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.
This work was partially funded by DFG grant SCHA 550/15 (Germany), Etoiles Montantes CTASP at Region Pays de la Loire (France), Xunta de Galicia grant GPC ED431B 2022/33, and MCIN AEI/10.13039/501100011033 grant PID2020-116201GB-I00 (Spain).
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Notes
- 1.
For simplicity, we admit here a set of atoms in the right part of the semantic consequence operator. By
we mean
, for all \(p \in T\).
we mean
, for all References
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Cabalar, 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_23
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