Grounded Fixpoints
Authors: Bart Bogaerts, Joost Vennekens, Marc Denecker
AAAI 2015 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | Algebraical fixpoint theory is an invaluable instrument for studying semantics of logics. For example, all major semantics of logic programming, autoepistemic logic, default logic and more recently, abstract argumentation have been shown to be induced by the different types of fixpoints defined in approximation fixpoint theory (AFT). In this paper, we add a new type of fixpoint to AFT: a grounded fixpoint of lattice operator O : L L is defined as a lattice element x L such that O(x) = x and for all v L such that O(v x) v, it holds that x v. On the algebraical level, we show that all grounded fixpoints are minimal fixpoints approximated by the well-founded fixpoint and that all stable fixpoints are grounded. On the logical level, grounded fixpoints provide a new mathematically simple and compact type of semantics for any logic with a (possibly non-monotone) semantic operator. We explain the intuition underlying this semantics in the context of logic programming by pointing out that grounded fixpoints of the immediate consequence operator are interpretations that have no non-trivial unfounded sets. We also analyse the complexity of the induced semantics. |
| Researcher Affiliation | Academia | Bart Bogaerts Department of Computer Science KU Leuven 3001 Heverlee, Belgium bart.bogaerts@cs.kuleuven.be Joost Vennekens Department of Computer Science Campus De Nayer, KU Leuven 2860 Sint-Katelijne-Waver, Belgium joost.vennekens@cs.kuleuven.be Marc Denecker Department of Computer Science KU Leuven 3001 Heverlee, Belgium marc.denecker@cs.kuleuven.be |
| Pseudocode | No | The paper does not contain structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not provide concrete access to source code for the methodology described. It is a theoretical paper. |
| Open Datasets | No | The paper does not mention any datasets used for training or empirical evaluation, as it is a theoretical paper. |
| Dataset Splits | No | The paper does not provide specific dataset split information, as it is a theoretical paper without empirical experiments. |
| Hardware Specification | No | The paper does not provide specific hardware details, as it is a theoretical paper without empirical experiments. |
| Software Dependencies | No | The paper does not provide specific ancillary software details, as it is a theoretical paper without empirical experiments. |
| Experiment Setup | No | The paper does not contain specific experimental setup details, as it is a theoretical paper without empirical experiments. |