Abstract. In Datalog, missing values are represented by Skolem constants. More generally, in logic programming missing values, or existentially quantified variables, are represented by terms built from Skolem functors. The CLP(BN) language represents the joint probability distribution over missing values in a database or logic program by using constraints to represent Skolem functions. Algorithms from inductive logic programming (ILP) can be used with only minor modification to learn CLP(BN) programs. An implementation of CLP(BN) is publicly available as part of YAP Prolog at

Cost-Based Abduction (CBA) is an AI model for reasoning under uncertainty. In CBA, evidence to be explained is treated as a goal which is true and must be proven. Each proof of the goal is viewed as a feasible explanation and has a cost equal to the sum of the costs of all hypotheses that are assumed to complete the proof. The aim is to find the Least Cost Proof. This paper uses CBA to develop a novel method for modeling Genetic Regulatory Networks (GRN) and explaining genetic knock-out effects. Constructing GRN using multiple data sources is a fundamental problem in computational biology. We show that CBA is a powerful formalism for modeling GRN that can easily and effectively integrate multiple sources of biological data. In this paper, we use three different biological data sources: Protein-DNA, Protein–Protein and gene knock-out data. Using this data, we first create an un-annotated graph; CBA then annotates the graph by assigning a sign and a direction to each edge. Our biological results are promising; however, this manuscript focuses on the mathematical modeling of the application. The advantages of CBA and its relation to Bayesian inference are also presented. 1

Gene products are key players in the interaction networks within a cell. We analyze an experiment in which a yeast knockout library was assayed for the effects of host gene deletion on the replication of Brome Mosaic Virus (BMV). These observations, integrated with the partially known yeast interaction network, may be used to infer which host processes and gene products are involved in the mechanism of BMV’s replication. We approach this task using Inductive and Abductive Logic Programming (ILP and ALP). We use ALP to abduce causal explanations for each observation, including possible host interfaces with BMV. Some notable aspects of our task that differ from previous work using abduction in systems biology include a highly incomplete background model and a large number of observations to explain. Additionally, we expect that there are many interfaces between the host cell and the virus, and that each abduced interface will serve to explain a handful of observations. We determine that ILP is unable to identify general, informative models that characterize host-virus interactions accurately. Using ALP, however, we are able to construct causal explanations that link multiple observations to the same host interface.

To Mom, for making this dream possible, Ian, for supporting and sharing it and Lillian for making it all worthwhile. ii In this era where healthcare is one of the world’s largest and fastest growing industries, there is great interest in understanding what is happening within our cells and organs at the molecular level. Fortunately, innovations and improvements in technology continue to spur the quantity and types of high-throughput (a process where large amounts of samples can be measured by a system at once) biological data that can be measured. Additionally, abundant information from many years of detailed research can be found in annotated or computationally extracted databases. These data sets, especially combined, have great potential for novel discoveries that can lead to advances in biology and medicine. The main focus of this thesis is the investigation of machine learning techniques for inferring gene regulatory networks from the combination of high-throughput time series gene expression array data and other data sources. A gene regulatory network is a collection