By Christian Straßer
This e-book provides adaptive logics as an intuitive and strong framework for modeling defeasible reasoning. It examines a variety of contexts during which defeasible reasoning comes in handy and provides a compact creation into adaptive logics.
The writer first familiarizes readers with defeasible reasoning, the adaptive logics framework, mixtures of adaptive logics, and quite a number valuable meta-theoretic houses. He then deals a scientific research of adaptive logics in response to quite a few functions.
The ebook offers formal versions for defeasible reasoning stemming from assorted contexts, corresponding to default reasoning, argumentation, and normative reasoning. It highlights numerous meta-theoretic benefits of adaptive logics over different logics or logical frameworks that version defeasible reasoning. during this method the booklet substantiates the prestige of adaptive logics as a time-honored formal framework for defeasible reasoning.
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Extra info for Adaptive Logics for Defeasible Reasoning: Applications in Argumentation, Normative Reasoning and Default Reasoning
12 The next theorem shows that each minimally abnormal model validates a minimal choice set as its abnormal part and vice versa, for each minimal choice set ϕ there is a minimally abnormal model that validates ϕ as its abnormal part. 6. Where Γ ⊆ W + and MLLL (Γ ) is non-empty. 11 A binary relation ≺ ⊆ X × X is smooth (resp. stoppered) iff for every a ∈ X , either a is minimal or there is a ≺-minimal b ∈ X for which b ≺ a. The smoothness property will also play an important role when the standard format is generalized in Chap.
15 which A is derived on the condition Δ iff Γ LLL A ∨ The lemma gives immediately rise to the following rule: A Δ ˇ Dab(Δ) ∅ A∨ (RA) We now discuss the second conflict type: conflicts between defeasible inferences. Again, a look at the derived rule RD helps us to understand how ALs handle such a conflict. It expresses that whenever we have a conflict between two claims, one derived on the condition Δ on line l and another one derived on the condition Δ on line l , then we can derive (unconditionally) that one of the abnormalities in Δ ∪ Δ is true.
2 Conditional inference A A defeasible ¬( A ∧ ¬A ) assumption: 7 In order to reduce notational clutter I will often omit set brackets on the left hand side of . 4 The Adaptive Strategy 19 For the reliability strategy this is spelled out as follows: deriving A “on the condition Δ” means that A is derived on the condition that no member of Δ is unreliable. n 4, 5, 6; RU ∅ The first thing to notice is that, although for our applications we are interested in the adaptive consequence relation over the language L that characterizes our lower limit logic, the adaptive proofs are formulated in the enriched language L+ .
Adaptive Logics for Defeasible Reasoning: Applications in Argumentation, Normative Reasoning and Default Reasoning by Christian Straßer