kLog: A Language for Logical and Relational Learning with Kernels

We introduce kLog, a novel approach to statistical relational learning. Unlike standard approaches, kLog does not represent a probability distribution directly. It is rather a language to perform kernel-based learning on expressive logical and relational representations. kLog allows users to specify learning problems declaratively. It builds on simple but powerful concepts: learning from interpretations, entity/relationship data modeling, logic programming, and deductive databases. Access by the kernel to the rich representation is mediated by a technique we call graphicalization: the relational representation is first transformed into a graph --- in particular, a grounded entity/relationship diagram. Subsequently, a choice of graph kernel defines the feature space. kLog supports mixed numerical and symbolic data, as well as background knowledge in the form of Prolog or Datalog programs as in inductive logic programming systems. The kLog framework can be applied to tackle the same range of tasks that has made statistical relational learning so popular, including classification, regression, multitask learning, and collective classification. We also report about empirical comparisons, showing that kLog can be either more accurate, or much faster at the same level of accuracy, than Tilde and Alchemy. kLog is GPLv3 licensed and is available at http://klog.dinfo.unifi.it along with tutorials

Relational Foundations For Functorial Data Migration

We study the data transformation capabilities associated with schemas that are presented by directed multi-graphs and path equations. Unlike most approaches which treat graph-based schemas as abbreviations for relational schemas, we treat graph-based schemas as categories. A schema $S$ is a finitely-presented category, and the collection of all $S$-instances forms a category, $S$-inst. A functor $F$ between schemas $S$ and $T$, which can be generated from a visual mapping between graphs, induces three adjoint data migration functors, $\Sigma_F:S$-inst$\to T$-inst, $\Pi_F: S$-inst $\to T$-inst, and $\Delta_F:T$-inst $\to S$-inst. We present an algebraic query language FQL based on these functors, prove that FQL is closed under composition, prove that FQL can be implemented with the select-project-product-union relational algebra (SPCU) extended with a key-generation operation, and prove that SPCU can be implemented with FQL

A graph-theoretic account of logics

A graph-theoretic account of logics is explored based on the general notion of m-graph (that is, a graph where each edge can have a finite sequence of nodes as source). Signatures, interpretation structures and deduction systems are seen as m-graphs. After defining a category freely generated by a m-graph, formulas and expressions in general can be seen as morphisms. Moreover, derivations involving rule instantiation are also morphisms. Soundness and completeness theorems are proved. As a consequence of the generality of the approach our results apply to very different logics encompassing, among others, substructural logics as well as logics with nondeterministic semantics, and subsume all logics endowed with an algebraic semantics

A knowledge representation meta-model for rule-based modelling of signalling networks

The study of cellular signalling pathways and their deregulation in disease states, such as cancer, is a large and extremely complex task. Indeed, these systems involve many parts and processes but are studied piecewise and their literatures and data are consequently fragmented, distributed and sometimes--at least apparently--inconsistent. This makes it extremely difficult to build significant explanatory models with the result that effects in these systems that are brought about by many interacting factors are poorly understood. The rule-based approach to modelling has shown some promise for the representation of the highly combinatorial systems typically found in signalling where many of the proteins are composed of multiple binding domains, capable of simultaneous interactions, and/or peptide motifs controlled by post-translational modifications. However, the rule-based approach requires highly detailed information about the precise conditions for each and every interaction which is rarely available from any one single source. Rather, these conditions must be painstakingly inferred and curated, by hand, from information contained in many papers--each of which contains only part of the story. In this paper, we introduce a graph-based meta-model, attuned to the representation of cellular signalling networks, which aims to ease this massive cognitive burden on the rule-based curation process. This meta-model is a generalization of that used by Kappa and BNGL which allows for the flexible representation of knowledge at various levels of granularity. In particular, it allows us to deal with information which has either too little, or too much, detail with respect to the strict rule-based meta-model. Our approach provides a basis for the gradual aggregation of fragmented biological knowledge extracted from the literature into an instance of the meta-model from which we can define an automated translation into executable Kappa programs.Comment: In Proceedings DCM 2015, arXiv:1603.0053