Conditionals in Nonmonotonic Reasoning and Belief Revision: by Gabriele Kern-Isberner

By Gabriele Kern-Isberner

Conditionals are omnipresent, in way of life in addition to in clinical environments; they characterize common wisdom got inductively or discovered from books. They tie a versatile and hugely interrelated community of connections alongside which reasoning is feasible and which are utilized to various occasions. for this reason, conditionals are very important, but in addition really challenging gadgets in wisdom representation.
This booklet provides a brand new method of conditionals which captures their dynamic, non-proportional nature rather good via contemplating conditionals as brokers transferring attainable worlds in an effort to determine relationships and ideology. This realizing of conditionals yields a wealthy thought which makes complicated 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 info for Conditionals in Nonmonotonic Reasoning and Belief Revision: Considering Conditionals as Agents (Lecture Notes in Computer Science)

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Means classical logical equivalence, that is A ≡ B iff Mod (A) = Mod (B). L is extended to a conditional language (L | L) by introducing a conditional operator |: (L | L) = {(B|A) | A, B ∈ L} A is called the antecedent or the premise of (B|A), and B is the consequence of the conditional (B|A). (L | L) is taken to include L by identifying a proposition A with the conditional (A| ). 2 Probabilistic Logics The atoms in L may be looked upon as (binary) propositional variables, and possible worlds or complete conjuntions, respectively, correspond to elementary events.

The entropy P (ω) log P (ω) H(P ) = − ω∈Ω (with the convention 0 log 0 = 0) of a distribution P first appeared as a physical quantity in statistical mechanics and was later interpreted by Shannon as an information-theoretic measure of the uncertainty inherent to P (see [SW76]; for a historical review, cf. [Jay83a]). 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.

Then a revised probability function, P , taking into account the new information while obviously being related to the prior P is given by Jeffrey’s rule: 24 2. 12) for all propositions B ∈ L. Note that for x = 1, we obtain Bayesian conditioning. e. 12) satisfies P (B|A) = P (B|A) and P (B|¬A) = P (B|¬A) for all B ∈ L. So, many years before nonmonotonic reasoning and belief revision became important topics in Artificial Intelligence, not only had the issue of belief change been addressed in probability theory, but also the necessity of conditional preservation when revising epistemic states had been perceived.

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