Inductive Logic Programming (ILP) approaches like Meta \-/ Interpretive Learning (MIL) can learn, from few examples, recursive logic programs with invented predicates that generalise well to unseen instances. This ability relies on a background theory and negative examples, both carefully selected with expert knowledge of a learning problem and its solutions. But what if such a problem-specific background theory or negative examples are not available? We formalise this question as a new setting for Self-Supervised ILP and present a new MIL algorithm that learns in the new setting from some positive labelled, and zero or more unlabelled examples, and automatically generates, and labels, new positive and negative examples during learning. We implement this algorithm in Prolog in a new MIL system, called Poker. We compare Poker to state-of-the-art MIL system Louise on experiments learning grammars for Context-Free and L-System languages from labelled, positive example strings, no negative examples, and just the terminal vocabulary of a language, seen in examples, as a first-order background theory. We introduce a new approach for the principled selection of a second-order background theory as a Second Order Definite Normal Form (SONF), sufficiently general to learn all programs in a class, thus removing the need for a backgound theory tailored to a learning task. We find that Poker's performance improves with increasing numbers of automatically generated examples while Louise, bereft of negative examples, over-generalises.

A "model" is a theory that describes the state of an environment and the effects of an agent's decisions on the environment. A model-based agent can use its model to predict the effects of its future actions and so plan ahead, but must know the state of the environment. A model-free agent cannot plan, but can act without a model and without completely observing the environment. An autonomous agent capable of acting independently in novel environments must combine both sets of capabilities. We show how to create such an agent with Meta-Interpretive Learning used to learn a model-based Solver used to train a model-free Controller that can solve the same planning problems as the Solver. We demonstrate the equivalence in problem-solving ability of the two agents on grid navigation problems in two kinds of environment: randomly generated mazes, and lake maps with wide open areas. We find that all navigation problems solved by the Solver are also solved by the Controller, indicating the two are equivalent.

Answer Set Programming Modulo Theories (ASPMT) is a new framework of tight integration of answer set programming (ASP) and satisfiability modulo theories (SMT). Similar to the relationship between first-order logic and SMT, it is based on a recent proposal of the functional stable model semantics by fixing interpretations of background theories. Analogously to a known relationship between ASP and SA T, "tight" ASPMT programs can be translated into SMT instances. We demonstrate the usefulness of ASPMT by enhancing action language C + to handle continuous changes as well as discrete changes. We reformulate the semantics of C + in terms of ASPMT, and show that SMT solvers can be used to compute the language. We also show how the language can represent cumulative effects on continuous resources.

Answer Set Programming Modulo Theories (ASPMT) is an approach to combining answer set programming and satisfiability modulo theories based on the functional stable model semantics. It is shown that the tight fragment of ASPMT programs can be turned into SMT instances, thereby allowing SMT solvers to compute stable models of ASPMT programs. In this paper we present a compiler called {\sc aspsmt2smt}, which implements this translation. The system uses ASP grounder {\sc gringo} and SMT solver {\sc z3}. {\sc gringo} partially grounds input programs while leaving some variables to be processed by {\sc z3}. We demonstrate that the system can effectively handle real number computations for reasoning about continuous changes.

As large language models (LLMs) become more powerful and pervasive across society, ensuring these systems are beneficial, safe, and aligned with human values is crucial. Current alignment techniques, like Constitutional AI (CAI), involve complex iterative processes. This paper argues that the Method of Wide Reflective Equilibrium (MWRE) -- a well-established coherentist moral methodology -- offers a uniquely apt framework for understanding current LLM alignment efforts. Moreover, this methodology can substantively augment these processes by providing concrete pathways for improving their dynamic revisability, procedural legitimacy, and overall ethical grounding. Together, these enhancements can help produce more robust and ethically defensible outcomes. MWRE, emphasizing the achievement of coherence between our considered moral judgments, guiding moral principles, and relevant background theories, arguably better represents the intricate reality of LLM alignment and offers a more robust path to justification than prevailing foundationalist models or simplistic input-output evaluations. While current methods like CAI bear a structural resemblance to MWRE, they often lack its crucial emphasis on dynamic, bi-directional revision of principles and the procedural legitimacy derived from such a process. While acknowledging various disanalogies (e.g., consciousness, genuine understanding in LLMs), the paper demonstrates that MWRE serves as a valuable heuristic for critically analyzing current alignment efforts and for guiding the future development of more ethically sound and justifiably aligned AI systems.

The discovery of scientific formulae that parsimoniously explain natural phenomena and align with existing background theory is a key goal in science. Historically, scientists have derived natural laws by manipulating equations based on existing knowledge, forming new equations, and verifying them experimentally. In recent years, data-driven scientific discovery has emerged as a viable competitor in settings with large amounts of experimental data. Unfortunately, data-driven methods often fail to discover valid laws when data is noisy or scarce. Accordingly, recent works combine regression and reasoning to eliminate formulae inconsistent with background theory. However, the problem of searching over the space of formulae consistent with background theory to find one that fits the data best is not well-solved. We propose a solution to this problem when all axioms and scientific laws are expressible via polynomial equalities and inequalities and argue that our approach is widely applicable. We further model notions of minimal complexity using binary variables and logical constraints, solve polynomial optimization problems via mixed-integer linear or semidefinite optimization, and prove the validity of our scientific discoveries in a principled manner using Positivestellensatz certificates. Remarkably, the optimization techniques leveraged in this paper allow our approach to run in polynomial time with fully correct background theory, or non-deterministic polynomial (NP) time with partially correct background theory. We demonstrate that some famous scientific laws, including Kepler's Third Law of Planetary Motion, the Hagen-Poiseuille Equation, and the Radiated Gravitational Wave Power equation, can be derived in a principled manner from background axioms and experimental data.

We present Locksynth, a tool that automatically derives synchronization needed for destructive updates to concurrent data structures that involve a constant number of shared heap memory write operations. Locksynth serves as the implementation of our prior work on deriving abstract synchronization code. Designing concurrent data structures involves inferring correct synchronization code starting with a prior understanding of the sequential data structure's operations. Further, an understanding of shared memory model and the synchronization primitives is also required. The reasoning involved transforming a sequential data structure into its concurrent version can be performed using Answer Set Programming and we mechanized our approach in previous work. The reasoning involves deduction and abduction that can be succinctly modeled in ASP. We assume that the abstract sequential code of the data structure's operations is provided, alongside axioms that describe concurrent behavior. This information is used to automatically derive concurrent code for that data structure, such as dictionary operations for linked lists and binary search trees that involve a constant number of destructive update operations. We also are able to infer the correct set of locks (but not code synthesis) for external height-balanced binary search trees that involve left/right tree rotations. Locksynth performs the analyses required to infer correct sets of locks and as a final step, also derives the C++ synchronization code for the synthesized data structures. We also provide a performance analysis of the C++ code synthesized by Locksynth with the hand-crafted versions available from the Synchrobench microbenchmark suite. To the best of our knowledge, our tool is the first to employ ASP as a backend reasoner to perform concurrent data structure synthesis.

AI-Descartes, an AI scientist developed by researchers at IBM Research, Samsung AI, and the University of Maryland, Baltimore County, has reproduced key parts of Nobel Prize-winning work, including Langmuir's gas behavior equations and Kepler's third law of planetary motion. Supported by the Defense Advanced Research Projects Agency (DARPA), the AI system utilizes symbolic regression to find equations fitting data, and its most distinctive feature is its logical reasoning ability. This enables AI-Descartes to determine which equations best fit with background scientific theory. The system is particularly effective with noisy, real-world data and small data sets. The team is working on creating new datasets and training computers to read scientific papers and construct background theories to refine and expand the system's capabilities.

In 1918, the American chemist Irving Langmuir published a paper examining the behavior of gas molecules sticking to a solid surface. Guided by the results of careful experiments, as well as his theory that solids offer discrete sites for the gas molecules to fill, he worked out a series of equations that describe how much gas will stick, given the pressure. Now, about a hundred years later, an "AI scientist" developed by researchers at IBM Research, Samsung AI, and the University of Maryland, Baltimore County (UMBC) has reproduced a key part of Langmuir's Nobel Prize-winning work. The system--artificial intelligence (AI) functioning as a scientist--also rediscovered Kepler's third law of planetary motion, which can calculate the time it takes one space object to orbit another given the distance separating them, and produced a good approximation of Einstein's relativistic time-dilation law, which shows that time slows down for fast-moving objects. A paper describing the results is published in Nature Communications on April 12.

Scientists have long aimed to discover meaningful equations which accurately describe data. Machine learning algorithms automate construction of accurate data-driven models, but ensuring that these are consistent with existing knowledge is a challenge. We developed a methodology combining automated theorem proving with symbolic regression, enabling principled derivations of laws of nature. We demonstrate this for Kepler's third law, Einstein's relativistic time dilation, and Langmuir's theory of adsorption, in each case, automatically connecting experimental data with background theory. The combination of logical reasoning with machine learning provides generalizable insights into key aspects of the natural phenomena.