Abstract
The stable-model semantics has been generalised from logic programs to arbitrary theories. We explore a further generalisation and consider sequences of atoms as models instead of sets. The language is extended by suitable order operators to access this additional information. We recently introduced an extension of classical logic by a single order operator with a temporal interpretation for activity reasoning. The logic envisaged here is a nonmonotonic version thereof. Our definition of what we call stable-ordered models is based on the stable-model semantics for theories due to Ferraris and Lifschitz with the necessary changes. Compared to related nonmonotonic versions of temporal logics, our approach is less costly as checking model existence remains at the second level of the polynomial hierarchy. We demonstrate versatile applications from activity reasoning, combinatorial testing, debugging concurrent programs, and digital forensics.
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Notes
- 1.
Note that \({\circ }\) was not part of the initial version of the logic to avoid unintended effects when used under the open-world assumption [16]. Also, note that we do not consider strong negation.
- 2.
Although this result was formulated for \(\mathcal {L}\) without \({\circ }\), it is applicable for \(\mathcal {L}\) mutatis mutandis.
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Oetsch, J., Nieves, JC. (2019). Stable-Ordered Models for Propositional Theories with Order Operators. In: Calimeri, F., Leone, N., Manna, M. (eds) Logics in Artificial Intelligence. JELIA 2019. Lecture Notes in Computer Science(), vol 11468. Springer, Cham. https://doi.org/10.1007/978-3-030-19570-0_51
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