knowledge representation.doc

Unit Four: Knowledge Representations This chapter and the next will be concerned with the different ways in which information is represented in memory. In this chapter we will consider two types of knowledge representations:Perception-based knowledge representationsMeaning-based knowledge representations 1. Perception-based knowledge representationsA. Spatial vs linear representations An experiment by Santa (1977) nicely illustrates the difference between spatial and linear representations. The two conditions of Santas experiment are illustrated in the following figure. Geometric Condition: (1) identical; (2) same elements, linear configuration; (3) different elements, same configuration; (4) different elements, linear configuration. In the first condition, Ss studied a spatial array of 3 geometric objects which had a face-like property. After a brief presentation, they were given one of a number of test arrays to verify: that the array contained the same elements, although not necessarily in the same spatial configuration, as the study array. Thus Ss should respond positively to the first two arrays in the figure and negatively to the other two arrays. Interest was focused on the contrast between the two positive test arrays: one is identical, in the other array, the elements are arrayed linearly. In the second condition, Ss studied words instead of geometric objects, the stimulus did not suggest a face, so they encode the word array according to normal reading order: left to right, top to bottom. The graph shows that the verbal and the geometric conditions display a sharp interaction. Some information (geometric objects) tends to be stored according to spatial position, whereas other information (words) tends to be stored according to linear order.B. Mental Rotation Most people are able to form an image in their minds eye of a familiar person, room, and scene. If they are given the task of verifying two images, they will make mental rotation of one image.C. Comparison of analog quantities When Ss transform a mental object spatially, processing time increases continuously with the amount of spatial transformation. However, other evidence shows that mental distance exerting the reverse effects: when Ss try to discriminate between two objects, their time to make this discrimination decreases continuously with the amount of difference between the two objects. Moyer was interested in the speed with which Ss could judge the relative size of two animals from memory:Which is larger, moose or roach?Which is larger, wolf or lion? People report that in making these judgments they experience images of the two objects and seem to compare the size of the objects in their image. Moyer also asked Ss to estimate the absolute size of these animals. In general, the judgment times decrease as the difference in estimated size increases. This has some implications for writing MC test items: When did the French revolution break out? Set 1 Set 2 a. 1789 a. 1789 b. 1917 b. 1804 c. 1848 c. 1776 d. 1941 d. 1825 Which set is more difficult? D. Judgments of abstract qualities Banks & Flora had one group of Ss rate animals on a 1-to-10 rating scale as to intelligence. The mean ratings of the eight animals rated by their Ss and by Chinese Ss were given below respectively:ape(9.20), dog(7.36), cat(6.57), horse(5.57), cow(3.58), sheep(3.42), chicken(3.36), fish(1.68)ape(9), dog(7.64), cat(7.05), horse(6.7), chicken (4.65), sheep(4.52), cow(3.35), fish(2.23) R = .97 Then another group of Ss was presented with a pair of these animals and asked to judge which member of the pair was the more intelligent. The results were: judgment time decreased as the distance in rated intelligence between the two animals increased. E. Images vs mental pictures Images should be distinguished from pictures in the minds (1) They are abstract and not tied to visual property. (2) Some operations are easy to perform on a picture, but hard to perform in an image. Consider the following example given by Simon. It is a very difficult imaginal task. If presented with a physical picture of the image, we could easily provide the answer. Imagine but do not draw a rectangle 2 inches wide and 1 inch high, with a vertical line cutting it into two 1- inch squares. Imagine a diagonal from the upper left-hand corner to the lower right-hand corner of the 2*1-inch rectangle. We will call this line diagonal A. Imagine a second diagonal from the upper-hand corner to the lower left-hand corner of the right square. Call this line diagonal B. Consider where diagonal A cuts diagonal B. What is the relationship of the length of B above the cut to the length of B below the cut? (3) Images can be distorted by general knowledge. Ss were exposed to the above shape with one of the two verbal descriptions. When asked to draw the object from memory, however, Ss drawing were distorted in the direction of the named category: (4) Images consist of parts, whereas pictures do not. Reed in an experiment presented Ss with forms like the following figure (a) and asked them to hold images of the forms in their minds. The form was removed and Ss were presented with parts of them.F. Linear orderings Most of the research use a memory paradigm of one sort or another. Ss commit or try to commit to memory elements in a fixed order. By looking at Ss ability to access this information, it is possible to make inferences about the structure of that information in memory. So Ss might learn a conso-nant string KRTB. They also learned to associate a digit to the string, e.g. 7. After this learning phase, they were presented with 4 consonants, and they had to recall the digit. We were interested in how fast they could make their recall, which we interpreted as a measure of how long it took to recognize the consonant string. The major experimental manipulation involved the order in which the four consonants were presented. The consonants were not always presented in the order in which they had been studied. For instance, Ss had to recognize RTKB as a variation of KRTB that they had studied. (a) identical: KRTB 1.55 sec (b) same first two letters: KRBT 1.55 sec (c) same first letter: KTBR 1.59 sec (d) same last two letters: RKTB 1.59 sec (e) same last letter: TKRB 1.64 sec (f) totally different: TKBR 1.74 sec These data show two major effects governing access to ordinal structure. (1) front anchoring. Better access to the structure from the beginning of the string. (2) end anchoring. Less pronounced, but some advantage when the end of the string matches. nHierarchical encoding of orderings. As to longer sequences, Ss tend to store them hierarchically, with subsequences as units in larger sequences. So, for instance, consider how people might represent the order of the 26 letters in the alphabet. A possible hierarchical representation is based on the Alphabet Song, which is in turn based on the rhythm and melody of Twinkle, Twinkle Little Star . Thus the alphabet is a hierarchical structure whose major constituents are: ABCD, EFG, HIJK,LMNOP,QRS,TUV,WXYZ. Klahr et al did an experiment to look for effects of this hierarchical structure on time to generate the next letter in the alphabet.Thus the S might be given K and asked to generate the next letter in the alphabet. Note that generation times are fastest at the beginning of a major constituent and progressively slower toward the end of the constituent. Thus, within a constituent, Ss judgment times show the same front-anchoring effect. Klahr et al theorize that Ss have access to the beginning of a sublist and search forward for the target letter. 2. Meaning-Based Knowledge RepresentationsA. Memory for verbal information We seem to use linear orderings to encode some verbal information: we can remember verbatim lines from poems, songs, plays, and speeches. However, doubt exists as to whether all or even most of our memory form verbal communication can be accounted for in terms of memory for verbatim message. Wanners experiment illustrates circum-stances in which people do and do not remember information about exact wording. Ss listened to tape-recorded instructions for the warn group, the tape began like this: The materials for this test, including the instructions, have been recorded on tape. Listen very carefully to the instructions because you will be tested on your ability to recall particular sentences which occur in the instructions. The second group received no such warning and so had no idea that they be responsible for the verbatim instructions. After this point, the instructions were the same for both groups. At a later point in the instructions, one of four possible critical sentences occurred: (1) When you score your results, do nothing to correct your answers but mark carefully those answers which are wrong. (2) When you score your results, do nothing to correct your answers but carefully mark those answers which are wrong. (3) When you score your results, do nothing to your correct answers but carefully mark those answers which are wrong. (4) When you score your results, do nothing to your correct answers but mark carefully those answers which are wrong. Immediately after presentation of this sentence, all Ss (warned or not) heard the following conclusion to the instructions: To begin the test, please turn to page 2 of the answer booklet and judge which of the sentences printed there occurred in the instructions you just heard. On page 2 they found the critical sentence they had just heard plus a similar alternative. Suppose they had heard sentence 1. They might have to choose between 1 and 2 or between 1 and 3. Both pairs differ in the ordering of two words. However the difference between 1 and 2 does not contribute critically to the meaning of the sentences (mark carefully vs carefully mark) ; the different is just stylistic. On the other hand, sentences 1 and 3 clearly do differ in meaning. Thus, by looking at Ss ability to discriminate between different pairs of sentences, Wanner was able to measure their ability to remember the meaning vs the style of the sentence and to determine how this ability interacted with whether or not they were warned. The relevant data are displayed in the following figure. If the Ss were just guessing, they would have scored 50% correct by chance; thus we would not expect any values below 50% (1) People normally extract the meaning from a linguistic message and do not remember its exact wording. Memory for meaning is equally good whether Ss are warned or not. (2) The warning did have an effect on memory for the stylistic change. Ss were almost at chance in remembering stylistic change when unwarned, but they were fairly good at remembering when warned. B. Memory for visual information Our memory capacity seems much greater for visual information than for verbal information. Picture recognition was compared with sentence recognition. Ss exhibited 11.8% errors in the sentence condition but only 1.5% errors in the picture condition. Standing (1973) showed that Ss could remember 73% of 10,000 pictures. Evidence seems to suggest that Ss are not likely to remember the exact visual details or spatial relations in a picture. Instead, they are remembering some rather abstract representation that captures the pictures meaning. It is useful to distinguish the meaning of a picture and the physical picture. Consider the picture on p.132 of Experimental Psycholinguistics, which appears to be a random collection of ink blobs. The picture seems to have no meaning, and Ss show poor memory for it. However, if you look carefully, you will see a dog hidden in the picture. If people are able to detect the hidden figure in pictures like these, they will show much better memory for the picture. In the following experiment, Ss were asked to study some pictures with or without an explanation of their meaning. Then they were given a memory test in which they had to redraw the pictures. Ss who were given labels showed better recall of these pictures (70%) than those who were not given the labels (51%). It seems that people normally extract and remember the meaning from a picture as they do with sentences. C. Propositional Representations A proposition is the smallest unit of knowledge that can stand as a separate assertion, i.e. the smallest unit about which it make sense to make the judgment true or false. Nixon gave a beautiful Cadillac to Brezhnev, who was leader of the USSRThis sentence is composed from the following sentences:Nixon gave a Cadillac to Brezhnev.The Cadillac was beautiful.Brezhnev was leader of the USSR Each simple sentence expresses a primitive unit of meaning. If any of these simple sentences were false, the complex sentence would not be true.One way of representing the proposition is to give a list containing a relation followed by an ordered list of arguments:Relations correspond to the verbs (e.g. give), adjective (beautiful) or other relational terms (is leader of) in the sentence, while arguments correspond to the nouns. The relations assert connections among the entities referred to by these nouns.1. (Give, Nixon, Cadillac, Brezhnev, Past); Give (Nixon, Cadillac, Brezhnev) 2. (Beautiful, Cadillac); Beautiful (Cadillac)3. (Leader of, Brezhnev, USSR); Leader (Brezhnev, USSR)D. Propositional Network Another way to represent the meaning of the sentence is by means of a propositional network. Beside the basic propositional structure, some other structures are needed to create adequate meaning representations. E.g. 4. Nixon gave Brezhnev a Cadillac. 5. Fred owns a Cadillac. 6. Fred shouted Nixon Freds shouting of Nixon is not the same as the agent in 4, the Cadillac Nixon gave to Brezhnev is not the same as the one that Fred owns. We need to draw a distinction between specific objects and the general classes. This distinction is made in Figure (b), where words and concepts have different nodes. In the network words are written within quotation marks, whereas concepts are represented by words without quotation marks. A link labeled word indicates the connection between the concept and the word. E. Propositional Networks as Associative Structures In the propositional (semantic) networks, ideas are represented by nodes, and associations between ideas by links between nodes. E.g. Children who are slow eat bread that is cold The sentence can be represented as a propositional network: F. Retrieval from Proposi-tional Networks This associative analysis of propositional structures has proven to be very useful in understanding variations in times the subjects take to retrieve information from memory. Collins & Quillian (1969) had Ss judge the truth of assertions about concepts such as the following.1. Robins eat worms. (1310 msec)2. Robins have feathers (1380 msec)3. Robin have skins (1470 msec)4. Apples have feathers.G. Schemas Propositions are fine for re-presenting small units of meaning, but they fail when it comes to repre-senting the large sets of organized information that we know about par-ticular concepts. We have a number of pro-positions about a house. The basic insight is that concepts like house are defined by a configuration of features, and each involves specifying a value the object has on some attribute. Schemas represent the structure of an object according to a slot structure, where slots specify values that the object has on some attributes. The schema representation is the way to capture this basic insight. So we have the following partial schema representation of a house. l l houses have roomsl l houses can be built of woodl l houses have roofsl l houses have wallsl l houses have windowsl l people live in houses House Attribute Value superset: building material: wood, brick contains: rooms function: human dwelling shape: rectilinear size: 500-5000 feet location: on ground It is also possible to represent events as schemas. That is, we can encode our knowledge about stereotype events, such as going to a movie, eating at a restaurant. Scene I: Entering Customer enters restaurant. / Customer looks for table./ Customer decides where to sit. / Customer goes to table. / Customer sits down. Scene II: Ordering Customer picks up menu./ Customer looks at menu./ Customer decides on food./ Customer signals waitress./ Waitress comes to table./ Customer orders food./ Waitress goes to cook./ Waitress gives food order to cook./ Cook prepares food. Scene III Eating Cook gives food to waitress. / Waitress brings food to customer./ Customer eat