1 / 50

A Core Course on Modeling

A Core Course on Modeling. Week 2 – the Art of Omitting. Organizing concepts trees tables Organizing meaning objects semantics Notation Mapping ACCEL aggregation: vectors quantified expressions user defined functions. A Core Course on Modeling. Week 2 – the Art of Omitting.

tivona
Download Presentation

A Core Course on Modeling

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. A Core Course on Modeling Week 2 – the Art of Omitting • Organizingconcepts • trees • tables • Organizingmeaning • objects • semantics • Notation • Mapping • ACCEL • aggregation: vectors • quantified expressions • user defined functions

  2. A Core Course on Modeling Week 2 – the Art of Omitting concepts: trees ‘Where do you live?’

  3. A Core Course on Modeling Week 2 – the Art of Omitting Organizing concepts: trees country (e.g., Netherlands) province (e.g., North Brabant) city (e.g., Eindhoven) quarter (e.g., Woensel)

  4. A Core Course on Modeling Week 2 – the Art of Omitting Organizing concepts: trees partOf() country (e.g., Netherlands) province (e.g., North Brabant) city (e.g., Eindhoven) quarter (e.g., Woensel)

  5. A Core Course on Modeling Week 2 – the Art of Omitting Organizing concepts: trees isA() kingdom (e.g., animalia) phylum (e.g., chordata) class (e.g., mammalia) order (e.g., cetacea) family (e.g., delphinidae), genus (e.g., orcinus), species (e.g., orca)

  6. A Core Course on Modeling Week 2 – the Art of Omitting Organizing concepts: trees Extensional definition: • enumerate existing things • grouping in (sub)sets isA()

  7. A Core Course on Modeling Week 2 – the Art of Omitting Organizing concepts: trees Hierarchy: often too restrictive Subsets often relate to meaning Several hierarchies co-exist

  8. A Core Course on Modeling Week 2 – the Art of Omitting Organizing concepts: tables A B Alternative: table C X Y Z

  9. A Core Course on Modeling Week 2 – the Art of Omitting Organizing concepts: tables 9 A B Alternative: table C X Y Z property P values A,B,C property Q values x,y,z

  10. A Core Course on Modeling Week 2 – the Art of Omitting Organizing concepts: tables 10 A B Example: set of vehicles; P = ‘medium’, A,B,C= ‘land’, ‘water’, ‘air’, Q = ‘payload’, X,Y,Z = ‘passengers’, ‘freight’, ‘mail’. C X Y Z property P values A,B,C property Q values x,y,z

  11. A Core Course on Modeling Week 2 – the Art of Omitting Organizing concepts: tables A B C X Y Z property P values A,B,C (group) property Q values x,y,z (period)

  12. A Core Course on Modeling Week 2 – the Art of Omitting Organizing concepts: tables A B what to do with >2 properties? C X Y Z property P values A,B,C property Q values x,y,z

  13. A Core Course on Modeling Week 2 – the Art of Omitting Organizing concepts: tables A B c4, c5 are undistinguishable [P:B, Q:Y] does not occur C X Y Z

  14. A Core Course on Modeling Week 2 – the Art of Omitting Organizing concepts: tables 14 A B P Q … Q C X c1 A X M … Y c2 B X M … Z c3 C X … M c4 A Y … N c5 A Y … M c6 C Y … N c7 A Z … N c8 C Z … N c9 C Z … M orthogonal table: every property applies to each concept

  15. A Core Course on Modeling Week 2 – the Art of Omitting Organizing concepts: tables 15 Not every tree leads to an orthogonal table (Orthogonal) table: better compression than tree Orthogonal table: with N properties, distinguish O(2N) concepts or log(M) properties for M concepts. (Arbitrary) tree: N internal nodes for N leaves.

  16. A Core Course on Modeling Week 2 – the Art of Omitting Organizing concepts: tables 16 orthogonal table ontology: helps explore option space image: http://www.emiliosanfilippo.it/?page_id=1172

  17. A Core Course on Modeling Week 2 – the Art of Omitting Organizing concepts: tables 17 orthogonal table ontology: helps explore option space image: http://www.emiliosanfilippo.it/?page_id=1172

  18. A Core Course on Modeling Week 2 – the Art of Omitting Organizing meaning: objects 18 ice1 = [taste:vanilla, holder:cone, cream:yes, topping:smarties, cherry:red] coneIce = [taste:{vanilla, choc, strawberry}, holder:cone, cream:{yes, no}, topping:{smarties, hazelnut}, cherry:{red, green, none}] ice = [taste:{vanilla, choc, strawberry}, holder:{cone, stick, bowl}, cream:{yes, no}, topping:{smarties, hazelnut}] image: http://www.emiliosanfilippo.it/?page_id=1172

  19. A Core Course on Modeling Week 2 – the Art of Omitting Organizing meaning: objects 19 Intensional definition: • specifiy things by properties • irrespective existence • extensional   intensional image: http://gagfunny.com/gag/index.php/tag/living-shadows-illusion/ image: http://www.emiliosanfilippo.it/?page_id=1172

  20. A Core Course on Modeling Week 2 – the Art of Omitting Organizing meaning: objects 20 x : Y means: if x and Y are sets: x  Y if x is an element: x  Y abbreviate ‘{a}’ by ‘a’ isA(x,Y) means: for every P in Y, x.P : Y.P. isA(x,Y): inheritance; x inherits from Y x is more concrete, Y is more abstract image: http://www.emiliosanfilippo.it/?page_id=1172

  21. A Core Course on Modeling Week 2 – the Art of Omitting Organizing meaning: objects 21 ice1 = [taste:vanilla, holder:cone, cream:yes, topping:smarties, cherry:red] coneIce = [taste:{vanilla, choc, strawberry}, holder:cone, cream:{yes, no}, topping:{smarties, hazelnut}, cherry:{red, green, none}] ice = [taste:{vanilla, choc, strawberry}, holder:{cone, stick, bowl}, cream:{yes, no}, topping:{smarties, hazelnut}] examples isA( ): ice1: coneIce; conIce : ice; isA(ice1, coneIce); isA(coneIce, ice); isA(ice, [holder:{cone, stick, bowl}]) isA(ice, [ ]) isA(coneIce, [ ]) a concept with just a single property (‘holder’) a very abstract concept, having no properties at all (‘a thing’) image: http://www.emiliosanfilippo.it/?page_id=1172

  22. A Core Course on Modeling Week 2- conceptual modeling Organizing meaning: objects 22 The anatomy of concepts: a concept can be an item (a concrete, unique thing)

  23. A Core Course on Modeling Week 2- conceptual modeling Organizing meaning: objects 23 The anatomy of concepts: a concept can be an item (a concrete, unique thing) or a concept can be a class

  24. designer: gustaveEiffel location: ChampsDeMars height: 320 m A Core Course on Modeling Week 2- conceptual modeling Organizing meaning: objects 24 The anatomy of concepts: a concept can be an item (a concrete, unique thing) an item can have properties a concept can be a class … with values that may be concepts with properties of their own

  25. such as: ‘bunch of steel girders’ such as:’monuments in Paris’ A Core Course on Modeling Week 2- conceptual modeling Organizing meaning: objects 25 The anatomy of concepts: a concepts can be an item (a concrete, unique thing) an item can have properties a concept can be a class … with values that may be concepts with properties of their own a class can be an aggregation or a class can be an abstraction

  26. A Core Course on Modeling Week 2- conceptual modeling Organizing meaning: objects 26 The anatomy of concepts: a concepts can be an item (a concrete, unique thing) an item can have properties a concept can be a class … with values that may be concepts with properties of their own a class can be an aggregation … of all similar things, called elements or members (sometimes numbered) a class can be an abstraction

  27. A Core Course on Modeling Week 2- conceptual modeling Organizing meaning: objects 27 The anatomy of concepts: a concepts can be an item (a concrete, unique thing) an item can have properties a concept can be a class … with values that may be concepts with properties of their own a class can be an aggregation … or all different things (elements, members - sometimes named) a class can be an abstraction

  28. A Core Course on Modeling Week 2- conceptual modeling Organizing meaning: objects 28 The anatomy of concepts: a concepts can be an item (a concrete, unique thing) an item can have properties a concept can be a class … with values that may be concepts with properties of their own a class can be an aggregation … or all different things (sometimes named) a class can be an abstraction

  29. A Core Course on Modeling Week 2- conceptual modeling Organizing meaning: objects 29 The anatomy of concepts: a concepts can be an item (a concrete, unique thing) an item can have properties a concept can be a class … with values that may be concepts with properties of their own a class can be an aggregation … or all different things (sometimes named) a class can be an abstraction … that typicaly has less properties than its concreter instances

  30. A Core Course on Modeling Week 2- conceptual modeling Organizing meaning: objects 30 The anatomy of concepts: a concepts can be an item (a concrete, unique thing) an item can have properties a concept can be a class … with values that may be concepts with properties of their own a class can be an aggregation … or all different things (sometimes named) a class can be an abstraction … that can be instantiated by a more concrete concept

  31. A Core Course on Modeling Week 2- conceptual modeling Organizing meaning: objects 31 The anatomy of concepts: a concepts can be an item (a concrete, unique thing) an item can have properties a concept can be a class use the right terms for the right things: • concept • item • class • aggregation, element • abstraction, instance • property … with values that may be concepts with properties of their own a class can be an aggregation … or all different things (sometimes named) a class can be an abstraction … that can be instantiated by a more concreteconcept

  32. A Core Course on Modeling Week 2- conceptual modeling Notation: denote aggregation 32 v = {1, 2, 3}, a set with three numerical elements – not separately accessible p = [1, 2, 3], an array with three numbered numerical elements, p[0] = 1 q = [a, b, c], an array with 3 numbered concepts, q[0] = a r = [‘a’, ’b’, ’c’], an array with three numbered strings, r[0] = ‘a’ s = [‘x’:1, ’y’:2, ’z’:3], an array with three named numerical elements, s[‘x’] = 1 {1, 2, 3} == {3, 2, 1} [1, 2, 3] != [3, 2, 1] whereas [‘x’:1, ‘y’:2, ‘z’:3 ] == [‘y’:2, ‘z’:3, ‘x’:1] image:http://www.robertpeake.com/archives/419-manuscript-anxiety.html

  33. A Core Course on Modeling Week 2- conceptual modeling Notation: denote aggregation 33 v = {1, 2, 3}, a set with three numerical elements – not separately accessible p = [1, 2, 3], an array with three numbered numerical elements, p[0] = 1 q = [a, b, c], an array with 3 numbered concepts, q[0] = a r = [‘a’, ’b’, ’c’], an array with three numbered strings, r[0] = ‘a’ s = [ x :1, y :2, z :3], an array with three named numerical elements, s[‘x’] = 1 {1, 2, 3} == {3, 2, 1} [1, 2, 3] != [3, 2, 1] whereas [‘x’:1, ‘y’:2, ‘z’:3 ] == [‘y’:2, ‘z’:3, ‘x’:1] • Quotes are optional for the names of properties image:http://www.robertpeake.com/archives/419-manuscript-anxiety.html

  34. A Core Course on Modeling Week 2- conceptual modeling Notation: denote aggregation 34 p = [1, 2, 3], an array with three numbered numerical elements, p[0] = 1 is an abbreviation for p = ['0': 1, '1': 2, '2': 3] which is the same as p = ['1': 2, '0': 1, '2': 3] (order doesn't matter) But in the abbreviation, naming ('0':…, '1':…, '2':…) is left out. To know which of [1, 2, 3] or [2, 1, 3] is meant, order convention is required. image:http://www.robertpeake.com/archives/419-manuscript-anxiety.html

  35. A Core Course on Modeling Week 2- conceptual modeling Notation: denote aggregation there is no notation to access an individual element 35 only use for numbers, weekdays, … but only for values that have total ordering. Sets, lists, concepts and accessing elements: P=[a, b, c]: ordered list, [a, b, c]  [b, a, c] access elements: P[0] == a, etc. P={a, b, c}: set (unordered), {a, b, c} == {b, a, c} P={a… b}: set containing all x, a  x  b P=['john':a, 'pete':b, 'suzy': c]: named list or concept access elements: P['pete'] == b, alternative: P.pete == b ['john':a, 'pete':b, 'suzy': c] == ['pete':b, 'john':a, 'suzy': c] image:http://www.robertpeake.com/archives/419-manuscript-anxiety.html

  36. A Core Course on Modeling Week 2 – the Art of Omitting Mapping 36 p = [1, 2, 3] q = [10, 20, 30] vector addition: sum = [p[0]+q[0], p[1]+q[1], p[2]+q[2]] = [11, 22, 33] Easier: sum = p + q ACCEL applies mapping whenever possible. image: http://www.corporatienl.nl/hoe-slaat-u-twee-vliegen-in-een-klap/

  37. A Core Course on Modeling Week 2 – the Art of Omitting ACCEL • Why ACCEL? • compare to MS Excel, not to BASIC, C++, Matlab, … • low threshold for non-programmers • follows to-do-list approach from Lectures • built-in features (chapters 5 & 6) • Pareto Genetic Optimization • Sensitivity Analysis with Condition Numbers • .. why NOT ACCEL?

  38. A Core Course on Modeling Week 2 – the Art of Omitting ACCEL: aggregation • allagregationbyvectors • vectorsaggregatearbitraryquantities • e.g.: v = [1, 2, 3]; v[1] : 2 • e.g.: v = [‘x’:1, ‘y’:2, ‘z’:3]; v[’y’] : 2 (v.y : 2) • also: v = [x:1, y:2, z:3]but NOT v[y] instead of v[‘y’] • e.g.: v = [1, [10, 20], 3]; v[0] : 1 v[1] : [10,20] v[1][1] : 20 v[0][1] :undefined … but ACCEL triesnot to disappointitsusers

  39. A Core Course on Modeling Week 2 – the Art of Omitting ACCEL: aggregation 39 index1=slider(0,0,10) index2=slider(0,0,10) printB=b printC=c printD=d a=[1,[10,20],3] b=a[index1] c=b[index2] d=a[index1][index2] … but ACCEL tries not to disappoint its users

  40. A Core Course on Modeling Week 2 – the Art of Omitting ACCEL: aggregation 40 netherlands=[… ,'provinces':p, …] p=[gr,fr,dr,ov,gl,ut,nh,zh,zl,nb,li] gr=['cap':'groningen', 'pop':582161,'area':2960.03] fr=['cap':'leeuwarden','pop':647239,'area':5748.74] dr=['cap':'assen','pop': 489912, 'area':2680.37] ov=['cap':'zwolle','pop':1138571, 'area':3420.86] gl=['cap':'arnhem','pop':2013903 , 'area':5136.51] ut=['cap':'utrecht','pop':1243161 , 'area':1449.12] nh=['cap':'haarlem','pop':2719764 , 'area':4091.76] zh=['cap':'den haag','pop':3560205 , 'area':3418.50] zl=['cap':'middelburg','pop':381202 , 'area':2933.89] nb=['cap':'den bosch','pop':2470184 , 'area':5081.76] li=['cap':'maastricht','pop':1121483 , 'area':2209.22]

  41. A Core Course on Modeling Week 2 – the Art of Omitting ACCEL: aggregation 41 netherlands=[…, 'provinces':p, …] p=[gr,fr,dr,ov,gl,ut,nh,zh,zl,nb,li] gr=['cap':'groningen', 'pop':582161,'area':2960.03] …. prov0=p[0] prov1= … prov2= … pop0=prov0.pop pop1= … pop2= … totPop=pop0 + pop1 + … what is the exact population?  sum over provinces image: http://www.dontpaniconline.com/magazine/radar/a-boring-conference

  42. A Core Course on Modeling Week 2 – the Art of Omitting ACCEL: quantified expressions 42 netherlands=[…, 'provinces':p, …] p=[gr,fr,dr,ov,gl,ut,nh,zh,zl,nb,li] gr=['cap':'groningen', 'pop':582161,'area':2960.03] …. Alternative: quantified expressions totPop = #(dummy, seq, term, operation) dummy: a quantity that assumes subsequent values from seq seq: a set of values. E.g., vSequence(0,11) = [0,1,2,3,4,5,6,7,8,9,10] term: an expression,perhaps depending on dummy operation:what to do with the values ofterm

  43. A Core Course on Modeling Week 2 – the Art of Omitting ACCEL: quantified expressions 43 netherlands=[…, 'provinces':p, …] p=[gr,fr,dr,ov,gl,ut,nh,zh,zl,nb,li] gr=['cap':'groningen', 'pop':582161,'area':2960.03] …. Alternative: quantified expressions totPop = #(dummy, seq, term, operation) totPop = #(i , [1,2,3] ,i,add)  totPop = 6 t = [3,4,5,6,7] totPop = #(i , [1,2,3],t [i],add)  totPop = t [1] + t [2] + t [3] = 4 + 5 + 6 = 15 u = [[1,2],[3,4],[5,6]] totPop = #(i , [0,1,2],u[i][1],add)  totPop = ([1,2])[1] + ([3,4])[1] + ([5,6])[1] = 2 + 4 + 6 = 12

  44. A Core Course on Modeling Week 2 – the Art of Omitting ACCEL: quantified expressions 44 netherlands=[…, 'provinces':p, …] p=[gr,fr,dr,ov,gl,ut,nh,zh,zl,nb,li] gr=['cap':'groningen', 'pop':582161,'area':2960.03] …. Alternative: quantified expressions totPop = #(dummy, seq, term, operation) totPop = #(i, vSequence(0,11), p [i] . pop, add) maxPop = #(i, vSequence(0,11), p [i] . pop, max) minArea = #(i, vSequence(0,11), p [i] .area,min) … but suppose we need the most spacious province?

  45. A Core Course on Modeling Week 2 – the Art of Omitting ACCEL: quantified expressions 45 netherlands=[…, 'provinces':p, …] p=[gr,fr,dr,ov,gl,ut,nh,zh,zl,nb,li] gr=['cap':'groningen', 'pop':582161,'area':2960.03] …. Alternative: quantified expressions totPop = #(dummy, seq, term, operation) totPop = #(i, vSeq(0,11), p [i] . pop, add) maxPop = #(i, vSeq(0,11), p [i] . pop, max) minArea = #(i, vSeq(0,11), p [i] .area,min) … but suppose we need the most spacious province?

  46. A Core Course on Modeling Week 2 – the Art of Omitting ACCEL: quantified expressions 46 netherlands=[…, 'provinces':p, …] p=[gr,fr,dr,ov,gl,ut,nh,zh,zl,nb,li] gr=['cap':'groningen', 'pop':582161,'area':2960.03] …. spaciousness = area / population http://www.panoramio.com/photo/12605032

  47. A Core Course on Modeling Week 2 – the Art of Omitting ACCEL: user defined functions 47 netherlands=[…, 'provinces':p, …] p=[gr,fr,dr,ov,gl,ut,nh,zh,zl,nb,li] gr=['cap':'groningen', 'pop':582161,'area':2960.03] …. maxSpaciousness = #(i, vSeq(0,11), spaciousness(i), max) … but spaciousness is not a single quantity: depends on i, so takes different values during computation. Quantities that depend on other quantities:user defined functions. spaciousness(i) = p[i] . area / p[i] . pop Notice: i takes various values during the compuation; is not a quantity. Instead i is called a dummy.

  48. A Core Course on Modeling Week 2 – the Art of Omitting ACCEL: user defined functions 48 netherlands=[…, 'provinces':p, …] p=[gr,fr,dr,ov,gl,ut,nh,zh,zl,nb,li] gr=['cap':'groningen', 'pop':582161,'area':2960.03] …. maxSpaciousness=#(i,vSeq(0,11),spaciousness(i),max) spaciousness(i)=p[i].area/p[i].pop p=[Pgr,Pfr,Pdr,Pov,Pgl,Put,Pnh,Pzh,Pzl,Pnb,Pli] Pgr=['cap':'groningen','pop':582161,'area':2960.03] . . . Pli=['cap':'maastricht','pop':1121483,'area':2209.22]  so the most spacious province offers 8900 m2/person ! … But which province is that?

  49. A Core Course on Modeling Week 2 – the Art of Omitting ACCEL: user defined functions 49 netherlands=[…, 'provinces':p, …] p=[gr,fr,dr,ov,gl,ut,nh,zh,zl,nb,li] gr=['cap':'groningen', 'pop':582161,'area':2960.03] …. As follows: maxSpaciousness=#(i,vSeq(0,11),spaciousness(i),max) spaciousness(i)=p[i] . area / p[i] . pop mostSpacious=#(i,vSeq(0,11),if(spaciousness(i)==maxSpaciousness,i,0),max) capitalOfMostSpacious=p[mostSpacious] . cap  curious for result? Try yourself!

  50. A Core Course on Modeling Week 2 – the Art of Omitting ACCEL: user defined functions 50 idea: expression that is evaluated more than once in a computation:  user-defined functions • can be used whenever quantities are used • can have arbitrary arguments (one or more) • … with arbitrary names (no name clashes) • can return whatever you want, e.g. myFunc(a,b) = ['x':a,'y':b] p=myFunc(3,4) gives result p=['x':3,'y':4] p=myFunc(3,4)['x'] and myFunc(3,4).x both give result p=3 • use to organize your thinking • use to keep script readible • use to shorten script • use to keep formal and conceptual models similar

More Related