Learning possibilistic dynamic systems from state transitions

Learning from 1-step transitions (LF1T) has become a paradigm to construct a logical hypothesis of a dynamic system, such as a Boolean network, from its synchronized state transitions and background knowledge. While uncertain and incomplete information plays an important role in dynamic systems, LF1T and its successors cannot handle uncertainty modeled by possibility theory. This motivates our combination of inductive logic programming (ILP) and possibilistic normal logic program (poss-NLP) that applies to reasoning about uncertain dynamic systems. In this paper, we propose a learning task to learn a poss-NLP from given interpretation transitions and background knowledge. The sufficient and necessary condition for the existence of its solution is determined. We introduce an algorithm called iltp to learn a specific solution, which typically encompasses mass redundant rules. Additionally, we propose another algorithm called sp-iltp to identify global minimal solutions. Alongside theoretical correctness proofs, a synthetic experiment demonstrates the learning performance on six gene regulatory networks with possibilistic uncertainty. This work thus offers a rational framework for learning the dynamics of systems under uncertainty via poss-NLPs.