Download Abduction and Induction: Essays on their Relation and by Peter A. Flach, Antonis C. Kakas (auth.), Peter A. Flach, PDF

By Peter A. Flach, Antonis C. Kakas (auth.), Peter A. Flach, Antonis C. Kakas (eds.)

From the very starting in their research of human reasoning, philosophers have pointed out different kinds of reasoning, in addition to deduction, which we now name abduction and induction. Deduction is now particularly good understood, yet abduction and induction have eluded an analogous point of knowing. The papers gathered the following tackle the connection among abduction and induction and their attainable integration. The method is usually philosophical, occasionally that of natural good judgment, and a few papers undertake the extra task-oriented strategy of AI.
The ebook will command the eye of philosophers, logicians, AI researchers and machine scientists in general.

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Extra info for Abduction and Induction: Essays on their Relation and Integration

Example text

The hypothesis H changes T by requiring extra conditions on the observable predicates that drive the induction, unlike abduction where the extra conditions do not involve the observable predicates. In effect, H provides the link between observables and non-observables that was missing or incomplete in the original theory T. Analogously to the concept of abductive extension, we can define inductive extensions as follows. Consider a common given theory T with which we are able to perform abduction and induction.

Hence, while in abduction we select an abductive extension of T, with induction we extend each of the abductive extensions with H. The effect of induction is thus 'universal' on all the abductive extensions. If we now consider the new abductive theory T' = T U H, constructed by induction, we can view induction as a process of selecting a collection of abductive extensions, namely those of the new theory T'. Hence an inductive extension can be viewed as a set ofabductive extensions of the original theory T that are further (uniformly) conditioned by the common statement of the inductive hypothesis H .

First, it will be convenient to introduce some further terminology. Observables and abducibles. We will assume a common first-order language for all knowledge (known, observed, or hypothetical). We assume that the predicates of this language are separated into observables and non-observables or background predicates. Domain knowledge or background knowledge is a general theory concerning non-observable predicates only. Foreground knowledge is a general theory relating observable predicates to background predicates and each other.

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