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A notion of inconsistency between instantiations and variables is introduced, and is shown to be a useful tool for characterizing such well-known concepts as backtrack, backjump, and domain annihilation.
We are referring to this operator as a revision operator, but this is not a true revision operator in the sense of the AGM revision theory because there is no clear notion of "inconsistency" for sets of actions.
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A key concept in our framework is the notion of an inconsistency budget, which characterises how much inconsistency we are prepared to tolerate: given an inconsistency budget β, we would be prepared to disregard attacks up to a total weight of β.
That is the notion of logical inconsistency.
In Gabbay 1988, the notion of negation of inconsistency is introduced by requiring that the negation $*A$ of $A$ is derivable from a set of premises $\Delta$ iff there is an unwanted formula $U$ that is derivable from $\Delta \cup \{A\}$.
This notion of negation as inconsistency is reasonable if implication is taken to be primitive and not itself defined in terms of negation and disjunction (or negation and conjunction).
There are two ways that the laws of deductive logic have been thought to provide rational constraints on belief: (1) Synchronically, the laws of deductive logic can be used to define the notion of deductive consistency and inconsistency.
We then introduce a new notion of acceptable IMCMs, considering both inconsistency and indeterminacy levels in IMCMs.
One way to make this aim explicit is to extend the expressive power of our language by encoding the metatheoretical notions of consistency (and inconsistency) in the object language.
The theological notion of a host can dissolve the inconsistency.
In conclusion, if some supertasks are paradoxical, it is not because of any inherent inconsistency of the notion of supertask.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.
Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com