KM: The Knowledge Machine A knowledge representation and reasoning system.

KM: The Knowledge MachineA knowledge representation and reasoning system

What is KM?• A Knowledge Representation Language (KRL)

– (like KIF, or CycL, 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 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?– PartyAtMyHouseThisSaturday, ThePCInMyOffice

• 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 3:30pm, 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 p1 has a mother p2– most Computers c have a part h that is a Hard-Drive

• Instances– PartyAtMyHouseThisSaturday is an instance of Event– ThePCInMyOffice is an instance of Computer– ThisLecture is an instance of Event with time-of-occ 3:30pm– 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

– ThePCInMyOffice is an instance of Computer– the superclass of Computer is Device? Is ThePCInMyOffice a Device?

• FOPC– Computer(ThePCInMyOffice) x Computer(x) Device(x)? Device(ThePCInMyOffice)

• KM– (ThePCInMyOffice has

(instance-of (Computer)))

– (Computer has (superclasses (Device)))

? (ThePCInMyOffice 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

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 MonteCristo)(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)

The ‘*’ has no special meaningin KM; We use it as a handyvisual indicator to distinguishinstances and classes

How does it know?

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)(*BettyJo)

KM> (*Bryen has (father (*Thomas)))(*Bryen)

KM> (the grandmother of *Bryen)(*BettyJo)

KM> (save-kb "a-family2.km")a-family2.km saved!

Instances• Recall:

– an instance denotes some object in the world– a class is a collection of instances1

• An instance (individual) evaluates to itself

;;; --- instances ---

;;; "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)

‘;’ = comment to end of line

“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)(_Cat0) ; _Cat0 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))) )(_Cat1)

An instance together with all the knowledge attached to thatinstance is called a “Frame”

KM> (showme _Cat1)(_Cat1 has (instance-of (Cat)) (color (*Black)) (parts ((a Head) (a Tail))))

(_Cat1)

Guaranteed uniqueand fresh!

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)(_Car3)

KM> (_Car3 has (color (*Silver)))(_Car3)

KM> (showme _Car3)(_Car3 has (instance-of (Car)) (color (*Silver)))

KM> (a Car with (color (*Silver)))(_Car4)

KM> (showme _Car4)(_Car4 has (instance-of (Car)) (color (*Silver)))

FrameSlot

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)) (domain (Physobj)) (range (Number)) (inverse (is-age-of)) ; name of the inverse slot (cardinality (N-to-1))) ; one age per thing

Frame

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 (_Car3 _Car4)))(Car)

KM> (the subclasses of Vehicle)(Car)

The Taxonomy (Inheritance Hierarchy)

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 PersonI *FredI *Joe…. etc…..

• Classes can themselves be subclasses of (multiple) other classes

• (taxonomy) shows the entire taxonomy

Thing

Physobj Number

Car Person ….

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)(32) Frame (identifier)

SlotValue

Slot Inverses • KM keeps track of inverse relations also

X→r→YY→r-1→X

;;; "Fred owns a car."KM> (*Fred has (owns ((a Car))))

;;; "What does Fred own?"KM> (the owns of *Fred)(_Car1) ; (Skolem _Car1 created, denoting that car)

;;; "Show me the frame representing that last car."KM> (showme (thelast Car))(_Car1 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))(*Red)

KM> (the owns of *Joe)( )KM> (the color of )(*Red)

evaluates to a Frame

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)(_Car1 _Teddy-Bear2)

;;; "What vehicles does Joe own?"KM> (the Vehicle owns of *Joe))(_Car1)

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)(_House3)

;;; "What are the parts of the thing which Joe lives in?"KM> (the parts of (the lives-in of *Joe))(_Door4 _Roof5)

Self

;;; "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)

• Within a class frame, Self refers to the instance inheriting the information.

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 car2. Create a KM frame describing the concept of a Car (the Car class):

(every Car has ...)

Answers to Exercises1a. (the Car owns of (a Professor))1b. (the age of (the Car owns of (a Professor)))1c. (the location of (the made-by of (the Car owns of (a Professor))))

2. For example...(every Car has

(color ((a Color))) (age ((a Age-Value))) (made-by ((a Manufacturer))) (parts ((a Chassis) (a Engine) (a 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. _Bottle8 (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))))(_Electrophoresis5)

KM> (a Electrophoresis with (sample ((a Albumin))))(_Electrophoresis5)




(the location of (the Remove subevents of _Electrophoresis5))





KM> (showme _Electrophresis5)(_Electrophoresis5 has (instance-of (Electrophoresis)) (sample ((a Albumin))) (subevents ((a Remove) (a Insert))))

KM> (showme _Electrophresis5)(_Electrophoresis5 has (instance-of (Electrophoresis)) (sample ((a Albumin))) (subevents ((a Remove) (a Insert))))





(the location of _Remove6)






KM> (showme _Remove6)(_Remove6 has (instance-of (Remove)) (object ((the sample of _Electrophoresis5))) (location ((the delivery-medium of (the sample of _Electrophoresis5)))) (subevents-of (_Electrophoresis5)))

KM> (showme _Remove6)(_Remove6 has (instance-of (Remove)) (object ((the sample of _Electrophoresis5))) (location ((the delivery-medium of (the sample of _Electrophoresis5)))) (subevents-of (_Electrophoresis5)))






(the delivery-medium of (the sample of _Electrophoresis5))







KM> (showme _Electrophresis5)(_Electrophoresis5 has (instance-of (Electrophoresis)) (sample ((a Albumin))) (subevents (_Remove6 (a Insert))))

KM> (showme _Electrophresis5)(_Electrophoresis5 has (instance-of (Electrophoresis)) (sample ((a Albumin))) (subevents (_Remove6 (a Insert))))







(the delivery-medium of _Albumin7)








KM> (showme _Alubmin7)(_Albumin7 has (instance-of (Albumin)) (sample-of (_Electrophoresis5)) (delivery-medium ((a Bottle))) (storage-medium ((a Fridge))))

KM> (showme _Alubmin7)(_Albumin7 has (instance-of (Albumin)) (sample-of (_Electrophoresis5)) (delivery-medium ((a Bottle))) (storage-medium ((a Fridge))))








(a Bottle)








(a Bottle)

_Bottle8

Simple Data Types

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)

• KM has numbers, integers, strings, booleans

x = y if [x equals y +/- (0.0001 or 0.01% of max(x,y),whichever is smaller (so 0.0001 ≠ 0.0002))]

mind the gap

Rules

;;; "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)

• 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

Why?

;;; "Is some generic person a voter?"KM> (the is-voter of (a Person))NIL

Exercise4. 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 PositionValue))))) (brightness (...)))

(*Up has (instance-of (PositionValue)))(*Down has (instance-of (PositionValue)))

(*Bright has (instance-of (BrightnessValue)))(*Dark has (instance-of (BrightnessValue))))

Answers to Exercises4. (every Light has (part ((a Switch with

(position ((a PositionValue)))))) (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

;;; "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 1st, 2nd and 3rd"KM> (a Tournament with (finishers ((:seq *Mike *John *Jason))))(_Tournament6)

;;; "Mike had scores of 66, 67, 73 and 67KM> (*Mike has (round-score ((:bag 66 67 73 67))))(*Mike)

• KM also has sets, sequences, bags

Arithmetic

;;; "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)

• KM has infix operators +, -, *, /, ^• Also has arithmetic slots: (the sum of ….), etc.

– sum, difference, product, quotient, and others

Set Expressions

;;; "Show me every person [in the KB so far]?"KM> (every Person)(*Joe *Fred)

;;; or equivalentlyKM> (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)

• 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

Aside: Tracing in KMKM> (*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

;;; "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)) ) )(_Car11 _House13)

• A slightly more general form allows for nestediterators– (allof <var> in <set> where <filter-condition>)– (forall <var> in <set> where <filter-condition> <expression>)

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)(_Puppy25)

;;; "Victor is a puppy"KM> (*Victor has (instance-of (Puppy)) (color (*brown)))(*Victor)

• Is it possible that _Puppy25 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

(_Person3 has (parts ((a Brain))) (name ("Albert"))))

(_Student4 has (parts ((a Body))) (gpa (9.6))))

(_Student4 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 Person has (parts ((a Brain))))

(every Student has (gpa ((a Number))))

(_Student4 has (parts ((a Brain) (a Body))) (gpa ((a Number))))

(every Living-Thing has (parts ((a Body))))

isa

superclasses

superclasses

_Living-Thing832

_Person834

_Student836

_Student4 = _Living-Thing832 & _Person834 & _Student836 & _Student4

Multiple Inheritance and Unification

;;; Can a pet and a fish unify?KM> ((a Pet) &? (a Fish))(t)

;;; Unify these two objects togetherKM> ((a Pet) & (a Fish))(_Pet1)

KM> (showme _Pet1)(_Pet1 has (instance-of (Pet Fish)))

;;; Unify these two sets togetherKM> (((a Cat) (a Dog)) && ((a Cat) (a Rabbit)))(_Cat1 _Dog2 _Rabbit3)

• 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)

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: (_Engine7 && _Engine8) unified to be _Engine7)(_Engine7)

KM> (showme (thelast Engine))(_Engine7 has (instance-of (Engine)) (size (*Large)) (power (*Lots)) (parts-of (_Suburban6)))

Here KM decides the 2 enginesare coreferential because (i) same class (or one’s classes

subsumes the others’) (ii) unification doesn’t violate constraints

Note result of unification: Engine is both large and has lots of power.

Inheritance & Unification: Another Example

;;; "Every person has two legs and a head."KM> (every Person has (parts ((a Head) (a Leg) (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)(_Leg9 _Head10 _Leg11)

• Again, the different contributing value sets are unified together.

Defeating Inheritance

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)

• There are several tools in KM to control unification• One powerful tool is inherit-with-overrides

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 (TheValue = *Black)))))• (a Witch with

(pet ((constraint ((the color of TheValue) = *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 TheValues) = 3)))))

Value Constraints

;;; "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))

• Checks each value in turn, when the slot is queried• keyword TheValue denotes the value being tested• must-be-a constraints are enforced (not just checked)

Set Constraints

;;; "Every Airplane has exactly two wings."KM> (every Airplane has (parts ((exactly 2 Wing))))(Airplane)

;;; General value constraints: TheValue denotes the value being checked.KM> (every Person has (leg-parts ((constraint (TheValue isa Leg)))))

;;; General set constraints: TheValues denotes the set of values being checked.KM> (every Person has (leg-parts ((set-constraint ((the number of TheValues) <= 2)))))

• Checks the entire set of values on a slot• Keyword TheValues denotes the set being tested• Useful for at most / at least constraints

Defined Classes and Automatic Classification

;;; "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)) (lives-in (*Texas)))

KM> (every Texan has (likes (*Willie)))

KM> (the instance-of of *Fred)(Person)

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)

• 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

Necessary featureof Texans

Sufficient to concludea Person is a Texan

Care with Automatic Classification

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)

• KM is eager with automatic classification– as soon as an instance is created or modified, KM

(re)checks all classification rules

Exercise

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

Answers to Exercise

5a. (every RedWine has-definition (instance-of (Wine)) (color (*Red)))

5b. (every Bachelor has-definition (instance-of (Man)) (spouse ((exactly 0 Thing))))

5c. (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

_Situation1 _Situation2 _Situation3

supersituations

subsituations

supersituationssubsituations

supersituations

subsituations

importimport

projectproject

next-situationnext-situation

prev-situation prev-situation

projectproject

Situations: Fluents and Non-Fluents

;;; "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)))

• Non-fluent: Fact is universally true• Inertial-fluent: Fact can propagate from one situation to the next• (Non-inertial) Fluent: Fact does not propagate

Situations: Projection (example);;; "Create a new situation."KM> (new-situation)(COMMENT: Changing to situation _Situation24)

;;; "In this situation, Mike is 27 years old."[_Situation24] KM> (*Mike has (age (27)))

;;; "What is Mike's age [in this situation]?"[_Situation24] KM> (the age of *Mike)(27)

;;; "Create and go to a new situation, the temporal successor of this one."[_Situation24] KM> (next-situation)(COMMENT: Changing to situation _Situation25)

;;; "What is Mike's age [in this situation]?"[_Situation25] KM> (the age of *Mike)(COMMENT: Projected *Mike age = (27) from _Situation24 to _Situation25)(27)

Situations: Projection (cont)

[_Situation25] KM> (next-situation)(COMMENT: Changing to situation _Situation26)(_Situation26)

;;; "In this situation, Mike is 28 years old."[_Situation26] 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.][_Situation26] KM> (the age of *Mike)(28)

• For “inertial fluents”, facts only propagate from one situation to the next if it is consistent to do so.

Querying Situations from the Global Situation

;;; "Exit this situation, and return to the 'global situation'."[_Situation26] 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)))(_Situation25 _Situation24)

• Can also query one situation from another– (in-situation <situation> <query>)

• KM remembers each situation (so can query over them all)

Specifying Actions

;;; "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)

• 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)

Frame Slot Value

Simulation

;;; "Create a new situation."KM> (new-situation)

;;; "There is a switch whose position [in this situation] is down."[_Situation27] KM> (a Switch with (position (*Down)))(_Switch28)

;;; "Create and enter the situation resulting from switching that switch on."[_Situation27] KM> (do-and-next (a Switching-On with (object (_Switch28))))(_Situation30)

;;; "What is the position [in this new situation] of that switch?"[_Situation30] KM> (the position of _Switch28)(*Up)

• do-and-next will ‘execute’ an action in a situation– creates a new situation– updates the facts in it, according to the action

Simulation (cont)

;;; --- previous situations are preserved ---

;;; "In the previous situation, what was the position of the switch?"[_Situation30] KM> (in-situation (the prev-situation of (curr-situation)) (the position of _Switch28))(*Down)

;;; "In which situations was the switch down?"[_Situation30] KM> (allof (the all-instances of Situation) where (in-situation It ((the position of _Switch28) = *Down)))(_Situation27)

• again, previous situations can be queried and quantified over

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)))

[_Situation1] KM> (a Door with (lock-state (*Unlocked)))(_Door2)

[_Situation1] KM> (a Open with (object (_Door2))) (_Open3)

[_Situation1] KM> (do-and-next _Open3)(COMMENT: Changing to Situation _Situation4)(_Situation4)

[_Situation4] KM> (the door-state of _Door2)(*Open)

Another Example of Simulation[_Situation4] KM> (a Door)(_Door5)

[_Situation4] KM> (do-and-next (a Open with (object (_Door5))))(COMMENT: Assuming (:triple _Door5 lock-state *Unlocked), to do action _Open6...)(COMMENT: Changing to Situation _Situation7)(_Situation7)

[_Situation7] KM> (in-situation _Situation4 (the lock-state of _Door5))(*Unlocked)

[_Situation7] KM> (a Door with (lock-state (*Locked)))(_Door8)

[_Situation7] KM> (do-and-next (a Open with (object (_Door8))))(do _Open9): Can't do this action as it would be inconsistent to assert

precondition(s): (:triple _Door8 lock-state *Unlocked)NIL

[_Situation7] KM>

Text Generation

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" _Sample14 "from" _Box15))

;;; "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.")

• A special type of instance is a sequence– (:seq v1 … vn)

• Text strings can be built up as a sequence of fragments

Slot Hierarchies

;;; "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-Engine23 _Fuselage24)

• Slots can have subslots• Values of subslots are also values of the superslot

– values “propagate up”)

Prototypes ExampleKM> (a Airplane with (has-part ((a Wing) (a Wing))))(_Airplane9)

KM> (showme _Airplane9)(Airplane9 has (instance-of (Airplane)) (has-part ((a Wing) (a Wing))))

KM> (showme Airplane)(Airplane has (superclasses (Device)) (instances (_Airplane9)))

KM> (the has-part of (a Airplane))NIL

Prototypes ExampleKM> (a-prototype Airplane)(_ProtoAirplane11)

[prototype-mode] KM> (_ProtoAirplane11 has (has-part ((a Wing) (a Wing))))(_ProtoAirplane11)

[prototype-mode] KM> (end-prototype)

KM> (showme Airplane)(Airplane has (superclasses (Device)) (instances (_Airplane9 _Airplane10 _ProtoAirplane11)) (prototypes (_ProtoAirplane11)))

KM> (the has-part of (a Airplane))(COMMENT: Cloned _ProtoAirplane11 -> _Airplane15 to find (the has-part of _Airplane14))(COMMENT: (_Airplane14 & _Airplane15) unified to be _Airplane14)(Wing16 _Wing17)

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, domain-

independent concepts (“components”)– a small vocabulary of relations to connect them

then domain experts build representations by instantiating and composing these components

small

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 t0

• The Ball must be held by the Person at t0

• The Ball must not be otherwise Restrained• The path to the Door must not be Blocked• At t1 the Ball is at the Door and no longer at the Person• At t1 the Ball is outside the Room but not shut out of it• The Door must not be Closed• The Ball passes through the Doorway• At t2 the Ball is inside the Room and no longer outside• At t2 the Room has the Ball among its contents• Blocked paths can be unblocked• Closed Doors can be Opened• …

http://www.cs.utexas.edu/users/mfkb/RKF/tree/

KM: The Knowledge Machine A knowledge representation and reasoning system.

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