Neural Symbolic Learning Systems: Neural Networks for Normative Reasoning

1 Introduction This thesis aims to study how to relate a symbolic representation of normative systems in Input/Output logic (I/O) with the computational model of Neural Networks. We will be using a Neural-Symbolic paradigm, a Neural-Symbolic Learning System to be more precise, that combines two different reasoning approaches: using the symbolic approach to represent the knowledge base and embedding it within a connectionist reasoning approach. To do this we relied on the methodology discussed in [2], using this methodology we managed to tackle some significant limitations of I/O logic. I/O logic is a powerful tool to specify normative systems but lacks of important features such as learning capacity and scalability. These properties are pivotal for modeling complex, dynamic and distributed entities such as normative systems. The problem that we want to tackle originates from the normative reasoning field where some of the knowledge needed to obtain the correct solution is not always explicit. We can take for instance a legislative environment where the judicial court formulates trials by following the normative code. The problem relies in the fact that when the judge formulates his trials, he also relies on the tacit part of the law that is not explicitly represented. This tacit part of the law is due to social conducts, previous trials made from other judges and other factors that makes the normative code alone insufficient to formulate a correct trial. We can use I/O logic to formalize the normative code, but it will not be suf- ficient to produce the trials like a real judge would have, to address this problem we should train the ”normative code” in order to make it learn the tacit part of the law but due to the symbolic nature of I/O logic presents certain limits re- garding the learning capacity, like the knowledge acquisition bottleneck discussed in [9]. Such limits are related to the expert systems which consist in the problem relative to the formalization of the knowledge base and the new rules that result from machine learning due to the symbolic knowledge representation. Moreover, the reasoning mechanism designed for I/O lacks of scalability w.r.t the number of rules that represent a normative code. 4