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Knowledge Representation
Published in Jay Liebowitz, The Handbook of Applied Expert Systems, 2019
Default logic: Default logic is a method for treating nonmonotonic problems. The basic idea is a distinction between general “hard” rules (facts) and their defaults, i.e., those rules which extend the world of the fact by exemptions and irregularities. (All birds fly but penguins do not) The method is similar to circumscription, the main difference is the theoretically well-formed idea of circumscription’s minimal set, related to the fixed point theorems. A weakness of default logic is the arbitrary and occasional nature of the default rules. They cannot be inferred within the system, they can be used for further inference with much caution, and they can yield trivial contradictions.
Certain knowledge representation
Published in Richard E. Neapolitan, Xia Jiang, Artificial Intelligence, 2018
Richard E. Neapolitan, Xia Jiang
Default logic derives conclusions if they are consistent with the current state of the knowledge base. A typical rule in default logic is as follows: bird(x):flies(x)flies(x) $$ \frac{{{\text{bird}}(x):{\text{flies}}(x)}}{{{\text{flies}}(x)}} $$
Sequent-type rejection systems for finite-valued non-deterministic logics
Published in Journal of Applied Non-Classical Logics, 2023
Rejection systems are particularly useful to build proof systems for non-monotonic reasoning. In particular, Bonatti and Olivetti (2002) pioneered the use of rejection systems for building sequent-style axiomatisations for the main non-monotonic reasoning formalisms, viz. for default logic (Reiter, 1980), autoepistemic logic (Moore, 1985), and circumscription (McCarthy, 1980). More recently, following the method of Bonatti and Olivetti (2002), Geibinger and Tompits (2020) introduced a general method for building sequent-style calculi for various non-monotonic paraconsistent logics based on minimal entailment over finite-valued logics, including the well-known approaches by Priest (1991) and by Arieli and Avron (1998). Similar systems can also be realised, e.g. for the approaches due to Besnard and Schaub (1997).