Logic can be divided into three basic types (Exhibit 23) [Curts, 1990b]:
1. Deductive: The process of reasoning in which a conclusion follows necessarily from the stated premise. Inference by reasoning from the general to the specific [Morris, 1976].
2. Inductive: A principle of reasoning to a conclusion about all the members of a class from examination of only a few members of the class. Inference by reasoning from the particular to the general [Morris, 1976].
3. Abductive: A form of deductive logic that provides only a “plausible inference” [Firebaugh, 1988]. The conclusion is possibly, but not nec- essarily, true.
Notice that these three types of logic are ordered by the confidence one can place in the new knowledge inferred from the given data. The assessment of the validity of a hypothesis is inductive in nature. However, the generation of new hypotheses and the determination of evidence relevant to these hypoth- eses involves deductive and abductive reasoning [Sage, 1990]. It is much easier to implement a decision support system on the rules of deduction than to use induction to derive general truths from a database full of particular facts.
Abduction appears to be more difficult by yet another order-of-magnitude.
Deduction
New knowledge based on deductive reasoning is always true if the assump- tions on which it is based are true. One basic rule of deductive inference is modus ponens, if X is true and if X being true implies Y is true, then Y is true:
Rule: All the beans from this bag are white.
Case: These beans are from this bag.
Result: These beans are white.
Induction:
Case: These beans are from this bag.
Result: These beans are white.
Rule: All the beans from this bag are white.
Abduction:
Rule: All the beans from this bag are white.
Result: These beans are white.
Case: These beans are from this bag.
44 Building A Global Information Assurance Program
All women are female.
Sally is a woman.
Therefore, by deduction, Sally is female.
Induction
New knowledge based on the observation of many specific cases (induction) is generally true as long as the systems studied are well-behaved. More formally, for a set of objects, X = {a, b, c, d,…} if property P is true for object a, and if P is true for object b, and if P is true for c, then P is true for all X:
IF 1 = 12
AND IF 1 + 3 = 22 AND IF 1 + 3 + 5 = 32 AND IF 1 + 3 + 5 + 7 = 42
THEN, by induction, Σ(n successive odd integers) = n2
Abduction
The term abduction was first introduced into philosophy and science by the renowned American philosopher Charles Sanders Peirce (1839–1914) to des- ignate a special kind of logical reasoning. In his view, abduction, deduction, and induction are the three fundamental logics of scientific inquiry [Peirce, 1934, 1955]. The Encyclopedia Britannica describes abduction as “reasoning that derives an explanatory hypothesis from a given set of facts.” Though loose and informal, this definition captures the basic meaning of the term.
Abduction makes its start from the facts. Induction makes its start from a hypothesis. Abduction seeks a theory. Induction seeks for facts. Abduction is, after all, nothing more than guessing. Abductive inference shades into perceptual judgment without any sharp line of demarcation between them.
Charles Sanders Peirce The first starting of a hypothesis and the entertaining of it, whether as a sample interrogation or with any degree of confidence, is an inferential step called abduction (sometimes called retroduction). Abductive inference shades into perceptual judgment without any sharp line of demarcation between them. Abduction is a heuristic for making plausible inferences. It is heuristic in the sense that it provides a plausible conclusion consistent with available information, but one which may, in fact, be wrong. Formally, if Y is true and X implies Y, then X is true [Peirce 1934, 1955]:
All successful entrepreneurs are rich.
Sally is rich.
Therefore, by abduction, Sally is a successful entrepreneur.
attributed to Sherlock Holmes by Sir Arthur Conan Doyle:
You know my method. It is founded on the observation of trifles.
Deduction versus Abduction
Human diagnostic reasoning differs from the deductive inference methods used in most existing decision support systems in that it is an abductive logic, which is considered to be a nonmonotonic logic. There are at least three differences that distinguish deduction and abduction [Peng, 1986]:
1. The relationships among entities are categorical implications in deduc- tion. They may be nondefinitive or probabilistic in abduction.
2. In deduction, the hypothetical statement to be proven is given. In abduction, hypotheses first have to be constructed during the inference process before they are “proven” or accepted.
3. In deduction, any inference chain leading to the proof of the theorem is acceptable. In abduction, however, a disambiguation process chooses from among all hypotheses those which are most plausible according to some criteria. Disambiguation is a complex process involving not only the use of associative knowledge, but also some meta-level criteria which are often global and context-sensitive. Empirical studies of human cognitive psychology have shown, and most researchers agree, that disambiguation in abductive inference is based on a repetitive hypoth- esize-and-test process [Peng, 1986].
Summary
In this chapter, we have covered a number of topics associated with infor- mation and information processing as a foundation on which to build. The rest of this book will consider methods to design and build information systems and to protect those systems and the information residing therein.
This page intentionally left blank
47