The process of developing theories and models and testing them with experiments is fundamental to the scientific method. Automating the entire scientific method then requires not only automation of the induction of theories from data, but also experimentation from design to implementation. This is the idea behind a robot scientist -- a coupled system of AI and laboratory robotics that has agency to test hypotheses with real-world experiments. In this chapter we explore some of the fundamentals of robot scientists in the philosophy of science. We also map the activities of a robot scientist to machine learning paradigms, and argue that the scientific method shares an analogy with active learning. We demonstrate these concepts using examples from previous robot scientists, and also from Genesis: a next generation robot scientist designed for research in systems biology, comprising a micro-fluidic system with 1000 computer-controlled micro-bioreactors and interpretable models based in controlled vocabularies and logic.

SMLP: Symbolic Machine Learning Prover an open source tool for exploration and optimization of systems represented by machine learning models. SMLP uses symbolic reasoning for ML model exploration and optimization under verification and stability constraints, based on SMT, constraint and NN solvers. In addition its exploration methods are guided by probabilistic and statistical methods. SMLP is a general purpose tool that requires only data suitable for ML modelling in the csv format (usually samples of the system's input/output). SMLP has been applied at Intel for analyzing and optimizing hardware designs at the analog level. Currently SMLP supports NNs, polynomial and tree models, and uses SMT solvers for reasoning and optimization at the backend, integration of specialized NN solvers is in progress.

Symbolic Machine Learning Prover (SMLP) is a tool and a library for system exploration based on data samples obtained by simulating or executing the system on a number of input vectors. SMLP aims at exploring the system based on this data by taking a grey-box approach: SMLP combines statistical methods of data exploration with building and exploring machine learning models in close feedback loop with the system's response, and exploring these models by combining probabilistic and formal methods. SMLP has been applied in industrial setting at Intel for analyzing and optimizing hardware designs at the analog level. SMLP is a general purpose tool and can be applied to systems that can be sampled and modeled by machine learning models.

We present the problem of selecting relevant premises for a proof of a given statement. When stated as a binary classification task for pairs (conjecture, axiom), it can be efficiently solved using artificial neural networks. The key difference between our advance to solve this problem and previous approaches is the use of just functional signatures of premises. To further improve the performance of the model, we use dimensionality reduction technique, to replace long and sparse signature vectors with their compact and dense embedded versions. These are obtained by firstly defining the concept of a context for each functor symbol, and then training a simple neural network to predict the distribution of other functor symbols in the context of this functor. After training the network, the output of its hidden layer is used to construct a lower dimensional embedding of a functional signature (for each premise) with a distributed representation of features. This allows us to use 512-dimensional embeddings for conjecture-axiom pairs, containing enough information about the original statements to reach the accuracy of 76.45% in premise selection task, only with simple two-layer densely connected neural networks.