Logic-based machine learning using a bounded hypothesis space: the lattice structure, refinement operators and a genetic algorithm approach

Rich representation inherited from computational logic makes logic-based machine learning a competent method for application domains involving relational background knowledge and structured data. There is however a trade-off between the expressive power of the representation and the computational costs. Inductive Logic Programming (ILP) systems employ different kind of biases and heuristics to cope with the complexity of the search, which otherwise is intractable. Searching the hypothesis space bounded below by a bottom clause is the basis of several state-of-the-art ILP systems (e.g. Progol and Aleph). However, the structure of the search space and the properties of the refinement operators for theses systems have not been previously characterised. The contributions of this thesis can be summarised as follows: (i) characterising the properties, structure and morphisms of bounded subsumption lattice (ii) analysis of bounded refinement operators and stochastic refinement and (iii) implementation and empirical evaluation of stochastic search algorithms and in particular a Genetic Algorithm (GA) approach for bounded subsumption. In this thesis we introduce the concept of bounded subsumption and study the lattice and cover structure of bounded subsumption. We show the morphisms between the lattice of bounded subsumption, an atomic lattice and the lattice of partitions. We also show that ideal refinement operators exist for bounded subsumption and that, by contrast with general subsumption, efficient least and minimal generalisation operators can be designed for bounded subsumption. In this thesis we also show how refinement operators can be adapted for a stochastic search and give an analysis of refinement operators within the framework of stochastic refinement search. We also discuss genetic search for learning first-order clauses and describe a framework for genetic and stochastic refinement search for bounded subsumption. on. Finally, ILP algorithms and implementations which are based on this framework are described and evaluated.Open Acces

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

Inductive logic programming at 30: a new introduction

Inductive logic programming (ILP) is a form of machine learning. The goal of ILP is to induce a hypothesis (a set of logical rules) that generalises training examples. As ILP turns 30, we provide a new introduction to the field. We introduce the necessary logical notation and the main learning settings; describe the building blocks of an ILP system; compare several systems on several dimensions; describe four systems (Aleph, TILDE, ASPAL, and Metagol); highlight key application areas; and, finally, summarise current limitations and directions for future research.Comment: Paper under revie

Automated Deduction – CADE 28

This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions

Superposition for Lambda-Free Higher-Order Logic

We introduce refutationally complete superposition calculi for intentional and extensional clausal $\lambda$-free higher-order logic, two formalisms that allow partial application and applied variables. The calculi are parameterized by a term order that need not be fully monotonic, making it possible to employ the $\lambda$-free higher-order lexicographic path and Knuth-Bendix orders. We implemented the calculi in the Zipperposition prover and evaluated them on Isabelle/HOL and TPTP benchmarks. They appear promising as a stepping stone towards complete, highly efficient automatic theorem provers for full higher-order logic

Efficient Learning and Evaluation of Complex Concepts in Inductive Logic Programming

Inductive Logic Programming (ILP) is a subfield of Machine Learning with foundations in logic programming. In ILP, logic programming, a subset of first-order logic, is used as a uniform representation language for the problem specification and induced theories. ILP has been successfully applied to many real-world problems, especially in the biological domain (e.g. drug design, protein structure prediction), where relational information is of particular importance. The expressiveness of logic programs grants flexibility in specifying the learning task and understandability to the induced theories. However, this flexibility comes at a high computational cost, constraining the applicability of ILP systems. Constructing and evaluating complex concepts remain two of the main issues that prevent ILP systems from tackling many learning problems. These learning problems are interesting both from a research perspective, as they raise the standards for ILP systems, and from an application perspective, where these target concepts naturally occur in many real-world applications. Such complex concepts cannot be constructed or evaluated by parallelizing existing top-down ILP systems or improving the underlying Prolog engine. Novel search strategies and cover algorithms are needed. The main focus of this thesis is on how to efficiently construct and evaluate complex hypotheses in an ILP setting. In order to construct such hypotheses we investigate two approaches. The first, the Top Directed Hypothesis Derivation framework, implemented in the ILP system TopLog, involves the use of a top theory to constrain the hypothesis space. In the second approach we revisit the bottom-up search strategy of Golem, lifting its restriction on determinate clauses which had rendered Golem inapplicable to many key areas. These developments led to the bottom-up ILP system ProGolem. A challenge that arises with a bottom-up approach is the coverage computation of long, non-determinate, clauses. Prolog’s SLD-resolution is no longer adequate. We developed a new, Prolog-based, theta-subsumption engine which is significantly more efficient than SLD-resolution in computing the coverage of such complex clauses. We provide evidence that ProGolem achieves the goal of learning complex concepts by presenting a protein-hexose binding prediction application. The theory ProGolem induced has a statistically significant better predictive accuracy than that of other learners. More importantly, the biological insights ProGolem’s theory provided were judged by domain experts to be relevant and, in some cases, novel

Inductive logic programming as satisfiability modulo theories

At the intersection of machine learning, program synthesis and automated reasoning lies the field of Inductive Logic Programming (ILP). The aim of ILP is to automatically learn relational programs from input/output examples, typically through logic-based techniques. Inspired by Karl Popper’s falsification perspective on science, this dissertation sets out a new approach to ILP: Learning From Failures (LFF). In science, starting from a huge set of a priori viable hypotheses, we select a hypothesis to test. This hypothesis typically gets falsified due to failing in some specific way. By examining the failure we learn that an entire space of related hypotheses is now ruled out. Having thus reduced our set of viable hypotheses, we subsequently select from just those that remain. LFF applies this methodology to program induction, codifying it as a three-stage loop. The generate stage maintains a formula whose satisfying assignments correspond to the set of viable hypotheses. The test stage takes a satisfying assignment, interprets it as a logic program and tests it against training examples – imperfect fit is considered a failure. The constrain stage turns a failure into constraints to add to the generate stage’s formula, thereby eliminating a class of hypotheses which will fail for the same reason. The thesis of this dissertation is three-fold. The first claim is that LFF frames the ILP problem as one of Satisfiability Modulo Theories (SMT). With the search for viable hypotheses handed-off to a SAT-solver, the test stage can be regarded as a theory solver collaborating with the SAT-solver, effectively making ILP’s notion of background knowledge into a (Horn) background theory. The second claim is that LFF’s three-stage loop is an effective basis for falsification-based program induction. Chapter 4 develops the above correspondence into a feature-rich and flexible three-stage ILP system. Experimental evidence is provided for this system going beyond the state-of-the-art in ILP, e.g., by supporting large hypothesis spaces and large domains. The third claim is that the LFF-as-SMT-perspective helps apply satisfiability solving techniques to ILP, in particular to reduce hypothesis space exploration. In Chapter 5, we show that SMT-based techniques for explaining conflicts have a natural analog in terms of explaining which parts of a hypothesis are responsible for its failure. In Chapter 6, we incorporate other theory solvers alongside the test stage to reason about the (satisfiability of) over-approximating properties of hypotheses. We show that both of these techniques can significantly reduce the number of iterations of the three-stage loop

A workbench to develop ILP systems

Tese de mestrado integrado. Engenharia Informática e Computação. Faculdade de Engenharia. Universidade do Porto. 201