rule is evaluated when the slot-value is queried • The tests and result of the rule are themselves KM expressions ; ; ; "A person is a voter if he/she is older than 18. " KM> (every Person has (is-voter ((if ((the age of Self) >= 18) then *Yes else (if ((the age of Self) < 18) then *No))))) ; ; ; "Is Fred a voter? " [Fred is 32, asserted earlier] KM> (the is-voter of *Fred) (*Yes) ; ; ; "Joe is 12 years old. " KM> (*Joe has (instance-of (Person)) (age (12))) (*Joe) ; ; ; "Is Joe a voter? " KM> (the is-voter of *Joe) (*No) ; ; ; "Is some generic person a voter? " KM> (the is-voter of (a Person)) NIL Why?

Exercise 4. Complete the expression on the “brightness” slot for the concept of a Light, so that the result depends on the light’s switch position. (every Light has (part ((a Switch with (position ((a Position. Value))))) (brightness (. . . ))) (*Up has (instance-of (Position. Value))) (*Down has (instance-of (Position. Value))) (*Bright has (instance-of (Brightness. Value))) (*Dark has (instance-of (Brightness. Value))))

Answers to Exercises 4. (every Light has (part ((a Switch with (position ((a Position. Value)))))) (brightness ( (if ((the position of (the Switch part of Self)) = *Up) then *Bright else (if ((the position of (the Switch part of Self)) = *Down) then *Dark))))) Note that if the position is unknown, then the brightness will be unknown also (which is what we want).

Complex Types • KM also has sets, sequences, bags ; ; ; "Jason has two favorite colors" KM> (*Jason has (favorite-color (*Blue *Green))) (*Jason) KM> (the favorite-color of *Jason) (*Blue *Green) ; ; ; "So does Mike" KM> (*Mike has (favorite-color ((: set *Blue *Green)))) (*Mike) KM> (the favorite-color of *Mike) (*Blue *Green) ; ; ; "Mike, John and Jason finished 1 st, 2 nd and 3 rd" KM> (a Tournament with (finishers ((: seq *Mike *John *Jason)))) (_Tournament 6) ; ; ; "Mike had scores of 66, 67, 73 and 67 KM> (*Mike has (round-score ((: bag 66 67 73 67)))) (*Mike)

Arithmetic • KM has infix operators +, -, *, /, ^ • Also has arithmetic slots: (the sum of …. ), etc. – sum, difference, product, quotient, and others ; ; ; "What is 1 + 1? " KM> (1 + 1) (2) ; ; ; "A person's age in days is their age [in years] times 365. " KM> (every Person has (age-in-days (((the age of Self) * 365)))) (Person) ; ; ; "What is Fred's age in days? " KM> (the age-in-days of *Fred) (11680) ; ; ; "What was Mike's total score last week? “ KM> (*Mike has (round-score ((: bag 66 67 73 67)))) (Mike) KM> (the sum of (the round-score of *Mike)) (273)

Set Expressions • Procedurally, KM iterates over a set of values • Two main iterators – (allof <set> where <filter-condition>) – (forall <set> where <filter-condition> <expression>) • Keyword It denotes the value in each iteration ; ; ; "Show me every person [in the KB so far]? " KM> (every Person) (*Joe *Fred) ; ; ; or equivalently KM> (the all-instances of Person) (*Joe *Fred) ; ; ; "Which people are over 18? " KM> (allof (the all-instances of Person) where ((the age of It) > 18)) (*Fred) ; ; ; "What is the favorite color(s) of the people over 18? " KM> (forall (the all-instances of Person) where ((the age of It) > 18) (the favorite-color of It)) (*Blue)

Aside: Tracing in KM KM> (*Lily has (instance-of (Person)) (favorite-color (*Lilac)) (age (21))) (*Lily) KM> (trace) (Tracing of KM switched on) KM> (forall (the all-instances of Person) where ((the age of It) > 18) (the favorite-color of It)) 1 -> (forall (the all-instances of Person) where ((the age of It) > 18) (the favorite-color of It)) 2 -> (the all-instances of Person) 2 <- (*Joe *Fred *Lily) [(the all-instances of Person)] 2 -> ((the age of *Joe) > 18) 3 -> (the age of *Joe) 3 <- (12) [(the age of *Joe)] 2 <- FAIL! [((the age of *Joe) > 18)] 2 -> ((the age of *Fred) > 18) 3 -> (the age of *Fred) 3 <- (32) [(the age of *Fred)] 2 <- (t) [((the age of *Fred) > 18)] 2 -> (the favorite-color of *Fred) 2 <- (*Blue) [(the favorite-color of *Fred)] 2 -> ((the age of *Lily) > 18) 3 -> (the age of *Lily) 3 <- (21) [(the age of *Lily)] 2 <- (t) [((the age of *Lily) > 18)] 2 -> (the favorite-color of *Lily) 2 <- (*Lilac) [(the favorite-color of *Lily)] 1 <- (*Blue *Lilac) [(forall. . . (*Blue *Lilac) KM> (untrace) (Tracing of KM switched off)

What’s Wrong with Set Expressions? • Two main iterators – (allof <set> where <filter-condition>) – (forall <set> where <filter-condition> <expression>) • Keyword It denotes the value in each iteration • Hint: – if <expression> can be any KM expression, could it be an iterator? – could <set> and <filter-condition> contain iterators?

Set Expressions with Variables • A slightly more general form allows for nested iterators – (allof <var> in <set> where <filter-condition>) – (forall <var> in <set> where <filter-condition> <expression>) ; ; ; "Which people are over 18? " KM> (allof ? x in (the all-instances of Person) where ((the age of ? x) > 18)) (*Fred *Lily) ; ; ; "What is the favorite color(s) of the people over 18? " KM> (forall ? y in (the all-instances of Person) where ((the age of ? y) > 18) (the favorite-color of ? y)) (*Blue *Lilac) ; ; ; "What things do people over 18 own that are their favorite colors? " KM> (forall ? p in (the all-instances of Person) where ((the age of ? p) > 18) (allof ? t in (the owns of ? p) where ((the color of ? t) = (the favorite-color of ? p)) ) ) (_Car 11 _House 13)

Unification ; ; ; "Johanne likes some cute puppy" KM> (*Johanne has (likes ((a Puppy with (trait (*cute)))))) (*Johanne) ; ; ; "What puppy does Johanne like? “ KM> (the likes of *Johanne) (_Puppy 25) ; ; ; "Victor is a puppy" KM> (*Victor has (instance-of (Puppy)) (color (*brown))) (*Victor) • Is it possible that _Puppy 25 and *Victor are the same puppy? • What would we then know about *Victor?

Unification • The assertion of equality of two objects • The merging of data structures associated with instances (_Person 3 has (parts ((a Brain))) (name ("Albert"))) ) (_Student 4 has (parts ((a Body))) (gpa (9. 6))) ) (_Student 4 has (parts ((a Brain) (a Body))) (name ("Albert"))) (gpa (9. 6)) )

Vertical Unification (Inheritance) • Inheritance is a kind of unification • An instance of a class is the unification of anonymous instances of all its ancestor classes (every Living-Thing has (parts ((a Body))) ) _Living-Thing 832 superclasses (every Person has (parts ((a Brain))) ) _Person 834 superclasses (every Student has (gpa ((a Number))) ) _Student 836 isa (_Student 4 has (parts ((a Brain) (a Body))) (gpa ((a Number))) ) _Student 4 = _Living-Thing 832 & _Person 834 & _Student 836 & _Student 4

Multiple Inheritance and Unification • If several frames contribute to a slot’s values, KM will unify the different sets of values together – set unification is heuristic, not deductive • “&” unifies two instances together • “&&” unifies two sets together • “&? ” and “&&? ” check if unification is possible (without doing the unification) ; ; ; Can a pet and a fish unify? KM> ((a Pet) &? (a Fish)) (t) ; ; ; Unify these two objects together KM> ((a Pet) & (a Fish)) (_Pet 1) KM> (showme _Pet 1) (_Pet 1 has (instance-of (Pet Fish))) ; ; ; Unify these two sets together KM> (((a Cat) (a Dog)) && ((a Cat) (a Rabbit))) (_Cat 1 _Dog 2 _Rabbit 3)

Inheritance and Unification: Example ; ; ; "Every big car has a large engine. " KM> (every Big-Car has (parts ((a Engine with (size (*Large)))))) ; ; ; "Every powerful car has a powerful engine. " KM> (every Powerful-Car has (parts ((a Engine with (power (*Lots)))))) ; ; ; "Suburbans are both big and powerful cars. " KM> (Suburban has (superclasses (Big-Car Powerful-Car))) ; ; ; "What are the parts of a Suburban? " KM> (the parts of (a Suburban)) (COMMENT: (_Engine 7 && _Engine 8) unified to be _Engine 7) (_Engine 7) KM> (showme (thelast Engine)) (_Engine 7 has (instance-of (Engine)) (size (*Large)) (power (*Lots)) (parts-of (_Suburban 6))) Note result of unification: Engine is both large and has lots of power. Here KM decides the 2 engines are coreferential because (i) same class (or one’s classes subsumes the others’) (ii) unification doesn’t violate constraints

Inheritance & Unification: Another Example • Again, the different contributing value sets are unified together. ; ; ; "Every person has two legs and a head. " KM> (every Person has (parts ((a Head) (a Leg)))) (Person) ; ; ; "Fred has a leg. " KM> (*Fred has (parts ((a Leg)))) (*Fred) ; ; ; "What are the parts of Fred? " ; ; ; [Note: two legs -- KM unifies one of the two legs on Person ; ; ; with the leg on Fred] KM> (the parts of *Fred) (_Leg 9 _Head 10 _Leg 11)

Defeating Inheritance • There are several tools in KM to control unification • One powerful tool is inherit-with-overrides KM> (birth has (domain (Animal)) (instance-of (Slot)) (cardinality (N-to-1))) (birth) KM> (every Mammal has (birth (*Live))) (Mammal) KM> (Platypus has (superclasses (Mammal))) (Platypus) KM> (every Platypus has (birth (*Egg))) (Platypus) KM> (the birth of (a Platypus)) ERROR! Unification (*Egg & *Live) failed! NIL KM> (birth has (inherit-with-overrides (t))) (birth) KM> (the birth of (a Platypus)) (*Egg)

Constraints • Can attach constraints to a slot – constrains the allowed values on that slot – checked when that slot is queried • Two types: – value constraints: applies to each value in turn • • (every Witch has (pet ((must-be-a Cat with (color (*Black)))))) (every Witch has (pet ((mustnt-be-a Dog)))) (every Sedan has (doors ((<> 3)))) (a Cat with (color ((constraint (The. Value = *Black))))) • (a Witch with (pet ((constraint ((the color of The. Value) = *Black))))) – set constraints: applies to the set of values • • (every Animal has (parts ((at-least 2 Leg)))) (every Human has (parts ((at-most 2 Leg)))) (every Bipod has (parts ((exactly 2 Leg)))) (a Triumvirate with (member ((set-constraint ((the number of The. Values) = 3)))))

Value Constraints • Checks each value in turn, when the slot is queried • keyword The. Value denotes the value being tested • must-be-a constraints are enforced (not just checked) ; ; ; "A person's friends must all be of class Person. " KM> (every Person has (friends ((must-be-a Person)))) ; ; ; "A person cannot marry him/herself. " (<> means "cannot equal") KM> (every Person has (spouse ((<> Self)))) ; ; ; "Fred's spouse is himself (and Smilla). " KM> (*Fred has (spouse (*Fred *Smilla))) KM> (showme *Fred) (*Fred has (instance-of (Person)) (age (32)) (favorite-color (*Blue)) (spouse (*Fred *Smilla)) (spouse-of (*Fred))) (*Fred) ; ; ; "Who is Fred's spouse? " [The constraint violation is detected at query time] KM> (the spouse of *Fred) ERROR! Constraint violation! Discarding value *Fred (conflicts with (<> *Fred))

Set Constraints • Checks the entire set of values on a slot • Keyword The. Values denotes the set being tested • Useful for at most / at least constraints ; ; ; "Every Airplane has exactly two wings. " KM> (every Airplane has (parts ((exactly 2 Wing)))) (Airplane) ; ; ; General value constraints: The. Value denotes the value being checked. KM> (every Person has (leg-parts ((constraint (The. Value isa Leg))))) ; ; ; General set constraints: The. Values denotes the set of values being checked. KM> (every Person has (leg-parts ((set-constraint ((the number of The. Values) <= 2)))))

Defined Classes and Automatic Classification • Defining properties of a class: – Any object with these properties is in that class – (every <classname> has-definition (instance-of (<generalclass>)) (<slot> (<value>)). . . ) • If new info found about an instance, its classes are re-checked ; ; ; "A Texan is a person who lives in Texas, ; ; ; AND every person living in Texas is a Texan. " KM> (every Texan has-definition (instance-of (Person)) Sufficient to conclude (lives-in (*Texas))) a Person is a Texan KM> (every Texan has (likes (*Willie))) KM> (the instance-of of *Fred) (Person) Necessary feature of Texans KM> (*Fred has (lives-in (*Texas))) (COMMENT: *Fred satisfies definition of Texan, ) (COMMENT: so changing *Fred's classes from (Person) to (Texan)) (*Fred) KM> (the instance-of of *Fred) (Texan) KM> (the likes of *Fred) (*Willie)

Care with Automatic Classification • KM is eager with automatic classification – as soon as an instance is created or modified, KM (re)checks all classification rules KM> (Island-Country has (superclasses (Country))) (Island-Country) KM> (every Island-Country has-definition (instance-of (Country)) (neighbors ((exactly 0 Country)))) (Island-Country) KM> (*USA has (instance-of (Country))) (COMMENT: *USA satisfies definition of Island-Country, ) (COMMENT: so changing *USA's classes from (Country) to (Island-Country)) (*USA) KM> (*Canada has (instance-of (Country)) (neighbors (*USA))) (*Canada) KM> (*Spain has (instance-of (Country)) (neighbors (*Portugal))) (COMMENT: *Spain satisfies definition of Island-Country, ) (COMMENT: so changing *Spain's classes from (Country) to (Island-Country)) (*Spain)

Exercise 5. Create KM frames defining – the concept of a Red. Wine (a red wine) – a bachelor – a square

Answers to Exercise 5 a. (every Red. Wine has-definition (instance-of (Wine)) (color (*Red))) 5 b. (every Bachelor has-definition (instance-of (Man)) (spouse ((exactly 0 Thing)))) 5 c. (every Square has-definition (instance-of (Rectangle)) (length ((the width of Self))) (width ((the length of Self))))

Situations • A situation is a partition of the knowledge base – Mainly to represent “snapshots” of the world at different times • Facts can differ in each situation • But each situation acquires all the facts of the global situation • Situations can be temporally ordered • Can define actions which change a situation, and thus perform simulation *Global supersituations subsituations import prev-situation _Situation 1 project next-situation supersituations prev-situation _Situation 2 project next-situation _Situation 3

Situations: Fluents and Non-Fluents • Non-fluent: Fact is universally true • Inertial-fluent: Fact can propagate from one situation to the next • (Non-inertial) Fluent: Fact does not propagate ; ; ; "Mike was born in 1977. " KM> (*Mike has (birthdate (1977))) (*Mike) ; ; ; "birthdate is a constant ('non-fluent')" KM> (birthdate has (instance-of (Slot)) (cardinality (N-to-1)) (fluent-status (*Non-Fluent))) ; ; ; "age may vary, but by default will remain unchanged. " KM> (age has (instance-of (Slot)) (cardinality (N-to-1)) (fluent-status (*Inertial-Fluent)))

Situations: Projection (example) ; ; ; "Create a new situation. " KM> (new-situation) (COMMENT: Changing to situation _Situation 24) ; ; ; "In this situation, Mike is 27 years old. " [_Situation 24] KM> (*Mike has (age (27))) ; ; ; "What is Mike's age [in this situation]? " [_Situation 24] KM> (the age of *Mike) (27) ; ; ; "Create and go to a new situation, the temporal successor of this one. " [_Situation 24] KM> (next-situation) (COMMENT: Changing to situation _Situation 25) ; ; ; "What is Mike's age [in this situation]? " [_Situation 25] KM> (the age of *Mike) (COMMENT: Projected *Mike age = (27) from _Situation 24 to _Situation 25) (27)

Situations: Projection (cont) • For “inertial fluents”, facts only propagate from one situation to the next if it is consistent to do so. [_Situation 25] KM> (next-situation) (COMMENT: Changing to situation _Situation 26) (_Situation 26) ; ; ; "In this situation, Mike is 28 years old. " [_Situation 26] KM> (*Mike has (age (28))) (*Mike) ; ; ; "What is Mike's age [in this situation]? " ; ; ; [Note '27' is not projected, as '28' overrides it and this slot cannot ; ; ; have multiple values. ] [_Situation 26] KM> (the age of *Mike) (28)

Querying Situations from the Global Situation • Can also query one situation from another – (in-situation <situation> <query>) • KM remembers each situation (so can query over them all) ; ; ; "Exit this situation, and return to the 'global situation'. " [_Situation 26] KM> (global-situation) (COMMENT: Changing to situation *Global) (t) ; ; ; "In the last situation created, what was Mike's age? " KM> (in-situation (thelast Situation) (the age of *Mike)) (28) ; ; ; "In which situations was Mike 27? " KM> (allof (the all-instances of Situation) where (in-situation It ((the age of *Mike) = 27))) (_Situation 25 _Situation 24)

Specifying Actions • Actions define how an event changes the world • They specify – preconditions: facts which must be true for the action to be performable – add-list, del-list: facts which become true/false as a result of the action • Facts are stated as “triples” (frame-slot-value structures) ; ; ; "Every switching on is an Action. " KM> (Switching-On has (superclasses (Action))) (Switching-On) ; ; ; "Every switching on changes a switch's position from down to up. " KM> (every Switching-On has (object ((a Switch))) (del-list ((: triple (the object of Self) position *Down))) (add-list ((: triple (the object of Self) position *Up)))) (Switching-On) Frame Slot Value

Simulation will ‘execute’ an action in a situation – creates a new situation – updates the facts in it, according to the action • do-and-next ; ; ; "Create a new situation. " KM> (new-situation) ; ; ; "There is a switch whose position [in this situation] is down. " [_Situation 27] KM> (a Switch with (position (*Down))) (_Switch 28) ; ; ; "Create and enter the situation resulting from switching that switch on. " [_Situation 27] KM> (do-and-next (a Switching-On with (object (_Switch 28)))) (_Situation 30) ; ; ; "What is the position [in this new situation] of that switch? " [_Situation 30] KM> (the position of _Switch 28) (*Up)

Simulation (cont) • again, previous situations can be queried and quantified over ; ; ; --- previous situations are preserved --; ; ; "In the previous situation, what was the position of the switch? " [_Situation 30] KM> (in-situation (the prev-situation of (curr-situation)) (the position of _Switch 28)) (*Down) ; ; ; "In which situations was the switch down? " [_Situation 30] KM> (allof (the all-instances of Situation) where (in-situation It ((the position of _Switch 28) = *Down))) (_Situation 27)

Another Example of Simulation (Open has (superclasses (Action))) (every Open has (object ((a Door))) (pcs-list ((: triple (the object of Self) lock-state *Unlocked))) (add-list ((: triple (the object of Self) door-state *Open))) (del-list ((: triple (the object of Self) door-state *Closed))) ) (lock-state has (instance-of (Slot)) (cardinality (N-to-1))) (door-state has (instance-of (Slot)) (cardinality (N-to-1))) [_Situation 1] KM> (a Door with (lock-state (*Unlocked))) (_Door 2) [_Situation 1] KM> (a Open with (object (_Door 2))) (_Open 3) [_Situation 1] KM> (do-and-next _Open 3) (COMMENT: Changing to Situation _Situation 4) (_Situation 4) [_Situation 4] KM> (the door-state of _Door 2) (*Open)

Another Example of Simulation [_Situation 4] KM> (a Door) (_Door 5) [_Situation 4] KM> (do-and-next (a Open with (object (_Door 5)))) (COMMENT: Assuming (: triple _Door 5 lock-state *Unlocked), to do action _Open 6. . . ) (COMMENT: Changing to Situation _Situation 7) (_Situation 7) [_Situation 7] KM> (in-situation _Situation 4 (the lock-state of _Door 5)) (*Unlocked) [_Situation 7] KM> (a Door with (lock-state (*Locked))) (_Door 8) [_Situation 7] KM> (do-and-next (a Open with (object (_Door 8)))) (do _Open 9): Can't do this action as it would be inconsistent to assert precondition(s): (: triple _Door 8 lock-state *Unlocked) NIL [_Situation 7] KM>

Text Generation • A special type of instance is a sequence – (: seq v 1 … vn) • Text strings can be built up as a sequence of fragments KM> (every Remove has (text ( (: seq "Remove" (the object of Self) "from" (the location of Self))))) ; ; ; "What is are the text for a remove of a sample from a box? ” KM> (the text of (a Remove with (object ((a Sample))) (location ((a Box))))) ((: seq "Remove" _Sample 14 "from" _Box 15)) ; ; ; "Make a sentence from these fragments. " KM> (make-sentence (the text of (a Remove with (object ((a Sample))) (location ((a Box)))))) ("Remove the sample from the box. ")

Slot Hierarchies • Slots can have subslots • Values of subslots are also values of the superslot – values “propagate up”) ; ; ; "parts has subslots mechanical-parts. " KM> (parts has (instance-of (Slot)) (subslots (mechanical-parts structural-parts))) (parts) ; ; ; "Every airplane has a jet engine as one of its mechanical parts ; ; ; and a fuselage as one of its structural parts. " KM> (every Airplane has (mechanical-parts ((a Jet-Engine))) (structural-parts ((a Fuselage)))) (Airplane) ; ; ; "What are the parts of an airplane? " KM> (the parts of (a Airplane)) (_Jet-Engine 23 _Fuselage 24)

Prototypes Example KM> (a Airplane with (has-part ((a Wing)))) (_Airplane 9) KM> (showme _Airplane 9) (Airplane 9 has (instance-of (Airplane)) (has-part ((a Wing)))) KM> (showme Airplane) (Airplane has (superclasses (Device)) (instances (_Airplane 9))) KM> (the has-part of (a Airplane)) NIL

Prototypes Example KM> (a-prototype Airplane) (_Proto. Airplane 11) [prototype-mode] KM> (_Proto. Airplane 11 has (has-part ((a Wing)))) (_Proto. Airplane 11) [prototype-mode] KM> (end-prototype) KM> (showme Airplane) (Airplane has (superclasses (Device)) (instances (_Airplane 9 _Airplane 10 _Proto. Airplane 11)) (prototypes (_Proto. Airplane 11))) KM> (the has-part of (a Airplane)) (COMMENT: Cloned _Proto. Airplane 11 -> _Airplane 15 to find (the has-part of _Airplane 14)) (COMMENT: (_Airplane 14 & _Airplane 15) unified to be _Airplane 14) (Wing 16 _Wing 17)

KM: Some Outstanding Issues • • Reasoning can get complex, and hard to debug No full truth maintenance Need for “defaults” – added during RKF Heuristic unification can sometimes get it wrong – Knowledge engineer can provide guidance • Use of prototypes important for KM in Shaken • Explanations: – store which rule derived which fact – being extended to store the “proof tree” for a fact

A KM Concept Library • Insight: even domain-specific representations contain common abstractions • Approach: we build a library consisting of – a small hierarchy of reusable, composable, domainindependent concepts (“components”) – a small vocabulary of relations to connect them then domain experts build representations by instantiating and composing these components

l smal A Library of Components • • easy to learn easy to use broad semantic distinctions (easy to choose) allows detailed pre-engineering

Component Library Contents • • actions — things that happen, change states – Enter, Copy, Replace, Transfer, etc. states — relatively temporally stable events – Be-Closed, Be-Attached-To, Be-Confined, etc. entities — things that are – Substance, Place, Object, etc. roles — things that are, but only in the context of things that happen – Container, Catalyst, Barrier, Vehicle, etc.

Library Contents • • relations between events, entities, roles – – agent, donor, object, recipient, result, etc. content, part, material, possession, etc. causes, defeats, enables, prevents, etc. purpose, plays, etc. properties between events/entities and values – – rate, frequency, intensity, direction, etc. size, color, integrity, shape, etc.

Informal Representation • “A person throws a ball toward the door of a room. The ball passes through the door and into the room…”

KM + CLib Representation (a Activity with (agent ((a Person))) (object ((a Ball))) (first-subevent ((the Throw subevent of Self))) (subevent ( (a Throw with (object ((the Ball object of Self))) (destination ((a Door))) (next-event ((the Move-Into subevent of Self))) ) (a Move-Into with (object ((the Ball object of Self))) (base ((a Room with (has-region ( (the Door destination of (the Throw subevent of Self))))))) )

Component Library Adds…

Component Library Adds… • • • • The Ball and the Person must be together at t 0 The Ball must be held by the Person at t 0 The Ball must not be otherwise Restrained The path to the Door must not be Blocked At t 1 the Ball is at the Door and no longer at the Person At t 1 the Ball is outside the Room but not shut of it The Door must not be Closed The Ball passes through the Doorway At t 2 the Ball is inside the Room and no longer outside At t 2 the Room has the Ball among its contents Blocked paths can be unblocked Closed Doors can be Opened …

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