An abductive-inductive algorithm for probabilistic inductive logic programming

The integration of abduction and induction has lead to a variety of non-monotonic ILP systems. XHAIL is one of these systems, in which abduction is used to compute hypotheses that subsume Kernel Sets. On the other hand, Peircebayes is a recently proposed logic-based probabilistic programming approach that combines abduction with parameter learning to learn distributions of most likely explanations. In this paper, we propose an approach for integrating probabilistic inference with ILP. The basic idea is to redefine the inductive task of XHAIL as a statistical abduction, and to use Peircebayes to learn probability distribution of hypotheses. An initial evaluation of the proposed algorithm is given using synthetic data

Learning Rules from User Behaviour

Accepted versio

Logic Programs as Declarative and Procedural Bias in Inductive Logic Programming

Machine Learning is necessary for the development of Artificial Intelligence, as pointed out by Turing in his 1950 article ``Computing Machinery and Intelligence''. It is in the same article that Turing suggested the use of computational logic and background knowledge for learning. This thesis follows a logic-based machine learning approach called Inductive Logic Programming (ILP), which is advantageous over other machine learning approaches in terms of relational learning and utilising background knowledge. ILP uses logic programs as a uniform representation for hypothesis, background knowledge and examples, but its declarative bias is usually encoded using metalogical statements. This thesis advocates the use of logic programs to represent declarative and procedural bias, which results in a framework of single-language representation. We show in this thesis that using a logic program called the top theory as declarative bias leads to a sound and complete multi-clause learning system MC-TopLog. It overcomes the entailment-incompleteness of Progol, thus outperforms Progol in terms of predictive accuracies on learning grammars and strategies for playing Nim game. MC-TopLog has been applied to two real-world applications funded by Syngenta, which is an agriculture company. A higher-order extension on top theories results in meta-interpreters, which allow the introduction of new predicate symbols. Thus the resulting ILP system Metagol can do predicate invention, which is an intrinsically higher-order logic operation. Metagol also leverages the procedural semantic of Prolog to encode procedural bias, so that it can outperform both its ASP version and ILP systems without an equivalent procedural bias in terms of efficiency and accuracy. This is demonstrated by the experiments on learning Regular, Context-free and Natural grammars. Metagol is also applied to non-grammar learning tasks involving recursion and predicate invention, such as learning a definition of staircases and robot strategy learning. Both MC-TopLog and Metagol are based on a $\top$-directed framework, which is different from other multi-clause learning systems based on Inverse Entailment, such as CF-Induction, XHAIL and IMPARO. Compared to another $\top$-directed multi-clause learning system TAL, Metagol allows the explicit form of higher-order assumption to be encoded in the form of meta-rules.Open Acces

Probabilistic abductive logic programming using Dirichlet priors

Probabilistic programming is an area of research that aims to develop general inference algorithms for probabilistic models expressed as probabilistic programs whose execution corresponds to inferring the parameters of those models. In this paper, we introduce a probabilistic programming language (PPL) based on abductive logic programming for performing inference in probabilistic models involving categorical distributions with Dirichlet priors. We encode these models as abductive logic programs enriched with probabilistic definitions and queries, and show how to execute and compile them to boolean formulas. Using the latter, we perform generalized inference using one of two proposed Markov Chain Monte Carlo (MCMC) sampling algorithms: an adaptation of uncollapsed Gibbs sampling from related work and a novel collapsed Gibbs sampling (CGS). We show that CGS converges faster than the uncollapsed version on a latent Dirichlet allocation (LDA) task using synthetic data. On similar data, we compare our PPL with LDA-specific algorithms and other PPLs. We find that all methods, except one, perform similarly and that the more expressive the PPL, the slower it is. We illustrate applications of our PPL on real data in two variants of LDA models (Seed and Cluster LDA), and in the repeated insertion model (RIM). In the latter, our PPL yields similar conclusions to inference with EM for Mallows models

Neurons and symbols: a manifesto

We discuss the purpose of neural-symbolic integration including its principles, mechanisms and applications. We outline a cognitive computational model for neural-symbolic integration, position the model in the broader context of multi-agent systems, machine learning and automated reasoning, and list some of the challenges for the area of neural-symbolic computation to achieve the promise of effective integration of robust learning and expressive reasoning under uncertainty

Abductive knowledge induction from raw data

For many reasoning-heavy tasks with raw inputs, it is challenging to design an appropriate end-to-end pipeline to formulate the problem-solving process. Some modern AI systems, e.g., Neuro-Symbolic Learning, divide the pipeline into sub-symbolic perception and symbolic reasoning, trying to utilise data-driven machine learning and knowledge-driven problem-solving simultaneously. However, these systems suffer from the exponential computational complexity caused by the interface between the two components, where the sub-symbolic learning model lacks direct supervision, and the symbolic model lacks accurate input facts. Hence, they usually focus on learning the sub-symbolic model with a complete symbolic knowledge base while avoiding a crucial problem: where does the knowledge come from? In this paper, we present Abductive Meta-Interpretive Learning (MetaAbd) that unites abduction and induction to learn neural networks and logic theories jointly from raw data. Experimental results demonstrate that MetaAbd not only outperforms the compared systems in predictive accuracy and data efficiency but also induces logic programs that can be re-used as background knowledge in subsequent learning tasks. To the best of our knowledge, MetaAbd is the first system that can jointly learn neural networks from scratch and induce recursive first-order logic theories with predicate invention