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Republished Jan 16 2009, from a an old tutorial article. Will be expanded and revised in coming months. Also see InterWiki on Logical Reasoning.

Note that while much of the following may seen dry and 'ho-hum', it is actually very controversial in its use of fuzzy, everyday notions about logic rather than exact and exacting mathematical formulations. What's the matter, haven't they heard of faith-based mathematics ? ;-)

The Ubiquity of Logical Inference

All people utilize some form of conceptual model to make inferences about in their everyday lives - buying things, crossing the street, solving a problems at work, preparing dinner. Logical inferences set conceptual frameworks in motion. Assuming that the conceptual model is accurate, inferences allow us to make useful decisions and sensible plans of action in the real world.

Yet how many people have actually examined the the way they go about using logical inference ? The answer is very few.

The term 'logical inference' may conjure up an image of crusty academics furiously splitting hairs over the obvious, perhaps with some justification. But sometimes what seems obvious is not all that obvious. It's a result of the difference between logic and language. Logic is precise and everyday language is imprecise. People like the fuzziness of language - it can bestow deep significance upon common things ( like toothpaste or soap ) or allow us to give answers which sound meaningful but are utterly devoid of meaning, as the situation requires. There is a warm and fuzzy feeling about everyday language because it works for us in ways that logic does not.

The Fuzziness of Everyday Language

Language is riddled with fuzzy logic that helps to describe the fuzziness of human situations and experiences. However, communicating with machines requires a logical type of language, one with sufficient precision to accomplish useful tasks in a predictable way. To speak the language of rules, one must master the rigors of basic logic. This requirement is frequently underplayed by companies selling business rule tools and methodologies. They tend to paint a picture of a brave new world where business people rather than programmers encode business logic for transaction processing systems. While the business rules approach shifts the focus from arcane computer languages to a more natural way of expressing business logic, that does not free business people from having to understand how logic works, quite the contrary.

Logical Boot Camp

The next few sections are a sort of 'logical boot camp', perhaps reviving memories of a sleepy afternoon in a high school or college math course many years ago. After reviewing the basics of logic, the following sections discuss the three mode of logical nference.