# On Axiomatic Rejection for the Description Logic ALC

@inproceedings{Berger2013OnAR, title={On Axiomatic Rejection for the Description Logic ALC}, author={Gerald Berger and Hans Tompits}, booktitle={KDPD}, year={2013} }

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…

## 3 Citations

Sequent-Type Calculi for Three-Valued and Disjunctive Default Logic

- Computer ScienceAxioms
- 2020

This paper introduces sequent-type calculi for two variants of default logic, viz., for three-valued default logic due to Radzikowska, and on the other hand, for disjunctive default Logic, due to Gelfond, Lifschitz, Przymusinski, and Truszczynski, which are introduced to address certain representational shortcomings of standard default logic.

Sequent-Type Proof Systems for Three-Valued Default Logic

- Computer ScienceArXiv
- 2019

This master's thesis introduces sequent-type calculi for a variant of default logic employing Lukasiewicz's three-valued logic as the underlying base logic, addressing some representational shortcomings of standard default logic.

Refutation Systems: An Overview and Some Applications to Philosophical Logics

- Philosophy
- 2020

An overview with comprehensive references on the historical development of the theory of refutation systems is provided and some of their applications to philosophical logics are discussed.

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