Reasoning and Problem Solving

Erwin Segal

Semantic Memory

    The basic idea behind Chapter 9 is that each of us knows a lot. This knowledge must be represented in our minds somehow. It is probably organized in some meaningful way. There are experimental methods by which we can gain insight into the structure of memory. For this class, we can think of this as background information on how we may solve simple problems such as answering questions based on this knowledge.

    Chapter 7 presents evidence that different mental tasks take time, and there are ways to try to find an algorithm that can do the tasks. It's implicit assumption is that each component of an algorithm takes time to perform. If the algorithm for Task B has more sequential components in it than the one for Task A; especially if the other components of the algorithm are the same, it should take longer to do. Chapter 9 adds to this analysis the idea that the information about the world in our memories is structured in some meaningful way. Reasoning on this memory depends on making explicit, relations among these components that are not directly expressed. It takes time to operate on the relations that we have in order to generate the ones that we need. These operations are often logical inferences based on the network of relations which are explicitly represented.

    If we are given certain simple problems to solve which depend on memory, the time to solve them should reflect the  structure. Perhaps we can gain some insight into the structure of memory by these tasks. Conceptual analysis and experimental research based on the times to do some of these tasks have been used to generate theories both about the structure of memory and about the process of memory search.

  1. Let us consider the words canary, robin, penguin, and piano. As speakers of English we know many things about canary. We know that it refers to a kind of bird. We know that the thing it refers to is often yellow, has wings, has a heart, and is warm-blooded. We know that canaries fly, sing, and lay eggs. We know that a robin is a kind of bird, is warm-blooded, has a red breast, flies, has a heart, eats worms and lays eggs. We know that a penguin is a kind of bird, is warm-blooded, swims, eats fish, and lays eggs. We know that the kind of object piano refers to, is quite different from all of these.
  2. How do we represent the knowledge that we all have about words? An important idea that is shared by many cognitive psychologists and other cognitive scientists is that concepts which are related meaningfully with one another are linked in some kind of a network. Each concept can be considered a 'node' and the relation between them an arc.
  3. There are many redundancies, and we know of many relationships among different concepts. Does that mean that words with similar meanings are in some sense share parts of their meaning representation? By what process or algorithm do we identify appropriate relationships? In order to demonstrate our knowledge, either directly by answering questions about it, or indirectly, by using the meaningful information appropriately, we must have access to and be able to operate on the right information.
  4. #1, #2, and #3 lead us to consider how lexical information is structured in memory and what the processes are that we use to interrogate that memory. We certainly feel that some of the things that we know about these concepts we did not learn directly, but we could figure it out.  From a reasoning or problem solving, or computational perspective, we have to be able to identify some procedure (recursive process) which can effectively do the task.
  5. Lexical items are of various sorts. The parts of speech in grammar help somewhat, but does not designate all of the differences that seem to exist. Content words such as nouns, verbs, and adjectives function differently from function words like prepositions, pronouns, and conjunctions. Each of these categories have words which function differently from one another. I am particularly interested in the fact that some nouns are Basic Level words. Examples in urban American English are chair, wall, tree, dog. These seem to have a special status, probably due to their means of acquisition. They tend to be learned directly from examples. Other level words, such as Furniture, animal, and German Shepherd, probably are learned as abstractions or subcategories of previously learned basic category words.
  6. Many researchers use some variant of a semantic network to represent the lexicon in memory. Basically this model has the lexical entries connected to one another by labeled links or edges. These links identify the kind of relation that exists between the items connected with one another.
  7. Answers are derived by traversing the network to find them. Some inferences that may be made are defeasible, which allows for normal or usual inferences to proceed. This works by including the concept of default reasoning which can be overruled by specific information.
  8. SNePS a semantic network system developed in Buffalo by S. Shapiro and his colleagues minimizes the kinds of links by making the links themselves accessible to the processor. In semantic network systems there are effective procedures designed to make explicit these links.
  • Some issues:
  • Cognitive economy versus processing efficiency. Performance in solving problems using semantic networks is a function of both the structured relations among the items and the processing mechanisms that use the data in the network. It would be more economical (less memory devoted to the concept) to store the fact that birds fly with the concept "bird", but it would be more efficient to go directly to the fact that canaries fly, rather than have to derive it. It's faster to agree that 'a canary is yellow', than 'a canary flies' which is faster than 'a canary has skin', but one can quickly agree that a canary. See diagrams on semantic nets

  • Decisions about properties which are used often in that context are quick, as if they are directly encoded, but decisions about properties which are used only infrequently take longer, and seem to be derived.
  • What kinds of links are there? Some things are subclasses of other things, some are instances of others, some are subparts, some are positions, some are labels, some are locations, etc. Aristotle knew of this problem, and it has not been totally solved.
  • Why do the same arcs have different response latencies? Category members do not all function equivalently. It is faster to agree that 'a robin is a bird' than that 'a chicken is a bird'. The closer in meaning two terms are, the faster you can categorize the member.
  • Some links, which logically should be closer, take more time than those further away. It is faster to respond that a lion is an animal, than that a lion is a mammal. Frequency of use is a strong variable in reaction time studies.

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    Some additional data:

    Subjects can identify a word as a word faster, if they are first presented with another word that is similar in meaning to it. The first word is the 'prime' and the second is the target'. If the word is unrelated, it does not decrease the identification time. In a 'lexical decision task' subjects are to decide whether a letter string is a word or not. This seems to work for question answering also. These data suggest that words which are related to one another are tied together in some way; perhaps stored near each other in the brain, or are linked such that when one is activated it activates similar items.