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KM: The Knowledge Machine A knowledge representation and reasoning system

KM: The Knowledge Machine A 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

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KM: The Knowledge Machine A knowledge representation and reasoning system

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  1. KM: The Knowledge MachineA knowledge representation and reasoning system

  2. 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

  3. 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?

  4. 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

  5. An Informal Knowledge Base • Classes • Event, Object, Artifact, Device, Computer, Person, Place, Hard-Drive are Classes • every Evente occurs at a time-of-occt and place-of-occp • The superclass of Computer is Device • every Personp1 has a motherp2 • most Computersc have a parth 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-occ3:30pm • You is an instance of Person with favorite-colorgreen • Thomas is an instance of Person with father Bob (a Person) • Texas is an instance of Place with is-part-of USA (a Place)

  6. 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)

  7. 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/users/mfkb/km.html

  8. 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> _

  9. The ‘*’ has no special meaning in KM; We use it as a handy visual indicator to distinguish instances and classes 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?

  10. 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!

  11. ‘;’ = comment to end of line 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)

  12. Guaranteed uniqueand fresh! An instance together with all the knowledge attached to that instance is called a “Frame” “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) KM> (showme _Cat1) (_Cat1 has (instance-of (Cat)) (color (*Black)) (parts ((a Head) (a Tail)))) (_Cat1)

  13. Frame Slot Value 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)))

  14. Frame Value Slot 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

  15. 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)

  16. Thing Physobj Number Car Person …. 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…..

  17. Frame (identifier) Slot Value 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)

  18. Slot Inverses • KM keeps track of inverse relations alsoX→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) (_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")

  19. evaluates to a Frame KM> (the owns of *Joe) ( ) KM> (the color of ) (*Red) 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)

  20. 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)

  21. 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)

  22. 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)

  23. 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 vehicle that a professor owns - the age of a professor’s vehicle - the location of the manufacturer of the professor’s vehicle 2. Create a KM frame describing the concept of a Car (the Car class): (every Car has ...)

  24. Answers to Exercises 1a. (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)))))))

  25. 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))))))

  26. 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))))))

  27. 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)

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

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

  30. 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)))))) (the location of (the Remove subevents of _Electrophoresis5)) (the location of _Remove6)

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

  32. 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)))))) (the location of (the Remove subevents of _Electrophoresis5)) (the location of _Remove6) (the delivery-medium of (the sample of _Electrophoresis5))

  33. 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)))))) (the location of (the Remove subevents of _Electrophoresis5)) (the location of _Remove6) (the delivery-medium of (the sample of _Electrophoresis5)) KM> (showme _Electrophresis5) (_Electrophoresis5 has (instance-of (Electrophoresis)) (sample ((a Albumin))) (subevents (_Remove6 (a Insert))))

  34. 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)))))) (the location of (the Remove subevents of _Electrophoresis5)) (the location of _Remove6) (the delivery-medium of (the sample of _Electrophoresis5)) (the delivery-medium of _Albumin7)

  35. 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)))))) (the location of (the Remove subevents of _Electrophoresis5)) (the location of _Remove6) (the delivery-medium of (the sample of _Electrophoresis5)) (the delivery-medium of _Albumin7) KM> (showme _Alubmin7) (_Albumin7 has (instance-of (Albumin)) (sample-of (_Electrophoresis5)) (delivery-medium ((a Bottle))) (storage-medium ((a Fridge))))

  36. 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)))))) (the location of (the Remove subevents of _Electrophoresis5)) (the location of _Remove6) (the delivery-medium of (the sample of _Electrophoresis5)) (the delivery-medium of _Albumin7) (a Bottle)

  37. 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)))))) (the location of (the Remove subevents of _Electrophoresis5)) (the location of _Remove6) (the delivery-medium of (the sample of _Electrophoresis5)) (the delivery-medium of _Albumin7) (a Bottle) _Bottle8

  38. mind the gap x = y if [x equals y +/- (0.0001 or 0.01% of max(x,y), whichever is smaller (so 1.0001 ≠ 1.0002))] 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

  39. Why? 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

  40. 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 PositionValue))))) (brightness (...))) (*Up has (instance-of (PositionValue))) (*Down has (instance-of (PositionValue))) (*Bright has (instance-of (BrightnessValue))) (*Dark has (instance-of (BrightnessValue))))

  41. Answers to Exercises 4. (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).

  42. 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

  43. 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)

  44. 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)

  45. 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)

  46. 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?

  47. Set Expressions with Variables • A slightly more general form allows for nestediterators • (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)) ) ) (_Car11 _House13)

  48. 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?

  49. 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)) )

  50. 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-Thing832 superclasses (every Person has (parts ((a Brain))) ) _Person834 superclasses (every Student has (gpa ((a Number))) ) _Student836 isa (_Student4 has (parts ((a Brain) (a Body))) (gpa ((a Number))) ) _Student4 = _Living-Thing832 & _Person834 & _Student836 & _Student4

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