Artificial Intelligence

A Logical Theory of Nonmonotonic Inference and Belief Change by Alexander Bochman

By Alexander Bochman

This is often the 1st e-book that integrates nonmonotonic reasoning and trust turn out to be a unmarried framework from a synthetic intelligence good judgment point-of-view. The method of either those matters is predicated on a strong inspiration of an epistemic kingdom that subsumes either present versions for nonmonotonic inference and present types for trust switch. Many effects and structures within the ebook are thoroughly new and feature now not seemed prior within the literature.

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Additional resources for A Logical Theory of Nonmonotonic Inference and Belief Change (Artificial Intelligence)

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And though language is the only tool we posses for describing our epistemic states, taking into account such a possibility may sometimes influence the conclusions we make. Infinite states and smoothness. , human) epistemic states. Accordingly, they are generated through a reasoning process that results in forming admissible combinations of defaults. In many cases such epistemic states will be finite. The following definition describes two important understandings of finiteness of epistemic states that will be used in what follows.

Moreover, by compactness, P,PI, ... ,Pn If- Cd, for some natural n. Consequently, for any k 2: n, at least one Cd from Cd must be a logical consequence of Bk. Since Cd does not have positive occurrences of p's, it must contain qk. Therefore, for any k 2: n, at least one disjunction from Cd must contain a positive atom qk. But this is impossible due to the finiteness of Cd. Thus, u is a theory ofthis consequence relation. Moreover, assume that there is another theory Uo such that P E Uo C u, and let Pi be an atomic proposition that does not belong to uo.

Proof. Follows from the fact that a set of theories is right-compact iff it includes the set of small theories. 1. A consequence relation is strongly grounded if and only if all its theories are unions of prime theories. Let us denote by P lfo the set of prime propositions of a consequence relation If-. Then the following consequence of the above result shows that any theory of a strongly grounded consequence relation is a deductive closure of the prime propositions included in it. 2. If a consequence relation If- is strongly grounded, then any theory u of If- is equal to Thlfo(u n Plfo).

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