REASONING AS EXTENDED RETRIEVAL
7.2 BEYOND EXACT RETRIEVAL
7.2.1 SOME FORMS OF NON-EXACT RETRIEVAL
The various kinds of retrieval systems discussed in the last two chapters can be characterized as exact retrieval, because the answers produced in these systems are either previously stored (in the cases of database and information retrieval) or derived on demand based on what was stored (in the case of knowledge retrieval). However, there are many situations where retrieval should be handled in a more flexible manner. If there is no exact match to a user's query, an approximate answer may be better than no answer at all. In addition, as we will see soon, non-exact, or approximate answers may have some other interesting aspects which exact retrieval may not possesses. The tricky thing here is that the word "approximate" may have different meanings. In the remaining part of this section, we provide several examples to illustrate what the non-exact retrieval means and what the advantages are.
We start with fuzzy queries in databases. Fuzzy set theory will be discussed in later chapters, and here we just want to raise questions instead of solving them. Roughly speaking, fuzzy set theory has been developed to deal with vagueness. A fuzzy query interface to a relational database allows giving fuzzy terms as values for the attributes, which are not stored in the relational database. An example of such a query is to retrieve company names which have made large profit in the first quarter of 1999. In this query, "large profit" is a fuzzy concept, because profits are usually stored in numerical numbers. Another approach in fuzzy information retrieval is to build fuzzy databases. There are several different approaches toward creating fuzzy databases, such as:
(a) The fuzzy database as an extension to a relational database. (b) Possibility-distribution relational databases.
(c) Modular fuzzy databases, which consists of three parts: (1) the value database which is same as (b); (2) the explanation database, which contains the definition of the fuzzy terms, and is subject to update depending on the particular applications; and (3) conversion rules for processing modifiers and qualifiers. There are many other forms of non-exact retrieval, and some of them involve the use of analogical reasoning. Analogical reasoning is pervasive in human reasoning. Briefly, analogical reasoning assumes that if two situations are known to be similar in some respects, it is likely that they will be similar in others. So if two brands of CD boom boxes have the same quality and are made in places with cheap labor, you may expect they should have similar price. Analogical reasoning has been studied extensively by computer scientists for many years. For example, the Copycat project (by Douglas Hofstadter and his research group [Hofstadter 1995]) is a computer program intended to be able to discover insightful analogies in a psychologically realistic manner. This research is a continuation of Hofstadter's original research goals set up during the late 1970's, namely, to uncover the secrets of creativity, and to uncover the secrets of consciousness, by modeling both phenomena on a computer.
Analogical reasoning can play an interesting role in non-exact retrieval, and here is a simple example. Suppose a relational database has information for average housing prices for a number of selected cities in the United States. Now a user wants to know the average housing price in Omaha but it is not available. A retrieval system with analogical reasoning ability may suggest the user try, say, Lincoln or Wichita. Here is why: Lincoln is close to Omaha and is in the same state of Nebraska, so their property values should be similar. And why Wichita? Because just like Omaha, it is also located in the heartland of the country, and it has the similar size of Omaha. Analogical reasoning is also useful in text mining, where analogy is used for guiding meta-data search [Soto 1998]. As a real-world example, according to CBS Morning Business Report (Jan. 18, 1999), Robert Morrow has 37 patterns for solving vibration problems in engineering. He has utilized his expertise to predict vibration in market with great success.
Due to the importance of analogical reasoning for approximate retrieval, in the next subsection we provide a brief discussion on analogical reasoning.
7.2.2 BASICS OF ANALOGICAL REASONING
According to the popular computational model of analogy [Gentner 1983], the two analogs involved in analogical reasoning are referred to as the source and the target. The source of an analogy is a problem solution, example, or theory that is relatively well understood. The target is only partly known. Analogy constructs a mapping between corresponding elements of the target and the source. Analogical inferences extend this mapping to unknown or missing elements of the target. Note that the source and the target are usually in different knowledge domains. For example, consider the "electricity is like water" analogy. Here "water" is the source, which is in the domain, say, of hydrodynamics; and "electricity" is the target, which is in the domain, say, of electrodynamics. Since electricity was a new concept in the 19th century, the knowledge of water and hydrodynamics had greatly helped human beings to understand this new concept. For example, if we know that this analogy maps switches onto valves, amperage onto quantity of flow, and voltage onto water pressure, we may reasonably infer that there should be some thing similar to the capacity (i.e., the cross-sectional area) of a water pipe; this could lead to an understanding of electrical resistance [Luger and Stubblefield, 1998].
We will get back to the issue of relationship between retrieval and reasoning, and discuss the role of analogical reasoning in this exploration. But before we leave, we give a brief remark on two related reasoning or learning approaches.
1) Case-based reasoning. In order to solve problems or answer questions using analogical reasoning, one important issue is how to effectively and efficiently retrieve source analogs. Case-based reasoning (CBR) is closely related to analogical reasoning (and can be used in combination with analogical reasoning) because it employs an explicit knowledge of problem solutions (referred to as cases) to address new problem-solving situations. Therefore, CBR provides an effective way to retrieve solutions of previously solved problems, and to adapt this solution to the current problem by mapping the old solution to a new one. For more detail of CBR, please see [Kolodner 1993].
2) Explanation-based learning. Analogical reasoning can be considered as a species of single instance induction. In contrast, explanation-based learning (EBL) also performs learning based on a training example, but uses deductive method. EBL uses an explicitly represented domain theory to construct an explanation of a training example, usually a proof that the example logically follows from the theory. By generalizing from the explanation of the instance, rather than from the instance itself, EBL organizes training data into a systematic and coherent structure.