Download e-book for iPad: 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 symbolize wide-spread wisdom got inductively or realized from books. They tie a versatile and hugely interrelated community of connections alongside which reasoning is feasible and which might be utilized to diversified events. hence, conditionals are vital, but additionally really not easy items in wisdom representation.
This e-book offers a brand new method of conditionals which captures their dynamic, non-proportional nature really good by way of contemplating conditionals as brokers moving attainable worlds with a view to identify relationships and ideology. This realizing of conditionals yields a wealthy conception which makes complicated interactions among conditionals obvious and operational. Moreover,it offers 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

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AGM’ *4) If K1 ≡ K2 and A1 ≡ A2 , then K1 ∗ A1 ≡ K2 ∗ A2 . (AGM’ *5) (K ∗ A) ∧ B implies K ∗ (A ∧ B). (AGM’ *6) If (K ∗A)∧B is satisfiable, then K ∗(A∧B) implies (K ∗A)∧B. The third important belief change operation presented in [G¨ ar88] is contraction (operator: −) dealing with the mere deletion of beliefs. AGM-postulates for contraction: (AGM -1) K − A is a belief set. (AGM -2) K − A ⊆ K. (AGM -3) if A ∈ / K then K − A = K (AGM -4) if not A then A ∈ / K − A. (AGM -5) if A ∈ K then K ⊆ (K − A) + A.

Of positive or negated atoms. Complete conjunctions are elementary conjunctions which contain each atom either in positive or negated form. Tautologies and contradictions will be denoted by and ⊥, respectively. e. Ω is a complete set of interpretations of L. Two worlds ω, ω ∈ Ω are called neighbors if they differ with respect to exactly one atom. 1. For a set of worlds {ω1 , ω2 , . } ⊆ Ω, we define form (ω1 , ω2 , . ) ∈ L to be that proposition in L which has ω1 , ω2 , . . as its models: Mod (form (ω1 , ω2 , .

Let A, B be sets of formulas of L∗ , φ be a single formula. A (nonmonotonic) inference operation C is called reflexive if A ⊆ C(A), and idempotent if C(C(A)) = C(A). C is said to satisfy cut if A ⊆ B ⊆ C(A) implies C(B) ⊆ C(A), and fulfills cautious monotonicity if A ⊆ B ⊆ C(A) implies C(A) ⊆ C(B). 1) guaranteeing a convenient stability of inference: Taking already inferred knowledge into account does not change inferences. A cumulative inference operation is assumed to satisfy reflexivity (synonym: inclusion) besides cumulativity.

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