On Axiomatic Rejection for the Description Logic ALC

  title={On Axiomatic Rejection for the Description Logic ALC},
  author={Gerald Berger and Hans Tompits},
Traditional proof calculi are mainly studied for formalising the notion of valid inference, i.e., they axiomatise the valid sentences of a logic. In contrast, the notion of invalid inference received less attention. Logical calculi which axiomatise invalid sentences are commonly referred to as complementary calculi or rejection systems. Such calculi provide a proof-theoretic account for deriving non-theorems from other non-theorems and are applied, in particular, for specifying proof systems… 
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