By Christian Straßer
This booklet offers adaptive logics as an intuitive and strong framework for modeling defeasible reasoning. It examines a variety of contexts during which defeasible reasoning turns out to be useful and gives a compact advent into adaptive logics.
The writer first familiarizes readers with defeasible reasoning, the adaptive logics framework, combos of adaptive logics, and various necessary meta-theoretic homes. He then deals a scientific learn of adaptive logics according to a number of purposes.
The ebook offers formal types for defeasible reasoning stemming from assorted contexts, similar to default reasoning, argumentation, and normative reasoning. It highlights numerous meta-theoretic merits of adaptive logics over different logics or logical frameworks that version defeasible reasoning. during this manner the publication substantiates the prestige of adaptive logics as a regular formal framework for defeasible reasoning.
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Extra resources for Adaptive Logics for Defeasible Reasoning: Applications in Argumentation, Normative Reasoning and Default Reasoning
Take for instance our premise ◦n. Since the premises give no reason for supposing ¬n (we will make this formally precise in a moment) the semantic selection corresponding to the reasoning of our detective neglects models M4 , M5 and M6 since these models validate the abnormality ◦n ∧ ¬n. This can be made more precise by introducing another central notion for ALs: minimal Dab-consequences. Where Δ ⊆ Ω is a finite and non-empty set of abnormalities, adaptive logicians use Dab(Δ) as a notation for the classical disjunction of memˇ Dab(Δ)’ denotes the empty string.
Since the retraction mechanism is fully determined by the analysis of the given premise set this is clearly an instance of the internal dynamics of defeasible reasoning. As pointed out already, the external dynamics is mirrored by the nonmonotonicity of the consequence relation: sometimes new information may lead to the situation in which some formula that was previously a consequence is not anymore a consequence as soon as the new information is considered. I already discussed that the primary focus in the research on defeasible reasoning is on the external rather than the internal dynamics.
Since we want to keep things simple we treat ◦ as a dummy operator and hence don’t attach any logical properties to ◦. As a lower limit logic we employ classical propositional logic CL equipped with ◦. 4 The semantics of CL◦ is like the semantics for CL, just besides the usual assignment function v that assigns to each propositional letter a truth value, we also use an enhanced assignment function v◦ that (independently from v) associates each well-formed formula with a truth-value. Truth in a model M is defined as usual for the classical operators: 4 In  we show that CL◦ gives rise to very simple ALs that represent the Rescher-Manor consequence relations .
Adaptive Logics for Defeasible Reasoning: Applications in Argumentation, Normative Reasoning and Default Reasoning by Christian Straßer