Inductive Logic Programming as Abductive Search

We present a novel approach to non-monotonic ILP and its implementation called TAL (Top-directed Abductive Learning). TAL overcomes some of the completeness problems of ILP systems based on Inverse Entailment and is the first top-down ILP system that allows background theories and hypotheses to be normal logic programs. The approach relies on mapping an ILP problem into an equivalent ALP one. This enables the use of established ALP proof procedures and the specification of richer language bias with integrity constraints. The mapping provides a principled search space for an ILP problem, over which an abductive search is used to compute inductive solutions

Learning with con gurable operators and RL-based heuristics

In this paper, we push forward the idea of machine learning systems for which the operators can be modi ed and netuned for each problem. This allows us to propose a learning paradigm where users can write (or adapt) their operators, according to the problem, data representation and the way the information should be navigated. To achieve this goal, data instances, background knowledge, rules, programs and operators are all written in the same functional language, Erlang. Since changing operators a ect how the search space needs to be explored, heuristics are learnt as a result of a decision process based on reinforcement learning where each action is de ned as a choice of operator and rule. As a result, the architecture can be seen as a `system for writing machine learning systems' or to explore new operators.This work was supported by the MEC projects CONSOLIDER-INGENIO 26706 and TIN 2010-21062-C02-02, GVA project PROMETEO/2008/051, and the REFRAME project granted by the European Coordinated Research on Long-term Challenges in Information and Communication Sciences & Technologies ERA-Net (CHIST-ERA), and funded by the Ministerio de Econom´ıa y Competitividad in Spain. Also, F. Mart´ınez-Plumed is supported by FPI-ME grant BES-2011-045099Martínez Plumed, F.; Ferri Ramírez, C.; Hernández Orallo, J.; Ramírez Quintana, MJ. (2013). Learning with con gurable operators and RL-based heuristics. En New Frontiers in Mining Complex Patterns. Springer Verlag (Germany). 7765:1-16. https://doi.org/10.1007/978-3-642-37382-4_1S1167765Armstrong, J.: A history of erlang. In: Proceedings of the Third ACM SIGPLAN Conf. on History of Programming Languages, HOPL III, pp. 1–26. 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A globalisation of the Gelfand duality theorem

AbstractIn this paper we bring together results from a series of previous papers to prove the constructive version of the Gelfand duality theorem in any Grothendieck topos E, obtaining a dual equivalence between the category of commutative C∗-algebras and the category of compact, completely regular locales in the topos E

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

Metascientific aspects of topoi of spaces

This thesis presents a study of the importance of topoi for Science. It is argued that whenever the concept of space enters the practice of Science then formal (mathematical) theories should be interpreted in a topos of spaces. It is claimed that these topoi encode knowledge of space arising directly out of the needs of Science, in that the constitutive questions of the Sciences can be traced back to their leading knowledge interests and these determine the role of mathematics as a methodical device. In the Natural Sciences the constitutive questions involve the study of non-intentional objects, in terms of a causal nexus to be explained geometrically, and this facilitates the introduction of geometric objects as the methodical device for posing questions to Nature. Although the study of intentional subjects in the Human Sciences requires ordinary language, not mathematics, to pose questions to each other, secondary methodological objectifications permit a conception of geometric objects analogous to that of the Natural Sciences. Lawvere*s axioms for the gros and petit topoi illustrate attempts to formalise the idea of topoi of spaces, as a rational reconstruction of categories in which geometric objects satisfying the formal theories of Science can be found. The catalysing function of this knowledge of topoi of spaces can lead to a diagnosis of mathematical difficulties caused by a failure to align mathematical conceptions with these topoi. This is illustrated through Varela's use of self-reference in Biology and Atkin's use of algebraic topology in Social Studies

ILP - Just trie it

Despite the considerable success of Inductive Logic Programming (ILP), deployed ILP systems still have efficiency problems when applied to complex problems. Several techniques have been proposed to address the efficiency issue. Such proposals include query transformations, query packs, lazy evaluation and parallel execution of ILP systems, to mention just a few. We propose a novel technique that avoids the procedure of deducing each example to evaluate each constructed clause. The technique takes advantage of the two stage procedure of Mode Directed Inverse Entailment (MDIE) systems. In the first stage of a MDIE system, where the bottom clause is constructed, we store not only the bottom clause but also valuable additional information. The information stored is sufficient to evaluate the clauses constructed in the second stage without the need for a theorem prover. We used a data structure called Trie to efficiently store all bottom clauses produced using all examples (positive and negative) as seeds. The technique was implemented and evaluated using two well known data sets from the ILP literature. The results are promising both in terms of execution time and accuracy