# Conditionals in Nonmonotonic Reasoning and Belief Revision: - download pdf or read online

By Gabriele Kern-Isberner

ISBN-10: 3540423672

ISBN-13: 9783540423676

Conditionals are omnipresent, in lifestyle in addition to in medical environments; they symbolize everyday wisdom bought inductively or discovered from books. They tie a versatile and hugely interrelated community of connections alongside which reasoning is feasible and that are utilized to diversified occasions. accordingly, conditionals are vital, but additionally rather troublesome gadgets in wisdom representation.

This publication offers a brand new method of conditionals which captures their dynamic, non-proportional nature quite good through contemplating conditionals as brokers transferring attainable worlds for you to identify relationships and ideology. This figuring out of conditionals yields a wealthy idea which makes advanced interactions among conditionals obvious and operational. Moreover,it presents a unifying and more advantageous framework for wisdom illustration, nonmonotonic reasoning, trust revision,and even for wisdom discovery.

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**Extra resources for Conditionals in Nonmonotonic Reasoning and Belief Revision: Considering Conditionals as Agents**

**Example text**

AGM *2) A ∈ K ∗ A. (AGM *3) K ∗ A ⊆ K + A. (AGM *4) If ¬A ∈ / K then K + A ⊆ K ∗ A. (AGM *5) K ∗ A is inconsistent iff A is contradictory. (AGM *6) If A and B are logically equivalent, then K ∗ A = K ∗ B. (AGM *7) K ∗ A ∧ B ⊆ (K ∗ A) + B. (AGM *8) If ¬B ∈ / K ∗ A then (K ∗ A) + B ⊆ K ∗ A ∧ B. 2 Belief Revision 15 Unlike for expansion, these postulates are not sufficient to describe uniquely one optimal revision operator; they only outline the scope of reasonable belief revision. Katsuno and Mendelzon [KM91a] rephrased the AGM-revision axioms more concisely for propositional logic (where K is supposed to be a single formula, too): (AGM’ *1) K ∗ A implies A.

Let K be a propositional belief set, that is, K ⊆ L is a set of propositions which is closed under classical consequence Cn. Let A be some proposition representing the newly acquired information which K is to be revised by. e. if A does not contradict any of the beliefs in K. This type of revision is called expansion, denoted by +. G¨ ardenfors [G¨ ar88] lists intuitive postulates for an expansion which are apt to characterize expansion uniquely within a classical logical framework: AGM-postulates for expansion: (AGM +1) K + A is a belief set.

It is generalized by the notion of cross-entropy Q(ω) Q(ω) log R(Q, P ) = P (ω) ω∈Ω = ∞ for Q(ω) = 0) between two distri(with 0 log 00 = 0 and Q(ω) log Q(ω) 0 butions Q and P . If P0 denotes the uniform distribution P0 (ω) = 1/m for all worlds ω, then R(Q, P0 ) = −H(Q) + log m relates absolute and relative entropy. Cross-entropy is a well-known information-theoretic measure of dissimilarity between two distributions and has been studied extensively (see, for instance, [Csi75, HHJ92, Jay83a, Kul68]; for a brief, but informative introduction and further references, cf.

### Conditionals in Nonmonotonic Reasoning and Belief Revision: Considering Conditionals as Agents by Gabriele Kern-Isberner

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