Deciphering the functioning of biological networks is one of the central tasks in systems biology. In particular, signal transduction networks are crucial for the understanding of the cellular response to external and internal perturbations. Importantly, in order to cope with the complexity of these networks, mathematical and computational modeling is required. We propose a computational modeling framework in order to achieve more robust discoveries in the context of logical signaling networks. More precisely, we focus on modeling the response of logical signaling networks by means of automated reasoning using Answer Set Programming (ASP). ASP provides a declarative language for modeling various knowledge representation and reasoning problems. Moreover, available ASP solvers provide several reasoning modes for assessing the multitude of answer sets. Therefore, leveraging its rich modeling language and its highly efficient solving capacities, we use ASP to address three challenging problems in the context of logical signaling networks: learning of (Boolean) logical networks, experimental design, and identification of intervention strategies. Overall, the contribution of this thesis is three-fold. Firstly, we introduce a mathematical framework for characterizing and reasoning on the response of logical signaling networks. Secondly, we contribute to a growing list of successful applications of ASP in systems biology. Thirdly, we present a software providing a complete pipeline for automated reasoning on the response of logical signaling networks.