Cabalar, PedroDiéguez Lodeiro, MartínLaferrière, FrançoisSchaub, TorstenStéphan, Igor2025-05-222025Cabalar, P., Diéguez, M., Laferrière, F., Schaub, T., Stéphan, I. (2025). A Fixpoint Characterisation of Temporal Equilibrium Logic. In: Dodaro, C., Gupta, G., Martinez, M.V. (eds) Logic Programming and Nonmonotonic Reasoning. LPNMR 2024. Lecture Notes in Computer Science(), vol 15245. Springer, Cham. https://doi.org/10.1007/978-3-031-74209-5_2397830317420881611-33490302-9743http://hdl.handle.net/2183/42066Presented in the following conference: LPNMR 2024: 17th International Conference on Logic Programming and Nonmonotonic Reasoning, Dallas, TX, USA, October 11–14, 2024This version of the conference paper has been accepted for publication, after peer review; it is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/978-3-031-74209-5_23.[Abstract]: Connections of intuitionistic and intermediate logics with logic programming have been extensively studied in the literature. Among the different results in the literature we find equilibrium logic (Pearce, 1996) and Safe beliefs (Osorio et al., 2005). Pearce’s approach admits a characterisation in terms of a fixpoint (consequence) operator on the here-and-there intermediate logic (Heyting, 1930), which is similar to the notion of theory completion in default and autoepistemic logics. Osorio’s safe beliefs are also given in terms of a fixpoint operator under intuitionistic logic semantics. In this latter case, intuitionistic logic can be replaced by any intermediate logic without altering the result. In this paper we consider temporal equilibrium logic, an combination of equilibrium logic and linear-time temporal logic. In this context we extend Pearce’s and Osorio’s approach to temporal case and we discuss the relation of intuitionistic temporal logic and temporal logic programming.eng© 2025 The Author(s), under exclusive license to Springer Nature Switzerland AG. This version is subject to Springer Nature’s AM terms of use - https://www.springernature.com/gp/open-research/policies/accepted-manuscript-termsLogic programmingTemporal logicComputer circuitsconference outputopen access10.1007/978-3-031-74209-5_23