The Butterfly Algorithm: A Contradiction Solving Algorithm based on Propositional Logic for TRIZ

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1 , pp he Butterfly Algorithm: A Contradiction Solving Algorithm based on Propositional Logic for RIZ Jung Suk Hyun 1 and Chan Jung Park 2 1 Department of Management Information Systems, Jeju National University, Jejudaehak-ro 102, Jeju-do, 63243,Republic of Korea 2 Department of Computer Education, Jeju National University, Jejudaehak-ro 102, Jeju-do, 63243,Republic of Korea {jsyun,cjpark}@jejunu.ac.kr Abstract Among creative and innovative problem solving algorithms, RIZ solves difficult problems by finding contradictions of the problems. In RIZ, there are two types of contradictions. One is a technical contradiction and the other is physial contradiction. A technical contradiction occurs between two desirable functions of a system. We call it a trade-off contradiction. On the other hand, a physical contradiction appears when two opposite properties are required from the same part of a system. In RIZ, the ARIZ has been developed by Altshuller for reducing trial-and-error while solving problems. It is known as an inventive problem solving. It transforms difficult technical contradictions of a given problem into the corresponding physical contradiction to solve the problem easily. However, ARIZ-85c, the most recent version of the ARIZ, has inefficient and timeconsuming features that cause trial-and-errors. In this paper, we propose the Butterfly algorithm based on the Butterfly diagram to reduce trial-and-error features by giving the right solution strategy based on propositional logic when selecting technical contradictions and physical contradictions for a given problem. he Butterfly algorithm can systematically find the solution strategy for the problem, and thus it helps to solve contradictions efficiently. Keywords: ARIZ, the Butterfly Diagram, the Butterfly Algorithm, Contradiction Problem Solving, RIZ, Creative Problem Solving 1. Introduction Historically, many creative and innovative solutions solved the contradictions of given problems. Among the creative problem solving methods, RIZ, the Russian acronym for the heory of Inventive Problem Solving, is the one of the best methods handle contradictions. RIZ was developed by Altshuller and his colleagues [1]. hey figured out that there was a common thing among innovative inventions. he common thing was that researchers have solved the contradictions included in given problems instead of compromising the conflicts [1-2]. RIZ can reduce the number of trial-and-errors by abstraction and analogical reasoning when engineers solve problems [1-2]. RIZ provides many useful tools to solve contradictions in a given problem. RIZ defines two types of contradictions when it solves problems. One is technical contradiction and the other is physical contradiction [3]. he technical contradictions are trade-offs. In other words, if one thing gets better, then the other thing gets worse [3]. or example, the speed of a bike forms a technical contradiction with the safety of a bike. On the other hand, the physical contradictions occur when two opposite requirements meet. or example, the width of a highway should be wide for easy traffic control and it should be narrow for low impact on communities [3]. ISSN: IJSEIA Copyright c 2016 SERSC

2 Among the RIZ tools, the ARIZ, algorithm for inventive problem solving, is the core analytical tool of RIZ [4]. It was also developed by Altshuller for reducing trial-anderrors while solving problems. he essence of the ARIZ is to transform an ill-structured problem into a well-structured problem to solve easily. It is composed of 85 step-by-step procedures to solve contradictions. he ARIZ transforms the technical contradiction of a given problem into the physical contradiction of the same problem. he ARIZ has continuously been evolved, and ARIZ-85c was published with 9 steps in 1985 as follows [5]. Step1: Analysis of a given problem Step2: Analysis of the problem s model. Step3: ormulation of the Ideal inal Result (IR). Step 4: Utilization of outside substances and field resources. Step5: Utilization of information data bank. Step 6: Change or reformulate the problem. Step7: Analysis of the method that removed the physical contradiction. Step 8: Utilization of found solution. Step 9: Analysis of steps that lead to the solution. In the early stages of the ARIZ Part 1, selecting the right contradiction is important for solving the problem. However, ARIZ-85c, the most recent version of the ARIZ, still has the brute-force feature inside. As shown in igure 1, the step 6 of ARIZ-85c says If the problem has not been solved yet, go to the step 1.4, and then choose the other technical contradiction for this problem. It represents that the ARIZ has the feature similar to the brainstorming. he step 1.4 is to select the technical contradiction that is suitable for the main function of a given system. However, the problem is that the main function of the system can be defined differently according to solvers. In addition, the ARIZ is a method whose efficacy depends on the problem solver s technical knowledge [5]. In this paper, we propose the Butterfly algorithm based on the Butterfly diagram to reduce the trial-and-errors generated by choosing a wrong solution strategy. We propose the logical way how to choose the right direction when selecting technical contradictions and physical contradictions with propositional logic. he Butterfly algorithm can systematically find the solution strategy for the problem, and thus it can reduce the trialand-errors and help to solve contradictions efficiently. he rest of this paper is consisted as follows: in Section 2, we present the Butterfly diagram that is the basis of our Butterfly algorithm. Next, in Section 3, we compare the Butterfly algorithm and the ARIZ-85c. And then, we explain the difference with the iron plate tank problem. inally, we conclude our paper in Section Copyright c 2016 SERSC

3 2. he Butterfly Diagram igure 1. he Step 6 of ARIZ-85c [6] A system has the interconnectivity of a system among the components of the system. It means that when some part of a system gets better, other part of the system gets worse, and vice versa [7-8]. he Butterfly diagram is the component of the Butterfly model [8-9]. Compared with RIZ, the Butterfly model can define the essence of a given problem by describing the relationships of its technical contradiction and physical contradiction. Physical contradictions belong to more concrete and narrow problem space than technical contradictions [8]. And then, the Butterfly model can find out the ideal solutions for the given problem easily by combining its technical and physical contradictions. After finding out its ideal solutions, according to the type of the problems, the time, the space, and the partial and the whole state model are applied to derive the problem solutions more precisely [8]. On the other hand, the Butterfly diagram assumes the interconnectivity of a system. Due to the interconnectivity, when some function of a system is enhanced (w, wanted function), other function is deteriorated (u, unwanted function) as shown in igure 2. In this situation, a trade-off relation occurs. he main cause, the system faces with a tradeoff relation, comes from the system state, s, and the contradictory system state, ~s. or solving the contradiction problems, a few terminologies are defined in the Butterfly diagram. [Definition 1] A system S is composed of 3 components, w, u, and s, where w is a wanted function of S, u is the unwanted function caused by satisfying a state s, which is a condition for supporting w [9].hen, ~s is a condition for supporting ~u. [Definition 2] w and ~u have a trade-off relation with each other when w becomes better, whereas ~u becomes less, and vice versa. Copyright c 2016 SERSC 29

4 igure 2. he Interconnectivity of a System [9] [Definition 3] s and ~s have a contradiction relation when s and ~s cannot be true at the same time. We explain a trade-off relation and a contradiction relation with the agility and the safety of the iron plate of a tank. If the iron plate is thick (s), then the iron plate protects shells well (w). However, the agility of the tank falls down (u) due to the thick plate. In order to elevate the agility of the tank (~u), the iron plate should be thin (~s). he thin iron plate also causes the problem that the tank cannot protect shells well (~w). In this case, w and ~u have a trade-off relation, whereas s and ~s have a contradiction relation. his problem is depicted with the Butterfly diagram shown in igure 3. igure 3. he Butterfly Diagram for the ank Problem o give more accurate direction for solving problems, the Butterfly model analyzed the problem types and the solution strategies based on Logics in [9]. In a Butterfly diagram, the relationships between w and s mean the conditional propositions between the wanted function, w, in a system and the system state, s, for performing w. Similarly, the relationships between u and s mean the conditional propositions between the unwanted function, u, in a system and the system state, s, for performing u. hen, there are 9 types of conditional proposition relationships, i.e., 3 (a sufficient, a necessary, and a necessary and sufficient condition between w and s) 3 (a sufficient, a necessary, and a necessary and sufficient condition between s and u). rom now on, we analyze each problem type and propose the problem solving objectives and the solution strategies for each problem type [9]. In the above problem, we describe the relations with the propositional logic. If the iron plate is thick (s), then the tank protects shells well (w). hus, we represent this relation as s w like in the propositional logic. Also, if the iron plate is thick (s), then the agility of the tank falls down (u). hus, we represent this relation as s u. By the contraposition 30 Copyright c 2016 SERSC

5 law, if s u then ~u ~s. Also, if s w then ~w ~s. hus, the iron plate problem of a tank can be described with the relations among w, u, and s. such as (s w) (s u). In addition, the solution objectives about the tank problem are to protect shells (safety) and to move quickly (agility) at the same time (w ~u). It means that the iron plate should be thin and the tank should protect well (~s w). he relations represented in the Butterfly diagram are transformed into a propositional logic expression as follows [9]: (s w) (s u) and (w ~u) (~s w). he above logical expression is proved with the truth table as shown in able 1. able 1 shows if we can describe the relations between technical contradictions and physical contradictions by the propositional logic, then we know the solution for solving the contradictions. able 1 means when the given problem conditions are given as (s w) (s u) and (w ~u), then the right direction for the solution strategy is (~s w). ~s w is the only one that satisfies true conditions in the logical expression. Since the solution direction is given, we can avoid trial-and-errors unlike the ARIZ-85c. able 1. Proof Based on a ruth able for Solution Strategy about the Iron Plate Problem of the ank s u w s w s u w ~u ~s w Based on the solution strategy by depicting the Butterfly diagram, one solution for the tank problem was giving 60 degree of slope in the iron plate of the tank as shown in igure 4. hen, the plate has the increasing effect in thickness due to the slope. he thickness of the plate becomes 90mm by slope when the original thickness is 45mm. hus, without the thicker plate, the tank protects shell better than before. igure 4. he Iron Plate of the ank Another example can be found in a bike problem. he larger front wheels gave higher speed. At the same time, the large front wheels threaten bike riders safety. By having the saddle set too high, the bike riders have difficulties when getting on and getting off. If bike has a big front wheel (s), then bike riders can not only run high speed (w) but also be dangerous to drive (u). Bike riders wanted a fast but safe bike (w ~u). In order to achieve the objectives of the bike, it should have a small front wheel (~s). Starley invented the Copyright c 2016 SERSC 31

6 first rear-driving bicycle, known as the Rover safety bike, in He solved the contradiction by using the pedal and the chain connecting the rear wheel. It guaranteed the high speed of the bike with safety [10]. 3. he Butterfly Algorithm In this Section, we present the Butterfly algorithm based on the propositional logic and the logical interpretations of problem types and their solution strategies. he Butterfly algorithm redefines the Step 1.4 of ARIZ-85c more accurately. It reduces the dependency on the problem solver s expertise. Other parts are the same as the ARIZ-85c. In the next Butterfly algorithm, we firstly describe the difference in step1 from the ARIZ-85c as follows: Step 1.1 Without specialized terminology, write down the conditions of the mini-problem. Step 1.2 Select the conflicting pair. Step 1.3 ormulate system contradictions (technical and physical) using the conflicting pair from Step 1.2 and create a Butterfly diagram for the system contradiction. Step 1.4 Select the right solution strategy from the two system contradictions relationship (the three relations between w and s, the three relations between s and u) classified by propositional logic. here are nine cases according to sufficient conditions, necessary conditions, and necessary and sufficient conditions of functions and states of the system. he rest of steps are the same as [6] and described as follows: Step 2 Existing resource analysis Step 3 Determination of ideal final result and physical contradiction Step 4 Utilization and application of modified time, space, substance and field resources Step 5 Application of information fund Step 6 We can skip the step 6 for changing problems Step 7 Analyzing the quality of the problem solution Step 8 Application of the problem solution to maximize use of the applied resources Step 9 Analysis of solution procedure to increase the creative potential of humanity inally, we compared our algorithm with the ARIZ-85C by representing the previous example, the iron plate of the tank problem. Step 1.1 o define the mini-problem. [he iron plate of a tank], [protecting shells], is composed of [shells and the iron plate]. 32 Copyright c 2016 SERSC

7 echnical contradiction 1: if [the iron plate is thick], then [the tank can protect shells well]. However, [the weight of the tank increases]. hus, [the agility of the tank decreases]. echnical contradiction 2: if [the iron plate is thin], then [the tank can move quickly]. However, [the tank cannot protect shells well]. At least, we minimally modify [the tank], and then we get the result such that [the agile tank that has a thin iron plate protects shells well]. Step 1.2 o define the contradictory factors. Objects: shells ools: the iron plate Step 1.3 o define the physical contradiction. At this state two algorithms are the same. However, in the Step 1.4, ARIZ describes the Step 1.4 as follows: Step 1.4 o determine the main function of the system. hus, according to problem solvers, different technical contradiction can be selected. hus, in the later step, trial-and-error can occur. However, in our algorithm, since sufficient condition and necessary condition can be determined, we can decide the solution so that (~s w), where s is the thick iron plate and w is to protect shells well. As a result, in our algorithm, step 1.4 can be described as follows: Step 1.4 o determine the technical contradiction as [thin iron plate and protecting shells well]. In summary, in the above problem, ARIZ-85C proposed that a problem solver should select one technical contradiction with respect to the main function of the system. However, it is difficult to determine which function is more important between two functions ((i) to protect shell and (ii) to have agility). wo functions are required in the iron plate tank. he Butterfly diagram performs a visual role in analyzing physical contradictions and technical contradictions easily. By applying the propositional logic, the Butterfly algorithm derives the right direction efficiently and logically. 4. Conclusions Simon supposed that when we solve a complex problem, we should define the type of problems and develop the appropriate representation method for the problem. Symbolic notations and systematic representations increase the problem solving abilities of problem solvers. he symbolic logic overcomes the ambiguity of a language, and then figures out the correct logical structure of a given problem. However, in symbolic logic, contradiction problems were not considered due to their problems complexity [11-12]. Polya indicated that if the type of a problem is classified, then the problem could be solved easier [12]. It means that when we know the structure of a contradiction problem and its solution type in advance, we can reduce the problem space so that we can solve the problem easily. If we figure out the solution strategy according to the problem types with logical proofs, the problem solving ability can be enhanced due to the efficient search of the problem space [13]. he Butterfly diagram helps to find out a solution by defining a solution strategy based on the analysis of the trade-off relation and the contradiction relation hidden in a given problem. he Butterfly algorithm replaces the brute-force feature of ARIZ with the Copyright c 2016 SERSC 33

8 components of the Butterfly diagram, which are represented based on the propositional logic. In other words, if the relationship between the technical contradiction and the physical contradiction in RIZ are analyzed with the propositional logic, then the solution strategy that resolves the problem can be decided in a right way without trial-and-errors. When the required functions and the states for the functions are examined from the sufficient condition point of view, problem solvers can eliminate the ambiguity of the given problems and can derive the right solution strategy. References [1] G. S. Altshuller, Creativity as an Exact Science: he heory of the Solution of Inventive Problems, CRC Press, (1984). [2] S. D. Savransky, Engineering of Creativity: Introduction to RIZ Methodology of Inventive Problem Solving, CRC Press, (2002). [3] E. Domb, Contradictions: Air Bag Applications, he RIZ Journal, (1997). [4] R. Langevin, ARIZ, echnical Innovation Center, Inc., [5] N. Becattini, Y. Borgianni, G. Cascini and. Rotini, ARIZ85 and Patent-driven Knowledge Support. [6] ARIZ-85C Algorithm for Inventive Problem Solving Structure, +ARIZ85C_structure_example_WEB_02_22_2012.Pdf. [7] J. S. Hyun and C. J. Park, A conflict-based model for problem-oriented software engineering and its application solved by dimension change and use of intermediary, in CCIS, vol. 59, (2009), pp [8] J. S. Hyun and C. J. Park, he butterfly model for supporting creative problem solving, Knowledge, Information, and Creativity Support Systems (KICSS), 2012 Seventh International Conference on IEEE, (2012), pp [9] J. S. Hyun and C. J. Park, Logical interpretation about problem types and solution strategies of the butterfly model for the automation of contradiction-based problem solving, eaching, Assessment and Learning (ALE), International Conference on. IEEE, (2014), pp [10]. Hadland and H.-E. Lessing, Bicycle design: An illustrated history, MI Press, (2014). [11] H.A. Simon, he Sciences of the Artificial, he MI Press, (1987). [12] H.A. Simon, he architecture of complexity, Proceedings of the American Philosophical Society, vol. 106, no. 6, (1962), pp [13] G. Polya, Mathematics and Plausible Reasoning: Induction and Analogy in Mathematics, vol. 1. Princeton University Press, (1990). Authors Jung Suk Hyun, received Ph.D. at Sogang University, Korea. Since 2002, he has worked for the Dept. of MIS at Jeju National University. In 2011, he was a visiting scholar at University of California, Berkeley. His research interests include behavioral decision theory and creative problem solving. He received awards of the Korean Intellectual Property Office (2012), the Best eacher Award (2011), the Award of Enhancing University Prestige of Jeju National University (2008), Best Professor Award of Achievement in Research of Jeju National University (2007). Chan Jung Park, received B.S. at Dept. of Computer Science of Sogang University, Korea. She received M.S. and Ph.D. at KAIS and Sogang University, respectively. rom 1990 to 1994, and also from 1998 to 1999, she worked for Korea elecom as a researcher. Since 1999, she has worked for the Dept. of Computer Education at Jeju National University. Currently, she is a professor in Jeju National University. In 2010, he was a visiting scholar at University of California, Berkeley. Her research interests include creative problem solving, web app development, and data mining. 34 Copyright c 2016 SERSC