An approach to supervised learning of three valued Lukasiewicz logic in Hölldobler's core method

The core method [6] provides a way of translating logic programs into a multilayer perceptron computing least models of the programs. In [7] , a variant of the core method for three valued Lukasiewicz logic and its applicability to cognitive modelling were introduced. Building on these results, the present paper provides a modified core suitable for supervised learning, implements and executes supervised learning with the backpropagation algorithm and, finally, constructs a rule extraction method in order to close the neural-symbolic cycle

Learning Lukasiewicz logic

The integration between connectionist learning and logic-based reasoning is a longstanding foundational question in artificial intelligence, cognitive systems, and computer science in general. Research into neural-symbolic integration aims to tackle this challenge, developing approaches bridging the gap between sub-symbolic and symbolic representation and computation. In this line of work the core method has been suggested as a way of translating logic programs into a multilayer perceptron computing least models of the programs. In particular, a variant of the core method for three valued Łukasiewicz logic has proven to be applicable to cognitive modelling among others in the context of Byrne’s suppression task. Building on the underlying formal results and the corresponding computational framework, the present article provides a modified core method suitable for the supervised learning of Łukasiewicz logic (and of a closely-related variant thereof), implements and executes the corresponding supervised learning with the backpropagation algorithm and, finally, constructs a rule extraction method in order to close the neural-symbolic cycle. The resulting system is then evaluated in several empirical test cases, and recommendations for future developments are derived

Trepan Reloaded: A Knowledge-driven Approach to Explaining Artificial Neural Networks

Explainability in Artificial Intelligence has been revived as a topic of active research by the need of conveying safety and trust to users in the `how' and `why' of automated decision-making. Whilst a plethora of approaches have been developed for post-hoc explainability, only a few focus on how to use domain knowledge, and how this influences the understandability of global explanations from the users' perspective. In this paper, we show how ontologies help the understandability of global post-hoc explanations, presented in the form of symbolic models. In particular, we build on Trepan, an algorithm that explains artificial neural networks by means of decision trees, and we extend it to include ontologies modeling domain knowledge in the process of generating explanations. We present the results of a user study that measures the understandability of decision trees using a syntactic complexity measure, and through time and accuracy of responses as well as reported user confidence and understandability. The user study considers domains where explanations are critical, namely, in finance and medicine. The results show that decision trees generated with our algorithm, taking into account domain knowledge, are more understandable than those generated by standard Trepan without the use of ontologies

Global Optimization by Energy Landscape Paving

We introduce a novel heuristic global optimization method, energy landscape paving (ELP), which combines core ideas from energy surface deformation and tabu search. In appropriate limits, ELP reduces to existing techniques. The approach is very general and flexible and is illustrated here on two protein folding problems. For these examples, the technique gives faster convergence to the global minimum than previous approaches.Comment: to appear in Phys. Rev. Lett. (2002

AGI and the Knight-Darwin Law: why idealized AGI reproduction requires collaboration

Can an AGI create a more intelligent AGI? Under idealized assumptions, for a certain theoretical type of intelligence, our answer is: “Not without outside help”. This is a paper on the mathematical structure of AGI populations when parent AGIs create child AGIs. We argue that such populations satisfy a certain biological law. Motivated by observations of sexual reproduction in seemingly-asexual species, the Knight-Darwin Law states that it is impossible for one organism to asexually produce another, which asexually produces another, and so on forever: that any sequence of organisms (each one a child of the previous) must contain occasional multi-parent organisms, or must terminate. By proving that a certain measure (arguably an intelligence measure) decreases when an idealized parent AGI single-handedly creates a child AGI, we argue that a similar Law holds for AGIs

Entropy-based analysis of the number partitioning problem

In this paper we apply the multicanonical method of statistical physics on the number-partitioning problem (NPP). This problem is a basic NP-hard problem from computer science, and can be formulated as a spin-glass problem. We compute the spectral degeneracy, which gives us information about the number of solutions for a given cost $E$ and cardinality $m$. We also study an extension of this problem for $Q$ partitions. We show that a fundamental difference on the spectral degeneracy of the generalized ($Q>2$) NPP exists, which could explain why it is so difficult to find good solutions for this case. The information obtained with the multicanonical method can be very useful on the construction of new algorithms.Comment: 6 pages, 4 figure

Crossover phenomena in spin models with medium-range interactions and self-avoiding walks with medium-range jumps

We study crossover phenomena in a model of self-avoiding walks with medium-range jumps, that corresponds to the limit $N\to 0$ of an $N$-vector spin system with medium-range interactions. In particular, we consider the critical crossover limit that interpolates between the Gaussian and the Wilson-Fisher fixed point. The corresponding crossover functions are computed using field-theoretical methods and an appropriate mean-field expansion. The critical crossover limit is accurately studied by numerical Monte Carlo simulations, which are much more efficient for walk models than for spin systems. Monte Carlo data are compared with the field-theoretical predictions concerning the critical crossover functions, finding a good agreement. We also verify the predictions for the scaling behavior of the leading nonuniversal corrections. We determine phenomenological parametrizations that are exact in the critical crossover limit, have the correct scaling behavior for the leading correction, and describe the nonuniversal lscrossover behavior of our data for any finite range.Comment: 43 pages, revte

Ultra-Strong Machine Learning: comprehensibility of programs learned with ILP

During the 1980s Michie defined Machine Learning in terms of two orthogonal axes of performance: predictive accuracy and comprehensibility of generated hypotheses. Since predictive accuracy was readily measurable and comprehensibility not so, later definitions in the 1990s, such as Mitchell’s, tended to use a one-dimensional approach to Machine Learning based solely on predictive accuracy, ultimately favouring statistical over symbolic Machine Learning approaches. In this paper we provide a definition of comprehensibility of hypotheses which can be estimated using human participant trials. We present two sets of experiments testing human comprehensibility of logic programs. In the first experiment we test human comprehensibility with and without predicate invention. Results indicate comprehensibility is affected not only by the complexity of the presented program but also by the existence of anonymous predicate symbols. In the second experiment we directly test whether any state-of-the-art ILP systems are ultra-strong learners in Michie’s sense, and select the Metagol system for use in humans trials. Results show participants were not able to learn the relational concept on their own from a set of examples but they were able to apply the relational definition provided by the ILP system correctly. This implies the existence of a class of relational concepts which are hard to acquire for humans, though easy to understand given an abstract explanation. We believe improved understanding of this class could have potential relevance to contexts involving human learning, teaching and verbal interaction