Constrained Consequence

Logica Universalis 5 (2):327-350 (2011)

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Abstract
There are various contexts in which it is not pertinent to generate and attend to all the classical consequences of a given premiss—or to trace all the premisses which classically entail a given consequence. Such contexts may involve limited resources of an agent or inferential engine, contextual relevance or irrelevance of certain consequences or premisses, modelling everyday human reasoning, the search for plausible abduced hypotheses or potential causes, etc. In this paper we propose and explicate one formal framework for a whole spectrum of consequence relations, flexible enough to be tailored for choices from a variety of contexts. We do so by investigating semantic constraints on classical entailment which give rise to a family of infra-classical logics with appealing properties. More specifically, our infra-classical reasoning demands (beyond ${\alpha\models\beta}$ ) that Mod(β) does not run wild, but lies within the scope (whatever that may mean in some specific context) of Mod(α), and which can be described by a sentence ${\bullet\alpha}$ with ${\beta\models\bullet\alpha}$ . Besides being infra-classical, the resulting logic is also non-monotonic and allows for non-trivial reasoning in the presence of inconsistencies
Keywords Constrained consequences  weakening operator  infra-classical entailment  non-monotonic reasoning  modal logic  action  causality  abduction  diagnosis  paradoxes
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DOI 10.1007/s11787-011-0037-2
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References found in this work BETA

Modal Logic.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2002 - Cambridge University Press.
Modal Logic: An Introduction.Brian F. Chellas - 1980 - Cambridge University Press.
How We Reason.Philip Johnson-Laird - 2006 - Oxford University Press.
Modal Logic.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2001 - Studia Logica 76 (1):142-148.

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