A {PDL} Approach for Qualitative Velocity
Abstract
We introduce the syntax, semantics, and an axiom system for a PDL-based extension of the logic for order of magnitude qualitative reasoning, developed in order to deal with the concept of qualitative velocity, which together with qualitative distance and orientation, are important notions in order to represent spatial reasoning for moving objects, such as robots. The main advantages of using a PDL-based approach are, on the one hand, all the well-known advantages of using logic in AI, and, on the other hand, the possibility of constructing complex relations from simpler ones, the flexibility for using different levels of granularity, its possible extension by adding other spatial components, and the use of a language close to programming languages.
Citation
Please, cite this work as:
[BMO11] A. Burrieza, E. Mu~noz-Velasco, and M. Ojeda-Aciego. “A PDL Approach for Qualitative Velocity”. In: Int. J. Uncertain. Fuzziness Knowl. Based Syst. 19.1 (2011), pp. 11-26. DOI: 10.1142/S021848851100685X. URL: https://doi.org/10.1142/S021848851100685X.
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Papers citing this work
The following is a non-exhaustive list of papers that cite this work:
[1] A. Burrieza, E. Muñoz-Velasco, and M. Ojeda-Aciego. “A Hybrid Approach to Closeness in the Framework of Order of Magnitude Qualitative Reasoning”. In: Hybrid Artificial Intelligent Systems. Springer International Publishing, 2016, p. 721–729. ISBN: 9783319320342. DOI: 10.1007/978-3-319-32034-2_60. URL: http://dx.doi.org/10.1007/978-3-319-32034-2_60.
[2] A. Burrieza, E. Muñoz-Velasco, and M. Ojeda-Aciego. “Logics for Order-of-Magnitude Qualitative Reasoning: Formalizing Negligibility”. In: Ewa Orłowska on Relational Methods in Logic and Computer Science. Springer International Publishing, 2018, p. 203–231. ISBN: 9783319978796. DOI: 10.1007/978-3-319-97879-6_8. URL: http://dx.doi.org/10.1007/978-3-319-97879-6_8.
[3] Q. Cohen-Solal. “Tractable Fragments of Temporal Sequences of Topological Information”. In: Principles and Practice of Constraint Programming. Springer International Publishing, 2020, p. 107–125. ISBN: 9783030584757. DOI: 10.1007/978-3-030-58475-7_7. URL: http://dx.doi.org/10.1007/978-3-030-58475-7_7.
[4] J. Goli ska-Pilarek and E. Munoz-Velasco. “A hybrid qualitative approach for relative movements”. In: Logic Journal of IGPL 23.3 (Apr. 2015), p. 410–420. ISSN: 1368-9894. DOI: 10.1093/jigpal/jzv012. URL: http://dx.doi.org/10.1093/jigpal/jzv012.
[5] J. Golińska-Pilarek and E. Muñoz-Velasco. “Reasoning with Qualitative Velocity: Towards a Hybrid Approach”. In: Hybrid Artificial Intelligent Systems. Springer Berlin Heidelberg, 2012, p. 635–646. ISBN: 9783642289422. DOI: 10.1007/978-3-642-28942-2_57. URL: http://dx.doi.org/10.1007/978-3-642-28942-2_57.
[6] E. Muñoz-Velasco, A. Burrieza, and M. Ojeda-Aciego. “A logic framework for reasoning with movement based on fuzzy qualitative representation”. In: Fuzzy Sets and Systems 242 (May. 2014), p. 114–131. ISSN: 0165-0114. DOI: 10.1016/j.fss.2013.07.014. URL: http://dx.doi.org/10.1016/j.fss.2013.07.014.
[7] M. Sioutis, J. Condotta, Y. Salhi, et al. “A Qualitative Spatio-Temporal Framework Based on Point Algebra”. In: Artificial Intelligence: Methodology, Systems, and Applications. Springer International Publishing, 2014, p. 117–128. ISBN: 9783319105543. DOI: 10.1007/978-3-319-10554-3_11. URL: http://dx.doi.org/10.1007/978-3-319-10554-3_11.
[8] P. A. Wałȩga. Reasoning for Moving Blocks Problem: Formal Representation and Implementation. 2013. DOI: 10.48550/ARXIV.1307.7405. URL: https://arxiv.org/abs/1307.7405.