Qualitative Spatial Reasoning about Line Segments
cultivate aesthetic quality -回复
cultivate aesthetic quality -回复如何培养审美品质。
第一步：了解审美品质的概念和重要性（150-200字）审美品质是指对于美的感觉和理解能力，以及对美学原则的应用能力。
它是个人对于美的主观感受与客观判断的综合体现。
培养审美品质对个人的成长和全面发展具有重要意义。
首先，它有助于提升个人对于艺术作品和自然景观的欣赏能力，能够让人更深入地体验和理解艺术创作的内涵。
其次，审美品质培养还能帮助个人鉴别真伪、区分高下，提高审美眼光，避免受伪劣产品的影响。
最后，审美品质的培养也有助于提高个人的创造力和想象力，对于各种领域的工作和生活有着积极的促进作用。
第二步：培养美的感受力（300-400字）培养美的感受力是培养审美品质的第一步。
而获得美的感受力的最佳方式就是通过参观艺术展览和博物馆。
艺术展览让人接触到各种形式的艺术作品，如绘画、雕塑和摄影等，有利于培养个人对于不同艺术形式的欣赏和理解能力。
博物馆则提供了与文化和历史相关的展品，通过与这些文化遗产接触，人们可以更好地理解艺术家的创作背景和时代背景，提升审美品质。
此外，观看电影、听音乐和参加舞台表演等也是培养美的感受力的重要途径。
电影是一种融合了音乐、摄影、绘画和文字等多种艺术形式的媒介，同时能够让观众通过影片剧情感受到导演的审美理念。
音乐是人类创作的一种高度抽象的艺术形式，通过欣赏音乐作品，人们可以培养对音乐的欣赏能力和审美品味。
而参加舞台表演则能够更直接地感受到演员的表演技巧和剧本的精彩。
批判性欣赏也是培养美的感受力的重要手段。
通过学习艺术史和文学理论等相关知识，人们能够进一步理解和分析艺术作品的内涵和创作意图，提高对作品的评判和欣赏能力。
第三步：学习美学原则和艺术技巧（400-500字）了解美学原则和艺术技巧是培养审美品质的另一个重要步骤。
美学原则是指古今中外对于美的规律和准则的总结，通过学习这些原则，人们可以更好地理解和应用美的规律。
Qualitative reasoning about perception and belief
delval@ai.ii.uam.es pedmayn@
Alvaro del Val
Pedrito Maynard-Reid IIy
Computer Science Department Stanford University Stanford, CA 94305
shoham@
In
Proceedings of the Fifteenth International Joint Conference on Arti cial Intelligence (IJCAI-97)
, pp. 508{513.
Qualitative Reasoning about Perception and Belief
Yoav Shohamຫໍສະໝຸດ AbstractWe present a qualitative model for reasoning about perceptions, sensors, and belief, and a logic to reason about this model. Basic to our model is a distinction between precision and accuracy, for both of which we provide qualitative de nitions. In our logic this distinction gives rise to two modal operators|P for actual perception, and Cp for perceptual capability, which is captured as a set of possible percepts. Adding to these operators the standard B operator to model belief, we end up with a logic combining standard Kripke-style semantics with the almost-standard `neighborhood semantics.' We de ne various agent types in the logic, from agents who believe all and only what the sensors tell them, to much more skeptical agents. We de ne each agent both axiomatically and model-theoretically, and provide soundness and completeness results relating the two types of de nitions. A great deal of attention in AI has been devoted to modeling states of information, whether qualitatively through, e.g., logics of knowledge and belief (cf. Moore, 1985; Konolige, 1986; Fagin et al., 1995]), or quantitatively. In contrast, relatively little attention has been paid to modeling information sources, on the basis of which the various information states are reached. In particular, there has been very little work on the relationship between belief and perception, the most common source of information in everyday life. This is the topic of this paper. (We hasten to add that there certainly has been some work on this topic in AI, notably
个人素质英文作文
个人素质英文作文英文：Personal qualities are essential for success in life, both personally and professionally. In my opinion, the most important personal qualities include self-discipline, adaptability, and communication skills.Self-discipline is crucial because it allows us to stay focused on our goals and achieve them. It means having the ability to control our impulses and resist temptation. For example, if I have a deadline for a project, I make sure to set aside time each day to work on it, even if I would rather do something else.Adaptability is also important because life is unpredictable, and we need to be able to adjust to changing circumstances. This means being open-minded and willing to try new things. For instance, if I am faced with a new challenge at work, I try to approach it with a positiveattitude and a willingness to learn.Finally, communication skills are essential forbuilding relationships and achieving success in both personal and professional settings. This means being ableto express oneself clearly and listen actively. For example, if I am working on a team project, I make sure to communicate my ideas clearly and listen to the ideas of my teammates.Overall, personal qualities are key to success in life, and self-discipline, adaptability, and communication skills are among the most important qualities to cultivate.中文：个人素质对于个人和职业生涯的成功至关重要。
个人素质英语作文
Personal qualities are the essential characteristics that define an individuals behavior, attitude,and values.They play a crucial role in shaping ones life and interactions with others.Here are some key personal qualities that are often emphasized in English compositions:1.Integrity:This is the quality of being honest and having strong moral principles.It involves telling the truth,keeping promises,and maintaining a consistent set of values.2.Resilience:Resilience is the ability to bounce back from adversity and to cope with stress and challenges.It is important for personal growth and success.3.Empathy:Empathy is the capacity to understand and share the feelings of others.It fosters strong relationships and promotes a supportive community.4.Responsibility:Taking responsibility means being accountable for ones actions and decisions.It is a sign of maturity and is essential for building trust.5.Courage:Courage is the ability to face fear,danger,or adversity with confidence.It is often required to make difficult decisions and to stand up for what is right.6.Creativity:Creativity is the use of imagination to create something new or original.It is a valuable quality in various fields,from art to science.7.Selfdiscipline:Selfdiscipline involves controlling ones impulses and emotions to achieve goals.It is crucial for maintaining focus and achieving longterm objectives.8.Adaptability:Being adaptable means being able to adjust to new conditions or changes easily.It is important in a rapidly changing world.9.Curiosity:Curiosity is the desire to learn or know more about something.It drives exploration and the pursuit of knowledge.10.Teamwork:Teamwork is the collaborative effort of a group to achieve a common goal or to complete a task in the most effective and efficient way.11.Leadership:Leadership involves guiding,directing,and influencing others towards achieving a common goal.It requires a combination of skills,including communication, decisionmaking,and motivation.12.Perseverance:Perseverance is the ability to continue in a course of action despitedifficulty or opposition.It is often the key to achieving longterm goals.13.Humility:Humility is the quality of being modest and respectful.It involves recognizing ones limitations and being open to learning from others.14.Openmindedness:An openminded person is willing to consider new ideas and perspectives.It is important for personal growth and for fostering diversity of thought.munication Skills:Effective communication is the ability to express oneself clearly and listen to others with understanding.It is vital in both personal and professional settings.When writing an English composition about personal qualities,its important to provide examples or anecdotes that illustrate these qualities in action.This helps to make the essay more engaging and relatable to the reader.Additionally,discussing the importance of these qualities in various contexts,such as in education,the workplace,or in social interactions,can add depth to the composition.。
初二英语写作风格与文体特色判断练习题40题
初二英语写作风格与文体特色判断练习题40题1.This story is full of vivid descriptions and exciting events. The writing style can be described as________.A.boringB.plainC.livelyD.dull答案：C。
本题考查记叙文写作风格判断。
A 选项boring 意为“无聊的”；B 选项plain 意为“平淡的”；C 选项lively 意为“生动活泼的”；D 选项dull 意为“枯燥的”。
题干中提到故事充满生动的描述和令人兴奋的事件，所以写作风格应是生动活泼的，答案是C。
2.The narrative has a simple plot and straightforward language. The writing style is________.plexB.confusingC.simplisticD.intricate答案：C。
本题考查记叙文写作风格判断。
A 选项complex 意为“复杂的”；B 选项confusing 意为“令人困惑的”；C 选项simplistic 意为“简单的”；D 选项intricate 意为“错综复杂的”。
题干中提到叙事有简单的情节和直白的语言，所以写作风格是简单的，答案是C。
3.The story is told in a slow-paced manner with detailed descriptions.The writing style is________.A.hurriedB.rushedC.leisurelyD.fast-paced答案：C。
本题考查记叙文写作风格判断。
A 选项hurried 意为“匆忙的”；B 选项rushed 意为“急促的”；C 选项leisurely 意为“悠闲的”；D 选项fast-paced 意为“快节奏的”。
Orientation and Qualitative Angle for Spatial Reasoning
Int. Joint Conf. on Artificial Intelligence (IJCAI 93), Chambéry, France, 1993 Orientation and Qualitative Angle for Spatial ReasoningLongin Jan Latecki Ralf RöhrigUniversity of HamburgDepartment of Computer ScienceBodenstedtstr. 162000 Hamburg 50, Germanye-mail: {latecki,roehrig}@informatik.uni-hamburg.deAbstractThough arrangement knowledge is well suitedfor qualitative representations of spatial situations, if we only use this kind of knowledge,we cannot do interesting inferences about relative positions of points in the plane. For example, if we know the orientation of two triangles over four points, we cannot say anything about the orientation of the other two triangles. In this paper, we show that the augmentation of arrangement knowledge by qualitative angles leads to interesting and useful inferences.IntroductionQualitative reasoning deals with reasoning on the conceptual level. Most approaches in the area of qualitative spatial reasoning define a set of spatial relations and show the connections of these relations in composition tables. Each entry in such a table is verified by informal considerations of some pictures showing the concepts, or by general quantitative considerations. This means there is an implicit quantitative semantics underlying the spatial relations. In this sense each qualitative inference is semantically verified in three steps: 1. definition of the qualitative concepts in quantitative terms, 2. quantitative reasoning, and 3. qualitative abstraction. Each of these steps has its inherent problems: The quantitative definition of spatial concepts is often context dependent, quantitative reasoning is a difficult problem in non-trivial domains, and the qualitative abstraction often entails a loss of information. For these reasons the underlying quantitative semantics is kept implicitly in most systems.Our approach takes two cognitively motivated spatial concepts, arrangement and angles, and offers a context independent well defined mapping of these concepts to quantitative regions which can be described by angle intervals. The quantitative reasoning process is fairly simple due to interval arithmetic, and the qualitative abstraction step performs without any loss of information due to the invertability of the well-defined mapping in the definition step.Problem descriptionReasoning about cognitive maps means explication of implicit relations among spatial objects of the domain. One of the possible formal descriptions of two dimensional cognitive maps is the abstraction of objects to points in the plane. Then spatial relations among objects can be represented by relative positions of the points. These relative positions are completely described by triangles among each triple of points. So, the reasoning task can be reduced to the problem of finding the descriptions of triangles. In this paper, we will concentrate on a basic version of this task: Given two triangles over four points in the plane, find the description of the other two. For example, in Figure 1 triangles ABC and CBD are given, and we are looking for a description of ABD and ACD.ABCDFigure 1. Triangles ABC and CBD are given, and we are looking for a description of ABD and ACD.It is a well known fact in classical geometry that the latter two triangles are completely determined by the first two. However, if we model reasoning processes in cognitive science, we usually do not deal with complete metric knowledge as is the case in classical geometry. Since people are able to do geometrical reasoning without complete metric knowledge, thequestion is which kind of knowledge they use. The simplest approach in cognitive science is to adopt arrangement information as described in [Schlieder, 1990]. There, relative positions are described in terms of the orientation of triangles, clockwise or counterclockwise. If, for example, a triangle ABC is oriented counterclockwise, then we know that point C is to the left of the straight line AB (see Figure 2). The distinction of a left and right hand side is clearly a cognitively motivated concept.Cright Figure 2. If triangle ABC is oriented counterclockwise, then weknow that C is to the left of the straight line AB. Arrangement knowledge has been successfully applied in Artificial Intelligence (see [Levitt andLawton, 1990; Schlieder, 1990]) and in Computational Geometry (see [Bokowski and Sturmfels, 1989]). Though arrangement knowledge is well suited for qualitative representations of spatial situations, if we only use this kind of knowledge, we cannot do inferences we are interested in, as the following example shows. Given the orientation of two triangles over four points, it is not possible to say anything about the orientation of the other two triangles. In bothFigures 3a and 3b, triangle ABC is oriented counterclockwise and BCD is oriented clockwise, but triangle ABD is oriented differently in Figures 3a and3b. Of course, the same situation can be constructed for triangle ACD.DBCADBCAa) b) Figure 3. Triangle ABC is oriented counterclockwise and BCD is oriented clockwise, but triangle ABD is oriented differently.Now the question is whether one can find another cognitively motivated concept for representing spatial situations without using metric information. There is psychological evidence that people are able to recognize the right angle (especially while treating the angle from the vertex perspective), and so are able to distinguish an acute angle from an obtuse angle. Therefore, it is straightforward to augment the concept of arrangement information by the qualitativedistinction of acute and obtuse angles. These two concepts of arrangement and qualitative angles fit together quite well, since both describe orientation information.NotationWhen introducing a system integrating arrangement and qualitative angles, for reasons of simplicity and transparency, we will treat neither the concept of collinearity of three points, nor the concept of right angles. This means that we will distinguish situations in which a point C is to the left or to the right of a straight line AB, but we will exclude situations where point C is on the line. In the same manner we willdistinguish situations where three points form an acute or an obtuse angle, but we will exclude situations where they form exactly the right angle. The augmentation of the system by these concepts is straightforward.Similar to the representation of arrangement information, the relative positions of triples of points will be described by triangles in our system. Each triangle will be represented by qualitative information about its three angles and its orientation. Orientation will be denoted by "+" for counterclockwise and "-" for clockwise. Qualitative angles will be abbreviated by "ac" for acute and "ob" for obtuse. For example, the representation of the triangle presented in Figure 4a isshown in Figure 4b. An obvious observation is the fact that if one angle is obtuse, the other two have to be acute. A CABC = + A = ac B = ac c = oba)b)Figure 4. Representation of triangle ABC.Since our inference processes are based on qualitativeangles, we will introduce a special notation for a single angle. We will denote an angle XYZ by an ordered pair consisting of the orientation of points XYZ and the qualitative angle in Y. For example, angle CAB of thetriangle presented in Figure 4 will be described as CAB(+, ac). As it is easy to note, if we know the orientation of one angle, we know the orientation of the whole triangle, so we can infer the orientation of the other angles. This simple fact together with the fact that every triangle can have only one obtuse angle forms some useful inference rules for reasoning about a single triangle.ReasoningInference RuleThe following examples show the profit in the reasoning process we get from combining arrangement and qualitative angle information. We have shown that given the orientation of two triangles over four points, it is not possible to infer anything about the orientation of a third triangle. However, the following example will demonstrate that when arrangement information is augmented with qualitative angles, we can conclude arrangement information about the third triangle. If we get the constellation presented in Figure 5, where ABC as well as CBD form counterclockwise oriented acute angles, then we know that D is to the left of line AB (i.e. triangle ABD is oriented counter-clockwise), though we do not know whether angle ABD is acute or obtuse, idicated by the dotted lineNow we present a rule that formalizes the above inferences. The general inference schema is to add two adjacent angles ABC and CBD in the vertex B to obtain a third angle ABD, as the following figure illustrates:ABC CBDABDFigure 8. The general inference schema is to add two adjacent angles ABC and CBD in the vertex B to obtain a third angle ABD.In the remainder of this section, we will show how arrangement and qualitative angle information will be passed through this schema. We are looking for a basic concept that underlies the above two concepts.As we mentioned above, arrangement information splits the plane into two disjoint regions, the left and the right hand side (of line AB in Figure 9a). Another observation is also that angle information splits the plane into two disjoint regions (at line perpendicular to line AB in Figure 9b). For any point C below the perpendicular line, angle ABC is acute, whereas for any point C above that line angle ABC is obtuse. If we combine these two observations, we obtain a division of the unit circle into four quadrants, which for computational reasons we name 0, 1, 2 and 3 as shown in Figure 9c.ABC(+, ac) CBD(+, ac)ABD(+, *)a)b)Figure 5. If ABC and CBD form counterclockwise oriented acute angles, then we know that D is to the left of line AB, though we do not know whether angle ABD is acute or obtuse.This inference is valid, because if we add two acute angles with the same orientation, we obtain an angle of less than 180o , which means that D stays to the left of line AB.left B Aright +-obright -left +As another example consider a configuration as depicted in Figure 6. Point C is to the right of line AB and angle ABC is acute.CABC(-, ac) CBD(+, ac)ABD(*, ac)a)b)c)a) b) Figure 9. a) Arrangement information splits the plane into the left and the right hand side of line AB. b) Angle information splits the plane into two disjoint regions at line perpendicular to line AB. c) If we combine these two observations, we obtain a division of theunit circle into four quadrants. Figure 6. If ABC is a negatively oriented acute angle and CBD is apositively oriented acute angle, then we can conclude that angleABD will be acute, though we do not know the orientation oftriangle ABD. Quadrant 0 corresponds to a position of point C forming a negatively oriented acute angle ABC, quadrant 1 to a negatively oriented obtuse angle,quadrant 2 to a positively oriented acute angle and quadrant 3 to a positively oriented obtuse angle.Now, if point D is to the left of line CB and angle CBD is acute, then we can conclude that angle ABD will be acute too. This is valid, because the difference of two acute angles is an acute angle itself. The dotted line shows that we cannot say anything about the position of D with respect to line AB, which will be denoted by "*".Now remember the example presented in Figure 6, where ABC was a negatively oriented acute angle and CBD a positively oriented acute angle. Using quadrants, we can express ABC(-, ac) as ABC(0) and CBD(+, ac) as CBD(3). The resulting angle ABD isacute, but without any orientation information, so either ABD(0) or ABD(3) holds, which we will denote ABD(0 | 3). This result can also be computed by the following general rule:If ABC(q1) and BCD(q2), then ABD(q3), whereq3 = ( (q1+q2 ) mod 4 | (q1+q2+1) mod 4 )and q1, q2 and q3 vary over quadrants 0, 1, 2 and 3. The correctness of this rule can easily be proved by simple angle interval addition, since the quadrants can be described as angle intervals of 90o magnitude. Because the quadrants of the resulting disjunction are always adjacent, the disjunction can be expressed in terms of either arrangement or qualitative angles. Therefore, we have the following correspondence:ABC(-, *) ABC(0 | 1)ABC(*, ob) ABC(1 | 2)ABC(+, *) ABC(2 | 3)ABC(*, ac) ABC(3 | 0)Figure 10. The correspondence between triangle description and adjacent quadrants.To demonstrate how to use this rule, we will go back to the example in Figure 5. Using quadrants, the two positively oriented acute angles ABC(+, ac) and CBD(+, ac) will be represented as ABC(3) and CBD(3). By our inference rule, the resulting angle will be ABD(2 | 3), which means that angle ABD is positively oriented and we do not know anything about the qualitative angle: ABD(+, *), as expected, due to the above example. The inference is illustrated in the following figure:ABC(+, ac) ABC(3)CBD(+, ac) CBD(3)_______ABD(+, *) ABD(2 | 3)Figure 11. Two positively oriented acute angles ABC and CBD result in a positively oriented triangle ABD.Problem SolutionIn this section, we will return to our original problem of finding the qualitative description in terms of arrangement and angles of the remaining triangles when given two triangles over four points in the plane. We will demonstrate that our inference rule provides a solution.The general problem is depicted in Figure 1. Knowing the orientation of a triangle ABC and the qualitative angles in A, B and C as well as the orientation and angles of a triangle BCD, we ask for the orientation and the angles of triangle ABD (the case for ACD will be treated analogously). The inference is based on the angle addition rule. Obviously, we can apply this rule only at point B, since this is the only point where two angles with one side in common are given, namely ABC and CBD. As an illustration, let us treat the situation presented in Figure 12.ABDCFigure 12. The angle addition is done at point B.Concerning the angles in point B, the situation is the same as in Figure 5. The resulting angle ABD can therefore be computed as shown in Figure 11. The obtained result ABD(+, *) will be interpreted as a counterclockwise orientation of triangle ABD. Let us note once more that knowing only orientation of triangles ABC and CBD, we could not make any inference, since a clockwise orientation of triangle ABD would be consistent with these orientation assumptions as well (cf. Figure 13).ABCDFigure 13. We would not know anything about the orientation of triangle ABD in Figure 12 if we only knew the orientation of triangles ABC and CBD.Another example where qualitative angles can be inferred is depicted in Figure 14: triangle ABC is oriented positively with an obtuse angle in B, whereas triangle CBD is oriented positively with an acute angle in B.ABCDFigure 14. The angle addition is done at point B.Again we can use our rule for angle addition in the vertex B, which leads to the following inference:ABC(+, ob) ABC(2) CBD(+, ac) CBD(3) _______ ABD(*, ob) ABD(1 | 2)Figure 15. Two positively oriented angles, an acute ABC and anobtuse CBD, result in an obtuse angle ABD. So, we obtain the qualitative angle information that angle ABD is obtuse. Knowing that one triangle canhave at most one obtuse angle, we can additionally infer that the other two angles in triangle ABD are acute. In this situation, we do not obtain any orientation information, as expected, because triangle ABD can be oriented positively (cf. Figure 14) as well as negatively (cf. Figure 16).AC DBFigure 16. We do not know anything about the orientation oftriangle ABD in Figure 14.ApplicationsIn the problem description we introduced triangles to describe relative positions of points in the plane. Now the question arises as to which relative positions of points can be described with arrangement and qualitative angle knowledge. Figure 17 shows the 8 possible positions of a point C with respect to a pair of points A and B that are distinguishable using ourFigure 17. Subdivision of the plane induced by arrangement andqualitative angle knowledge.The vertical line AB divides the plane into two regionswhich correspond to possible positions of point C withregard to arrangement knowledge (of course, we referto the line as "vertical" for purposes of illustrations, butit can in fact be oriented arbitrarily). If point C is to theleft of AB, then triangle ABC is orientedcounterclockwise, whereas if point C is to the right ofAB, then triangle ABC is in clockwise orientation. Thequalitative angle information provides furthersubdivision: If triangle ABC has an obtuse angle in B,then point C has to be above the horizontal line in B. In the same way, if the angle in A is obtuse, then C has to be below the horizontal line in A. In the case whereboth angles in A and B are acute, point C will be in the region between the horizontal lines. This region can be further subdivided into regions inside and outside of the circle, depending on whether the angle in C is obtuse or acute. Note that if point C were on one of thehorizontal lines or on the circle, then one of the angles in triangle ABC would be a right angle, but for reasons of simplicity we have not yet extended our representation to those singular cases. For the same reasons, we do not treat collinearity of A, B and C, which corresponds to the vertical line AB.The obtained subdivision of the plane can be interpreted as a refinement of the system of disjoint orientation relations used by Freksa [1992]. Freksa starts with a left/right and front/back dichotomy in a point B with respect to a reference vector AB. He endsup with 15 disjoint qualitative locations depicted inFigure 18.11Figure 18. Subdivision of the plane used by Freksa [1992].In Freksa´s system, the 15 locations have natural language correspondences, for example, straight-front of B (1), left-front of B (2), left-neutral of B (3), left-back ofB, and left-front of A (4), and so on. Spatial inferences are done through the same schema as in our representation (see Figure 8). Each inference step can be encoded in a table showing the composition of the15 qualitative locations. Freksa uses a neighborhoodrelation of the qualitative locations to reduce the size of the composition table. Since our inferences are based on an analytic calculus, we do not need any table look-ups.Freksa and Zimmermann [1992] use these qualitativedescriptions for route finding purposes. They illustratethe problems they treat by the following example:"Walk down the road (ab). You will see a church (c) inthe front of you on the left. Before you reach thechurch turn down the path that leads forward to theright (bd)." The question is where the church is withrespect to the path (bd):dFigure 19. Route finding scenario used in [Freksa and Zimmermann, 1992].To answer this question, Freksa and Zimmermann use special operations to transform the input information that (d) is right-front of vector (ab) to an expression based on vector (bd): (a) is right-back of (bd). Knowing this together with the input fact: (c) is left-front of (ab), we can infer that (c) is to the left of (bd), which answers the question.Due to the circle, our representation leads to a finer subdivision of the plane. If Freksa´s system is augmented by this circle, it turns out that the composition of the operations used to transform the input information is internal, and that these operations form an algebraic group. This is not the case in the original formalism of Freksa and Zimmermann. These algebraic properties simplify the route finding process. The description of these properties and their impact on the reasoning process will be the topic of a forthcoming paper.Arrangement knowledge is used successfully in [Levitt and Lawton, 1990] for qualitative navigation for mobile robots. Having augmented arrangement knowledge by qualitative angles, which leads to a finer subdivision of the plane, we expect further advantages in qualitative route finding.As the above example illustrates, our formalism can be used for performing inferences based on qualitative information treated from the observer´s perspective. Recently Jungert [1992] presented an extension of symbolic projections of [Chang et al., 1987] which is especially concerned with the observer´s point of view. We conjecture that combining these two formalisms would allow us to obtain a powerful system for qualitative spatial reasoning which could be used in motion planning and in building qualitative maps by autonomous systems. A big advantage of such a formalism is that it would not need any global coordinate system.It is also easy to incorporate arrangement and qualitative angle knowledge into a hybrid system for spatial reasoning which combines propositional and depictorial inferences, as presented in [Latecki and Pribbenow, 1992]. This is due to the propositional inference rule presented here and to the fact that using a finite grid as a representation frame for depictorial inferences, we can represent and retrieve arrangement and qualitative angle information in a simple way. AcknowledgementWe wish to thank Christian Freksa, whose work inspired us, and also Cao Yong, Rolf Sander, and Kai Zimmermann.References[Bokowski and Sturmfels, 1989] J. Bokowski and B. Sturmfels. Computational Synthetic Geometry. Springer-Verlag, Berlin, 1989.[Chang et al., 1987] S.-K. Chang, Q.Y. Shi, and C.W. Yan. Iconic indexing by 2D strings. IEEE transactions on Pattern Analysis and Machine Intelligence (PAMI), Vol. 9, No. 3, 413-428, 1987.[Freksa, 1992] C. Freksa. Using Orientation Information for Qualitative Spatial Reasoning. Proceedings of the International Conference GIS - From Space to Territory. Theories and Methods of Spatio-Temporal Reasoning. Pisa, Italy, September 1992. [Freksa and Zimmermann, 1992] C. Freksa and K. Zimmermann. On the Utilization of Spatial Structures for Cognitively Plausible and Efficient Reasoning. Proceedings of SMC ’92 – 1992 IEEE International Conference on Systems Man and Cybernetics, Chicago, October 1992.[Jungert, 1992] E. Jungert. The Observer´s Point of View: An extension of Symbolic Projections. Proceedings of the International Conference GIS - From Space to Territory. Theories and Methods of Spatio-Temporal Reasoning., 179-195, Pisa, Italy, September 1992.[Latecki and Pribbenow, 1992] L. Latecki and S. Pribbenow. On Hybrid Reasoning for Processing Spatial Expressions. Proceedings of the European Conference on Artificial Intelligence (ECAI 92), Vienna, Austria, August 1992.[Levitt and Lawton, 1990] T.S. Levitt and D.T. Lawton. Qualitative Navigation for Mobile Robots. Artificial Intelligence 44, 305-360, 1992.[Schlieder 1990a] C. Schlieder. Anordnung. Eine Fallstudie zur Semantik bildhafter Repräsentationen. In Freksa, C. and Habel C. (eds.): Repräsentation und Verarbeitung räumlichen Wissens, Springer-Verlag, Berlin, 1990.[Schlieder 1990b] C. Schlieder. Hamburger Ansichten oder Ein Problem der Repräsentation räumlichen Wissens. Proceedings of the 14th German Workshop on Artificial Intelligence (GWAI 90), 29-37, Springer-Verlag, Berlin, 1990.。
人的品质 英语作文
When discussing the qualities of a person,there are several key attributes that are often regarded as essential for personal development and social interaction.Lets explore some of these qualities in detail:1.Integrity:This is the quality of being honest and having strong moral principles.A person with integrity is consistent in their actions,values,and methodsregardless of who is watching.2.Empathy:The ability to understand and share the feelings of others.Empathetic individuals are sensitive to the emotional states of those around them and can offer comfort and support.3.Resilience:This refers to the capacity to recover quickly from difficulties.Resilient people are able to bounce back from setbacks and maintain a positive outlook despite challenges.4.Humility:A humble person does not think of themselves as more important than others. They are willing to listen and learn from others,and they do not boast about their achievements.5.Courage:The ability to face fear,danger,or pain without shrinking.Courageous individuals are willing to stand up for what they believe in,even when it is difficult.6.Kindness:A kind person is considerate and caring towards others.They are willing to help and show compassion without expecting anything in return.7.Responsibility:This is the ability to be accountable for ones actions.Responsible individuals take ownership of their decisions and are reliable in fulfilling their commitments.8.Patience:The capacity to accept or tolerate delays,problems,or suffering without becoming annoyed or anxious.Patient people are able to remain calm and composed in difficult situations.9.Openmindedness:Being open to new ideas and willing to consider different perspectives.Openminded individuals are not rigid in their thinking and are receptive to change.10.Selfdiscipline:The ability to control ones feelings and overcome immediate temptations in order to achieve longterm goals.Selfdisciplined people are able toprioritize their tasks and manage their time effectively.11.Curiosity:A desire to learn more about the world and to explore new ideas.Curious individuals are always asking questions and seeking knowledge.12.Perseverance:The determination to continue in a course of action in spite of difficulty or opposition.Persevering people do not give up easily and are committed to seeing their goals through to completion.13.Honesty:The quality of being truthful and sincere.Honest people are transparent in their communication and do not deceive others.14.Fairness:Treating people equally and without bias.Fair individuals ensure that everyone is given an equal opportunity and is treated justly.15.Creativity:The ability to think of new and original ideas.Creative people are able to approach problems in unique ways and come up with innovative solutions.These qualities are not only important for personal growth but also for building strong relationships and contributing positively to society.Cultivating these attributes can lead to a more fulfilling and successful life.。
个人素质英文作文素材模板
个人素质英文作文素材模板1. Personal qualities are essential for success in life. They include characteristics such as resilience, adaptability, and determination. These qualities help individuals navigate through challenges and setbacks, allowing them to achieve their goals and reach their full potential.2. Another important personal quality is empathy. Being able to understand and share the feelings of others is crucial for building strong relationships and fostering a sense of community. Empathy allows individuals to connect with others on a deeper level and offer support when needed.3. Creativity is also a valuable personal quality that can lead to innovation and problem-solving. Thinkingoutside the box and approaching situations from different perspectives can result in unique solutions andbreakthrough ideas. Creativity is a driving force behind progress and growth in various fields.4. Honesty and integrity are fundamental personal qualities that build trust and credibility. Being truthful and ethical in all interactions demonstrates a strong moral character and sets a positive example for others. Honesty and integrity are essential for maintaining strong relationships and upholding a sense of fairness and justice.5. Personal qualities such as humility and open-mindedness are important for personal growth and learning. Being willing to acknowledge one's limitations and being open to new ideas and perspectives can lead to self-improvement and a broader understanding of the world. Humility and open-mindedness foster a sense of curiosityand a willingness to embrace change and diversity.6. Lastly, resilience and perseverance are key personal qualities that enable individuals to overcome obstacles and achieve success. Facing challenges with a positive attitude and a determination to keep moving forward can lead to personal growth and accomplishment. Resilience andperseverance are essential for navigating through life's ups and downs and emerging stronger on the other side.。
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Reinhard Moratz Jochen Renz Diedrich Wolter123Qualitative Spatial Reasoning about Line SegmentsIn: In: W.Horn (ed.): ECAI 2000. Proceedings of the 14th European Conference on Artificial Intelligence, IOS Press, Amsterdam, 2000Abstract.Representing and reasoning about orientation infor-mation is an important aspect of qualitative spatial reasoning.We present a novel approach for dealing with intrinsic orientation in-formation by specifying qualitative relations between oriented line segments,the simplest possible spatial entities being extended and having an intrinsic direction.We identify a set of 24atomic relations which form a relation algebra and for which we compute relational compositions based on their algebraic semantics.Reasoning over the full algebra turns out to be NP -hard.Potential applications of the cal-culus are motivated with a small example which shows the reasoning capabilities of the dipole calculus using constraint-based reasoning methods.1IntroductionQualitative representation of space abstracts from the physical world and enables computers to make predictions about spatial relations,even when precise quantitative information is not available [2].Dif-ferent aspects of space can be represented in a qualitative way.The most important of these are topological information and orientation information about physical objects which are usually spatially ex-tended.While it is common for representing topological information to use extended spatial regions as the basic entities,most approaches to qualitatively representing and reasoning about orientation infor-mation deal with points as the basic entities.Those orientation ap-proaches that use extended spatial regions as the basic entities mostly approximate regions by using,for instance,minimal bounded rectan-gles whose sides are parallel to the axes of the global reference frame.This,however,does not account for representing intrinsic orientation information.In this paper we develop one of the simplest possible calculi for representing intrinsic orientation information,namely,by using ori-ented line segments represented by their start and end points as the basic entities.sAB A e A eBsBFigure 1.Orientation relation between two dipolesA rlrrB A rlll BA rllr BA lrrr BA lrll BA lrrlB A llrl BA llrrB A llll BA lllr BA rrll BA rrlr BA rrrl BA rrrr BA errs BA ells BA eses BA sese BA rser BA lsel BA srsl BA slsr BA rele BA lere BFigure2.The24atomic relations of the dipole calculusThe cases andcannot be realized on theplane.These14relations are similar to the relations between linesegments derived by Schlieder[13].However,in order to obtain arelation algebra,we also have to consider those relations where twodipoles share common points.Then can be equivalent to the startpoint of or to the end point of.This is denoted asor,ing these additional dipole-point rela-tions,we obtain the following ten additional dipole-dipole relations:.Altogether weobtain24different atomic relations.These relations are jointly ex-haustive and pairwise disjoint provided that all points are in generalposition.The relation sese is the identity relation.We use to referto the set of24atomic relations,and to refer to the powersetof which contains all possible unions of the atomic relations.The relations which are introduced above in an informal way canbe defined in an algebraic way.Every dipole on the plane is anordered pair of two points and,each of them is representedby its Cartesian coordinates and,with and.The basic relations are then described as polynomial equationswith the coordinates as variables.The set of solutions for a systemof equations describes all the possible coordinates for these points.As an example,we will have a more detailed look at the relation.We need tofind an equation,which is solvable iff a pointlies to the right of a given line.Then,we can use this equation to ex-press the premises of the relation:.The equation for“right of”is constructed as follows(servesas example):With,hence and.Whenever lies on the right of the line.The equation1is modified in a similar way for the premise“left of”(l)::with(3)Note that the equations will only have a solution,when.Constructing the dipole-point relations and is done by using thesame variables for the identical points.For the following substitutions,,,,,,,,and new introduced variables,the completeset of equations describing relation reads as:with.The other relations areconstructed in an analogous way.3Constraint Reasoning with the Dipole CalculusFor reasoning about the dipole relations we apply constraint-basedreasoning techniques which were originally introduced for temporalreasoning[1]and which also proved valuable for spatial reasoning[12].In order to apply these techniques to a set of relations,theserelations must form a relation algebra[8],i.e.,they must be closedunder composition(),intersection(),complement(of,and where no contradiction was detected,we have to construct a possible configuration of points in the plane.Instead of generating this configuration from the equations(which can be quite complicated),we simply search for a valid configuration of points on a grid.rrrl rrll rllr lrrrrrrr lrrr rrrl llrllllr llrr lrrl rllllrll llrl llll errsrllr rrll lrll lselrlrr rrlr rrrr ellsrele srsl rser eses rele srsl ells seselere slsr lsel eses Table1.Converse and reflection table of the dipole calculusThe composition table for the atomic relations is given in Table24. We use to mark places which can befilled with or.In order to reduce the size of the table,trivial cases(sese,eses)for the columns are omitted.Symmetric cases can be derived using the converse op-eration and a reflection operation(reflection on an axis,denoted, see also Table1).The missing entries can be calculated using the following equation:(4) Dipole constraints are written as where are variables for dipoles and is a relation.Given a set of dipole con-straints,an important reasoning problem is deciding whether is consistent,i.e.,whether there is an assignment of all variables of with dipoles such that all constraints are satisfied(a solution).We call this problem DSAT.DSAT is a Constraint Satisfaction Problem (CSP)[9]and can be solved using the standard methods developed for CSP’s with infinite domains(see,e.g.[8]).A partial method for determining inconsistency of a set of con-straints is the path-consistency method which enforces path-consistency on[9].A set of constraints is path-consistent if and only if for any two variables,there exists an instantiation of any third variable such that the three values taken together are consistent.It is necessary but not sufficient for the consistency of a set of constraints that path-consistency can be enforced.A naive way to enforce path-consistency is to strengthen relations by successively applying the following operation until afixed point is reached:where are nodes and is the relation between and.The resulting set of constraints is equivalent to the original set,i.e.,it has the same set of solutions.If the empty relation occurs while per-forming this operation is inconsistent,otherwise the resulting set is path-consistent.In Section6we use the path-consistency method to solve a small navigation problem with the dipole calculus.4Computational Properties of the Dipole Calculus Although we restricted the possible binary relations between dipoles to24atomic relations,is very expressive.For instance,it is(for)holds.The latter constraint guarantees that the graph formed by the dipoles is planar(see Figure4).Figure4.Reduction of a set to a graph ofdipoles(a)(b)(c)(d)Figure5.Reduction of a triple to dipole constraints.If is between and,the constraints are satisfied(see(a),(b)),if is betweenand,then either overlaps or or overlaps or whichcontradicts the constraints(see(c),(d)).For every ordered triple we introduce the two dipoles and the constraints,,,,.As it can be seen in Figure5,these constraints guarantee that the set of dipole constraints is consistent iff there a one-to-one function from to such that for eachin,or.We have so far neither been able to prove thatis a member of nor whether reasoning over the atomic relations is tractable.However,it follows from the algebraic semantics of the relations that is a member of.This is be-cause all relations can be expressed as equalities over polynomials with integer coefficients.Systems of such equalities can be solved using polynomial space[11].5An Extended Version of the Dipole CalculusIn certain domains we might want to represent spatial arrangements in which more than two start or end points of dipoles are on a straight line.Then we need three more dipole-point relations.The additional relations describe the cases when the point is straight behind the dipole(),in the interior of the dipole()or straight in front of the dipole().The corresponding regions are shown on Figure6.Such a set of relations was proposed by Freksa[4].3bsi e f rlFigure 6.Extended dipole-point relationsStreet DStreet BStreet CStreet A Figure 7.Navigating in an arrangement of one-way streetsUsing the same notation scheme like the one for the coarse DipoleRelation Algebrawe get the following 69atomic relations:rrrr,rrrl,rrlr,rrll,rlrr,rllr,rlll,lrrr,lrrl,lrll,llrr,llrl,lllr,llll,ells,errs,lere,rele,slsr,srsl,lsel,rser,sese,eses,lllb,llfl,llbr,llrf,lirl,lfrr,lril,lrri,blrr,irrl,frrr,rbrr,lbll,flll,brll,rfll,rlli,rrlf,illr,rilr,rrbl,rlir,rrfr,rrrb,ffbb,efbs,ifbi,bfii,sfsi,beie,ffbb,bsef,biif,iibf,sisf,iebe,ffff,fefe,fifi,fbii,fsei,ebis,iifb,eifs,iseb .The derived fine grain Dipole Relation Algebra is called .contains Allen’s interval relations [1]as a special case:In these cases the dipoles are on the same straight line and have the same direction.also contains 10additional relations which correspond to the case with dipoles on a line and opposite directions (only 10out of 13because there are more self-converse cases).The composition table for can be obtained at rmatik.uni-hamburg.de/WSV/DRA .6A Sample Application of the Dipole CalculusThe dipole calculus can be used in navigation domains.A small ex-ample shows a scenario in which a car navigates through a network of one-way streets (see Figure 7).The car starts from street and wants to reach a goal within street .Because of the direction of it cannot enter directly from .Therefore the car has to enter or to reach .It is unknown whether of meets .Only the position of the streets with respect to is known.We now can useto express our initial knowledge:The question is whether street or streetcan be used to drive intostreet :(6)(7)To decide this question we build two sets of constraints,contains the constraints (5),(6)(corresponding to the assumption meets )and contains the constraints (5),(7).By applying the path-consistency method to both sets it turns out that contains a con-tradiction while path-consistency can be enforced to .This gives us the following solution to the navigation problem:street cannot meet street ,street has a chance to meet street .Thus,we have a good reason to turn into street instead of street .7Related WorkSchlieder [13]suggested a calculus for reasoning about oriented line segments which is based on clockwise and counter-clockwise orientation of triples of points.Schlieder’s calculus does,however,not form a relation algebra (e.g.,it does not contain an identity re-lation)and as such does not allow using constraint based reason-ing methods.Instead,Schlieder uses inferences based on concep-tual neighborhood structures.The double-cross calculus by Freksa [4]describes relations between triples of points,which can be re-garded as relationships between a dipole and an isolated point.In contrast to Freksa’s ternary relations,our dipole relations are binary relations which makes reasoning much easier.Also,Freksa distin-guishes more possible relations between a dipole and a point than we do.Isli and Cohn [7]developed a ternary algebra for reasoning about orientations.Their algebra has a tractable subset containing the base relations.8Conclusion and PerspectiveWe presented a calculus for representing and reasoning about qual-itative intrinsic orientation information.We chose oriented line seg-ments as the basic entities since they are the simplest spatial entities that show two important features of physical objects:they have an intrinsic orientation and they are extended.We identified a system of 24atomic relations between dipoles and computed the composition table based on their algebraic semantics,which allows for applying constraint-based reasoning methods.We further proved that reason-ing over these relations is NP -hard and in PSPACE .It is a matter of further studies whether the calculus is in and whether reasoning over the atomic relations is even tractable.Potential applications of the calculus are demonstrated with a small navigation example.AcknowledgementThe authors would like to thank Christian Freksa and Amar Isli for interesting and helpful discussions related to the topic of the paper.This work was supported by the DFG priority program on Spatial Cognition,under grants Fr 806/7-2(Christian Freksa)and Ne 623/1-2(Bernhard Nebel).REFERENCES[1]J.F.Allen,‘Maintaining knowledge about temporal intervals’,Commu-nications of the ACM ,832–843,(1983).[2] A.G.Cohn,‘Qualitative spatial representation and reasoning tech-niques’,in KI-97:Advances in Artificial Intelligence ,eds.,G.Brewka,C.Habel,and B.Nebel,LNAI 1303,1–30,Springer,Berlin,(1997).[3] D.Cox,J.Little,and O’Shea,Ideals,Varieties,and Algorithms ,Springer,New York,1997.[4] C.Freksa,‘Using orientation information for qualitative spatial rea-soning’,in Proceedings of International Conference on Theories and Methods of Spatio-Temporal Reasoning in Geographic Space ,eds.,A U Frank,I Campari,and U Formentini,Springer,Berlin,(1992).[5]M.R Garey and D.S Johnson,Computers and intractability ,Freeman,New York,(1979).[6] E.G.Hoel and H.Samet,‘Efficient processing of spatial queries in linesegment databases’,in Proceedings of the 2nd Symp.on Large Spatial Databases (SSD’91),pp.237–255,Z¨u rich,(1991).[7] A.Isli and A.G Cohn,‘An algebra for cyclic ordering of 2d orien-tations’,in Proceedings AAAI-98,pp.643–649,Madison,WI:.MIT Press,(1998).[8]dkin and R.Maddux,‘On binary constraint problems’,Journal ofthe Association for Computing Machinery ,41(3),435–469,(1994).[9] A.K Mackworth,‘Consistency in networks of relations’,Artificial In-telligence ,8,99–118,(1977).4[10] A.Musto,K.Stein,A.Eisenkolb,and T.R¨o fer,‘Qualitative and quanti-tative representations of locomotion and their application in robot nav-igation’,in Proceedings IJCAI-99,pp.1067–1072,(1999).[11]J.Renegar,‘On the computational complexity and geometry of thefirstorder theory of the reals.Part I-III’,Journal of Symbolic Computation 13(3),255–352,(1992).[12]J.Renz and B.Nebel,‘Efficient methods for qualitative spatial reason-ing’,in Proceedings ECAI-98,pp.562–566,Brighton,(1998). [13] C.Schlieder,‘Reasoning about ordering’,in Spatial Information The-ory:a theoretical basis for GIS,ed.,W Kuhn A Frank,LNCS988,pp.341–349,Springer,Berlin,(1995)..Rel BC|llll|lllr|llrl|llrr|lrrl|lrrr|rlrr|srsl|errs|rele ||||||||||Rel AB||||||||||--------+------+------+------+------+------+------+------+------+------+------llll|sese|lsel|rser|eses|ells|ells|lsel|lrrr|lrrr|rlrr |lsel|lere|rele|lsel|slsr|errs|rser|lrll|lrll|rlll|rser|errs|ells|rser|*ll*|slsr|lere|llrr|llrr|llrr|lere|srsl|slsr|lere|l*ll|srsl|rele|lllr|lllr|llrl|rele|l**l|*ll*|rele|*l*r|*ll*|l**l|llll|llll|llll|ells|*r*l|r*l*|ells|l*rr|*r*l|r*l*||||errs|l*r*|*l*r|errs||**rr|**rr||||slsr|*rr*|r**r|slsr|||||||srsl|||srsl|||||||ll**|||ll**|||||||r*l*|||r*l*|||||||*r*l|||*r*l|||||||**rr|||**rr||||||--------+------+------+------+------+------+------+------+------+------+------lllr|lsel|lsel|rser|lsel|lere|lere|eses|lere|lere|ells |rser|srsl|slsr|rser|slsr|slsr|lsel|lrrr|lrrr|rllr|slsr|l**l|llr*|slsr|l*r*|l*r*|rser|lrrl|lrrl|rlll|srsl|lll*|*l*r|srsl|*l*r|*l*r|ells|llrr|llrr|llrl|ll**|*r*l|r**r|ll**|||errs|llrl|llrl|lllr|*r*l|||*r*l|||*ll*|lllr|lllr|llll|r**r|||r**r|||l**l||||||||||*rr*||||||||||r**r|||--------+------+------+------+------+------+------+------+------+------+------llrl|lere|lere|rele|lere|lsel|eses|lere|lsel|lsel|slsr |rele|errs|ells|rele|ells|lsel|slsr|lrrl|lrrl|rlrr|ells|l*r*|*ll*|ells|*ll*|rser|l*r*|lrll|lrll|rllr|errs|*rr*|ll*l|errs|l**l|ells|*l*r|llrl|llrl|llrr|ll**|ll*r|r*l*|ll**||errs||lllr|lllr|llrl|r*l*|||r*l*||*ll*||llll|llll|lllr|*rr*|||*rr*||l**l||||||||||*rr*||||||||||r**r||||--------+------+------+------+------+------+------+------+------+------+------llrr|**ll|lll*|ll*l|**ll|lsel|lsel|ells|lsel|lsel|ells 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|ells|rele|rele|errs|lsel|errs|slsr|lrrl|rrrr|rrrl|*ll*|ells|ells|l*r*|rser|*rr*|l*r*|lrll|rrrl|rrlr|ll*l|errs|errs|*rr*|ells|r**r|*l*r|llrl|rrlr|rrll|r*l*|ll**|ll**|ll*r|errs|||lllr|rlrr|lrrl|rr*l|r*l*|r*l*|rr*r|*ll*|||llll|rllr|lrll||*rr*|*rr*||l**l||||||||||*rr*||||||||||r**r|||||--------+------+------+------+------+------+------+------+------+------+------lrrr|ll*l|lll*|ll*l|lll*|lsel|rser|ells|lsel|rser|errs |r*ll|r*ll|r*ll|rrl*|rser|rele|slsr|lere|rele|srsl|llr*|rrr*|rr*r|l*rr|lere|r*l*|*ll*|lrrr|rrrr|rrrr|rrr*|l*rr|l*rr|*rrr|rele|r**r|*l*r|lrrl|rrlr|rrrl|||||l**l|*rrr|l*rr|lrll|rrll|rrll|||||r*l*|||llrr|rlrr|lrrr|||||**rr|||llrl|rllr|lrrl||||||||llll|rlll|lrll--------+------+------+------+------+------+------+------+------+------+------rlll|lsel|eses|sese|rser|ells|ells|rser|rrrr|lrrr|rlll |lere|lsel|lsel|rele|errs|slsr|rele|rrrl|llrr|llrr|errs|rser|rser|ells|slsr|*ll*|r*l*|rrll|lllr|llrl|srsl|lere|lere|slsr|srsl|*l*r|r**r|rlll|llll|llll|l**l|rele|rele|*ll*|*ll*|l*rr|*rrr||||*r*l|ells|ells|r*l*|*r*l||||||l*r*|errs|errs|*l*r|**rr||||||*rr*|slsr|slsr|r**r||||||||srsl|srsl|||||||||ll**|ll**|||||||||r*l*|r*l*|||||||||*r*l|*r*l|||||||||**rr|**rr|||||||--------+------+------+------+------+------+------+------+------+------+------rllr|lsel|lsel|lsel|rser|sese|lere|rser|rele|lere|ells |srsl|rser|rser|slsr|lere|slsr|errs|rrrl|lrrr|rllr|l**l|slsr|slsr|llr*|rele|l*r*|*rr*|rrlr|lrrl|rlll|lll*|srsl|srsl|rrr*|slsr|*l*r|r**r|rrll|llrr|llrl|*r*l|ll**|ll**|*l*r|srsl|||rllr|llrl|lllr|rrl*|*r*l|*r*l|r**r|r*l*|||rlll|lllr|llll||r**r|r**r||*r*l||||||||||l*r*||||||||||*l*r|||||rel BC|llll|lllr|llrl|llrr|lrrl|lrrr|rlrr|srsl|errs|rele |||||||||| rel AB||||||||||--------+------+------+------+------+------+------+------+------+------+------rlrr|lll*|lll*|ll*l|ll*l|lsel|lsel|errs|rser|lsel|ells 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