# Learning Dynamics with Synchronous, Asynchronous and General Semantics

## Abstract

Learning from interpretation transition *(LFIT)* automatically constructs a model of the dynamics of a system from the observation of its state transitions. So far, the systems that *LFIT* handles are restricted to synchronous deterministic dynamics, i.e., all variables update their values at the same time and, for each state of the system, there is only one possible next state. However, other dynamics exist in the field of logical modeling, in particular the asynchronous semantics which is widely used to model biological systems. In this paper, we focus on a method that learns the dynamics of the system independently of its semantics. For this purpose, we propose a modeling of multi-valued systems as logic programs in which a rule represents *what can occur rather than what will occur*. This modeling allows us to represent non-determinism and to propose an extension of *LFIT* in the form of a semantics free algorithm to learn from discrete multi-valued transitions, regardless of their update schemes. We show through theoretical results that synchronous, asynchronous and general semantics are all captured by this method. Practical evaluation is performed on randomly generated systems and benchmarks from biological literature to study the scalability of this new algorithm regarding the three aforementioned semantics.

## Keywords

Dynamical semantics Learning from interpretation transition Dynamical systems Inductive logic programming## References

- 1.Blair, H.A., Subrahmanian, V.: Paraconsistent foundations for logic programming. J. Non-classical Logic
**5**(2), 45–73 (1988)MathSciNetzbMATHGoogle Scholar - 2.Blair, H.A., Subrahmanian, V.: Paraconsistent logic programming. Theor. Comput. Sci.
**68**(2), 135–154 (1989)MathSciNetCrossRefGoogle Scholar - 3.Chatain, T., Haar, S., Paulevé, L.: Boolean networks: beyond generalized asynchronicity. In: Baetens, J.M., Kutrib, M. (eds.) AUTOMATA 2018. LNCS, vol. 10875, pp. 29–42. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-92675-9_3CrossRefGoogle Scholar
- 4.Dubrova, E., Teslenko, M.: A SAT-based algorithm for finding attractors in synchronous boolean networks. IEEE/ACM Trans. Comput. Biol. Bioinform. (TCBB)
**8**(5), 1393–1399 (2011)CrossRefGoogle Scholar - 5.Fitting, M.: Bilattices and the semantics of logic programming. J. Logic Program.
**11**(2), 91–116 (1991)MathSciNetCrossRefGoogle Scholar - 6.Garg, A., Di Cara, A., Xenarios, I., Mendoza, L., De Micheli, G.: Synchronous versus asynchronous modeling of gene regulatory networks. Bioinformatics
**24**(17), 1917–1925 (2008)CrossRefGoogle Scholar - 7.Ginsberg, M.L.: Multivalued logics: a uniform approach to reasoning in artificial intelligence. Comput. Intell.
**4**(3), 265–316 (1988)CrossRefGoogle Scholar - 8.Inoue, K.: Logic programming for Boolean networks. In: IJCAI Proceedings-International Joint Conference on Artificial Intelligence, vol. 22, p. 924 (2011)Google Scholar
- 9.Inoue, K., Ribeiro, T., Sakama, C.: Learning from interpretation transition. Mach. Learn.
**94**(1), 51–79 (2014)MathSciNetCrossRefGoogle Scholar - 10.Kifer, M., Subrahmanian, V.: Theory of generalized annotated logic programming and its applications. J. Logic Programm.
**12**(4), 335–367 (1992)MathSciNetCrossRefGoogle Scholar - 11.Martınez, D., Alenya, G., Torras, C., Ribeiro, T., Inoue, K.: Learning relational dynamics of stochastic domains for planning. In: Proceedings of the 26th International Conference on Automated Planning and Scheduling (2016)Google Scholar
- 12.Martínez, D.M., Ribeiro, T., Inoue, K., Ribas, G.A., Torras, C.: Learning probabilistic action models from interpretation transitions. In: Proceedings of the Technical Communications of the 31st International Conference on Logic Programming (ICLP 2015), pp. 1–14 (2015)Google Scholar
- 13.Ribeiro, T., Inoue, K.: Learning prime implicant conditions from interpretation transition. In: Davis, J., Ramon, J. (eds.) ILP 2014. LNCS (LNAI), vol. 9046, pp. 108–125. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-23708-4_8CrossRefGoogle Scholar
- 14.Ribeiro, T., Magnin, M., Inoue, K., Sakama, C.: Learning delayed influences of biological systems. Front. Bioeng. Biotechnol.
**2**, 81 (2015)CrossRefGoogle Scholar - 15.Ribeiro, T., Magnin, M., Inoue, K., Sakama, C.: Learning multi-valued biological models with delayed influence from time-series observations. In: 2015 IEEE 14th International Conference on Machine Learning and Applications (ICMLA), pp. 25–31, December 2015Google Scholar
- 16.Ribeiro, T., et al.: Inductive learning from state transitions over continuous domains. In: Lachiche, N., Vrain, C. (eds.) ILP 2017. LNCS (LNAI), vol. 10759, pp. 124–139. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78090-0_9CrossRefGoogle Scholar
- 17.Van Emden, M.H.: Quantitative deduction and its fixpoint theory. J. Logic Program.
**3**(1), 37–53 (1986)MathSciNetCrossRefGoogle Scholar