1. 4. Software environment ExpertPRIZ Overview of PRIZ - family systems SystemComputerYearAdditional- components SMPMinsk-221973 PRIZ-32Minsk-321975 PRIZ ESES (IBM-360/370)1978DB MISES1981 ELBRUS-I SM BESM-6 MicroPRIZApple II1982 -- “ --Labtam 30001984ES -- “ --IBM PC1985ES ExpertPRIZIBM PC1987ES, DB NUTLabtam-Kronos1988 SUN NEXT IBM PC(Linux) C-PRIZIBM PCES WExpPRIZIBM PC1991 CocovilaIBM PC (Linux)2004 (Windows) Basics of CAD * A.Kalja *

3. ExpertPRIZ User interface XpertSolverDatabase Expert Knowledge bases Conceptual Knowledge bases Databases Application The structure of ExpertPRIZ Basics of CAD * A.Kalja *

8. 4.1 Solver - to solve different computational problems - to perform data input-output (from problem model) - to perform database queries - to perform symbolic calculation Problem solving steps: -description of concepts -description of problem -solving of problem Basic concepts Object - any entity with name and specified properties; it may have a complicated internal structure. Object specification – a description of object in the input language of ExpertPRIZ. When describing an object, the name and the type of the object are specified: numeric, text, undefined, structure, concept. Concept - a specification of properties of a class of objects of some kind. Concepts are used for specifying objects. The object that is specified by means of a prototype concept acquires all the properties of this concept and contains all its components, too. Conceptual knowledge base – a set of concepts stored in a file Conceptual knowledge base – a set of concepts stored in a file.

9. Basics of CAD * A.Kalja * Problem specification - a text in the input language of ExpertPRIZ where objects and relations between the objects are specified. Relation - a specification showing how to derive values of some objects from the values of other objects. Relations can be presented as equations or modules. Problem model - an extended representation of problem specification, which is used in carrying out computations. Problem statement - a statement indicating the objects for whose values or analytical expression for dependencies of these numeric objects are to be found. Commands are intended to perform some actions without choosing them "manually" from the menu. Concept. KB. Concept Object Problem specification

10. Basics of CAD * A.Kalja * Square a numeric *side* s numeric *area* d numeric *diagonal* p numeric *perimeter* s=a^2 d^2=2*a^2 p=4*a Q square d=3 ? Q.s --> Q.s=4.5 1 Q1 square a=1 Q2 circle d=Q1.a x=Q1.s-Q2.s ?x --> x=0.2146 The algorithm for calculating x: Q1.a=1-->Q1.a Q2.d=Q1.a-->Q2.d Q2.pi=3.1416-->Q2.pi Q2.d=2*Q2.r-->Q2.r Q2.s=Q2.pi*Q2.r^2-->Q2.s Q1.s=Q1.a^2-->Q1.s x=Q1.s-Q2.s-->x * Solve the problem * Store the concept * Problem from a file

11. Basics of CAD * A.Kalja * 4.2 Input language Statements1)specifications 2)problem statements 3)commands 4)comments Names and identifiers x Ident. consist letters and numbers, A333always beginning with a letter. x_3_ is regarded equivalent to letters Identifikaat Capital and lover case Identifikletters are different. 8 letters. Errors: 3_kassix7$ kujund.ruut.diagonaal – compound name Keywords cannot be used - num, tex, und, sup Constants numerictext 3.14‘see on tekstikonstant’ -0.286 5E6 5e-5

12. Basics of CAD * A.Kalja * Specification of objects Primitive objects numeric text Objects of undefined type undefined Specification of structural objects ( …) Specification of objects by means of concepts [ …] is an equation in the form = Example:Car1 move Car2 move v=Car1.v S=1000 Example:S1(a b) T text S2(T) S3(S1 S2 T).

13. Basics of CAD * A.Kalja * Virtual objects [ ] * / ja ^ are equal to letters If a compound object contains components that are virtual objects, then the value of the compound object does not contain the values of its virtual components. When finding a value of such an object, it is not com- pulsory for the system to find values for its virt. comp. Example: * Concept move1 s=v*t [min]*60=t [h]*60=[min] [km]*1000=s [km/h]=[km]/[h] * Contains virtual components [min],[h], [km],[km/h] * Let us describe the object Car Car move1 v=30 [min]=25 * Finding value to Car, the system finds values * only for Car.[min],Car.s,Car.v and Car.t. * and outputs only the last three ?Car

14. Inheritance (super-concept) super Example: super move [min]*60=t [h]*60=[min] [km]*1000=s [km/h]=[km]/[h] NB! You can have more than one super ‑ concept for a concept or a problem, if there are no coincidences of names. Specification of relations: Equations Arithmetical equations: [+] = equation’ systems - num objects, binary operators + - * / ^ functions sin asin cos acos tan atan sqr sqrt exp ln log abs sign parentheses ( and ) Basics of CAD * A.Kalja *

15. Logical equations: = num-It contains at least one of the follo- wing operators and expressions - relational operators lt, le, gt, ge, eq, ne - logical operators and, or, not - conditional expressions if then else fi true - 1 false - 0 Text type objects will be compared lexicographically The order of these operations: - logical not; - arithmetical operations; - relational operations; - logical and; - logical or. If nonzero, then v. Basics of CAD * A.Kalja *

16. Equivalences: = Equivalences are used for three purposes: - to equalize a textual object with a textual constant or another object of textual type; - to assign type to an undefined object. - to "equalize" compound objects. not num-type Relations given by built in functions... ‑ > { }...... ‑ > { } Each subtask has the form: (... ‑ > ) Basics of CAD * A.Kalja *

17. Problem statement There are two kinds of problem statements: - to compute values of objects; -to find analytical expressions for dependences of some objects (of numeric type) on some other obj. Computing values: ? [ ]…, where... contains the names of objects of a problem model Meaning:-compute the values of the objects … ? - to find values of the all objects Finding dependencies: finding analytical dependences of some num­erical objects on some other numerical objects is represented by a statement : ?[ ]…->[ ]… [+|-] - if missing... results are constamts - if missing…for all obj. that are possible Commands ! [ …] !clear [y|n] !reset !file [# ] !expert !use !concept !show Comments * This is a comment Basics of CAD * A.Kalja *

18. Example: A) concepts * Resistor u=i*r g=i/r p=u*i *Serial connection super res x1 res i=i x2 res i=i u=x1.u+x2.u r=x1.r+x2.r * Parallel connection super res x1 res u=u x2 res u=u i=x1.i+x2.i g=x1.g+x2.g res u i r ser par x1x2 x1 x2 Basics of CAD * A.Kalja *

19. !clear y * r1 res r=5 r2 res r=15 r3 res r=20 r ser x1=r1 x2=r2 s par x1=r x2=r3 u=10 * ? s.i ? r1 r2 r3 ? ? r1.r r2.r r3.r s.u -> s.p ? r1.r r2.r r3.r -> s.r r s r1 r2 r3u=10v 55 15  20  Basics of CAD * A.Kalja *

20. Computational model M=(X,S), where X set of variables S set of relations CM graphical presentation Describing and solving a problem relation with input variable relation with weakly related variable relation with strongly related variable relation with a module A B C D U={A,B,C,D} M X Y=V Z Q Basics of CAD * A.Kalja * relation with output variable

21. CM in logic (representation on knowledge) Axioms X->Y (U-V)->(X->Y) Formulas |-X->Y; A|-X ------------------------- A|-Y’ |-(U->V)->(X->Y); A|-X; A,U|-V; -------------------------------------------------------------- -- A|-Y’ A,X|-Y ----------------- + A|-X->Y A|-Q Set of propositional formulas. Formula,, which shows the solvability of the prolem Compute V on model M by using U A B C Y Basics of CAD * A.Kalja *

22. THEORY PROBLEM PROGRAM PROOF LOGIC COMPUTING Basics of CAD * A.Kalja *