Pac-Learning Recursive Logic Programs: Efficient Algorithms

We present algorithms that learn certain classes of function-free recursive logic programs in polynomial time from equivalence queries. In particular, we show that a single k-ary recursive constant-depth determinate clause is learnable. Two-clause programs consisting of one learnable recursive clause and one constant-depth determinate non-recursive clause are also learnable, if an additional ``basecase'' oracle is assumed. These results immediately imply the pac-learnability of these classes. Although these classes of learnable recursive programs are very constrained, it is shown in a companion paper that they are maximally general, in that generalizing either class in any natural way leads to a computationally difficult learning problem. Thus, taken together with its companion paper, this paper establishes a boundary of efficient learnability for recursive logic programs.Comment: See http://www.jair.org/ for any accompanying file

Synchronous Online Philosophy Courses: An Experiment in Progress

There are two main ways to teach a course online: synchronously or asynchronously. In an asynchronous course, students can log on at their convenience and do the course work. In a synchronous course, there is a requirement that all students be online at specific times, to allow for a shared course environment. In this article, the author discusses the strengths and weaknesses of synchronous online learning for the teaching of undergraduate philosophy courses. The author discusses specific strategies and technologies he uses in the teaching of online philosophy courses. In particular, the author discusses how he uses videoconferencing to create a classroom-like environment in an online class

Human-like Few-Shot Learning via Bayesian Reasoning over Natural Language

A core tension in models of concept learning is that the model must carefully balance the tractability of inference against the expressivity of the hypothesis class. Humans, however, can efficiently learn a broad range of concepts. We introduce a model of inductive learning that seeks to be human-like in that sense. It implements a Bayesian reasoning process where a language model first proposes candidate hypotheses expressed in natural language, which are then re-weighed by a prior and a likelihood. By estimating the prior from human data, we can predict human judgments on learning problems involving numbers and sets, spanning concepts that are generative, discriminative, propositional, and higher-order.Comment: NeurIPS 2023 ora

Efficient instance and hypothesis space revision in Meta-Interpretive Learning

Inductive Logic Programming (ILP) is a form of Machine Learning. The goal of ILP is to induce hypotheses, as logic programs, that generalise training examples. ILP is characterised by a high expressivity, generalisation ability and interpretability. Meta-Interpretive Learning (MIL) is a state-of-the-art sub-field of ILP. However, current MIL approaches have limited efficiency: the sample and learning complexity respectively are polynomial and exponential in the number of clauses. My thesis is that improvements over the sample and learning complexity can be achieved in MIL through instance and hypothesis space revision. Specifically, we investigate 1) methods that revise the instance space, 2) methods that revise the hypothesis space and 3) methods that revise both the instance and the hypothesis spaces for achieving more efficient MIL. First, we introduce a method for building training sets with active learning in Bayesian MIL. Instances are selected maximising the entropy. We demonstrate this method can reduce the sample complexity and supports efficient learning of agent strategies. Second, we introduce a new method for revising the MIL hypothesis space with predicate invention. Our method generates predicates bottom-up from the background knowledge related to the training examples. We demonstrate this method is complete and can reduce the learning and sample complexity. Finally, we introduce a new MIL system called MIGO for learning optimal two-player game strategies. MIGO learns from playing: its training sets are built from the sequence of actions it chooses. Moreover, MIGO revises its hypothesis space with Dependent Learning: it first solves simpler tasks and can reuse any learned solution for solving more complex tasks. We demonstrate MIGO significantly outperforms both classical and deep reinforcement learning. The methods presented in this thesis open exciting perspectives for efficiently learning theories with MIL in a wide range of applications including robotics, modelling of agent strategies and game playing.Open Acces

Parameter Learning of Logic Programs for Symbolic-Statistical Modeling

We propose a logical/mathematical framework for statistical parameter learning of parameterized logic programs, i.e. definite clause programs containing probabilistic facts with a parameterized distribution. It extends the traditional least Herbrand model semantics in logic programming to distribution semantics, possible world semantics with a probability distribution which is unconditionally applicable to arbitrary logic programs including ones for HMMs, PCFGs and Bayesian networks. We also propose a new EM algorithm, the graphical EM algorithm, that runs for a class of parameterized logic programs representing sequential decision processes where each decision is exclusive and independent. It runs on a new data structure called support graphs describing the logical relationship between observations and their explanations, and learns parameters by computing inside and outside probability generalized for logic programs. The complexity analysis shows that when combined with OLDT search for all explanations for observations, the graphical EM algorithm, despite its generality, has the same time complexity as existing EM algorithms, i.e. the Baum-Welch algorithm for HMMs, the Inside-Outside algorithm for PCFGs, and the one for singly connected Bayesian networks that have been developed independently in each research field. Learning experiments with PCFGs using two corpora of moderate size indicate that the graphical EM algorithm can significantly outperform the Inside-Outside algorithm

The Epistemology of Simulation, Computation and Dynamics in Economics Ennobling Synergies, Enfeebling 'Perfection'

Lehtinen and Kuorikoski ([73]) question, provocatively, whether, in the context of Computing the Perfect Model, economists avoid - even positively abhor - reliance on simulation. We disagree with the mildly qualified affirmative answer given by them, whilst agreeing with some of the issues they raise. However there are many economic theoretic, mathematical (primarily recursion theoretic and constructive) - and even some philosophical and epistemological - infelicities in their descriptions, definitions and analysis. These are pointed out, and corrected; for, if not, the issues they raise may be submerged and subverted by emphasis just on the unfortunate, but essential, errors and misrepresentationsSimulation, Computation, Computable, Analysis, Dynamics, Proof, Algorithm

Artificial general intelligence: Proceedings of the Second Conference on Artificial General Intelligence, AGI 2009, Arlington, Virginia, USA, March 6-9, 2009

Artificial General Intelligence (AGI) research focuses on the original and ultimate goal of AI – to create broad human-like and transhuman intelligence, by exploring all available paths, including theoretical and experimental computer science, cognitive science, neuroscience, and innovative interdisciplinary methodologies. Due to the difficulty of this task, for the last few decades the majority of AI researchers have focused on what has been called narrow AI – the production of AI systems displaying intelligence regarding specific, highly constrained tasks. In recent years, however, more and more researchers have recognized the necessity – and feasibility – of returning to the original goals of the field. Increasingly, there is a call for a transition back to confronting the more difficult issues of human level intelligence and more broadly artificial general intelligence