Ground Nonmonotonic Modal Logic S5: New Results
| Autor: | José R. Arrazola Ramírez, Mauricio Osorio Galindo, Verónica Borja Macías, Juan Antonio Navarro Pérez |
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| Rok vydání: | 2005 |
| Předmět: |
Theoretical computer science
Logic Computer science Normal modal logic Classical logic Multimodal logic Modal logic Intermediate logic Theoretical Computer Science Algebra TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES Arts and Humanities (miscellaneous) Hardware and Architecture Many-valued logic Dynamic logic (modal logic) Autoepistemic logic Software |
| Zdroj: | Journal of Logic and Computation. 15:787-813 |
| ISSN: | 1465-363X 0955-792X |
| DOI: | 10.1093/logcom/exi042 |
| Popis: | We study logic programs under Gelfond's translation in the context of modal logic S5. We show that for arbitrary logic programs (propositional theories where logic negation is associated with default negation) ground nonmonotonic modal logics between T and S5 are equivalent. Furthermore, we also show that these logics are equivalent to a nonmonotonic logic that we construct using the well known F O U R bilattice. We will call this semantic GNM-S5 as a reminder of its origin in the logic S5. Finally we show that, for normal programs, our approach is closely related to theWell-Founded-by-Cases Semantics introduced by Schlipf and the WFS+ proposed by Dix. We prove that GNM-S5 has the properties of classicality and extended cut. While WFS+ also supports classicality it fails to satisfy the extended cut principle, an important property available in other semantics such as stable models. Hence, we claim that GNM-S5 is a good candidate for defining a nonmonotonic semantics closer to the direction of classical logic. |
| Databáze: | OpenAIRE |
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