Related papers: Learning higher-order logic programs

Probabilistic logic programs are logic programs in which some of the facts are annotated with probabilities. This paper investigates how classical inference and learning tasks known from the graphical model community can be tackled for…

Interpretation methods and their restrictions to polynomials have been deeply used to control the termination and complexity of first-order term rewrite systems. This paper extends interpretation methods to a pure higher order functional…

Formally verifying the correctness of mathematical proofs is more accessible than ever, however, the learning curve remains steep for many of the state-of-the-art interactive theorem provers (ITP). Deriving the most appropriate subsequent…

This book is a graduate-level introduction to probabilistic programming. It not only provides a thorough background for anyone wishing to use a probabilistic programming system, but also introduces the techniques needed to design and build…

Learning from Demonstration~(LfD) should capture not only how a task is executed, but also its high-level task structure that explains the demonstrated behavior. As robots become more autonomous, such task representations must be…

PIE is a Prolog-embedded environment for automated reasoning on the basis of first-order logic. It includes a versatile formula macro system and supports the creation of documents that intersperse macro definitions, reasoner invocations and…

Deep learning methods capable of handling relational data have proliferated over the last years. In contrast to traditional relational learning methods that leverage first-order logic for representing such data, these deep learning methods…

Machine learning components commonly appear in larger decision-making pipelines; however, the model training process typically focuses only on a loss that measures accuracy between predicted values and ground truth values. Decision-focused…

Traditional automated theorem provers for first-order logic depend on speed-optimized search and many handcrafted heuristics that are designed to work best over a wide range of domains. Machine learning approaches in literature either…

Large Language Models (LLMs) have rapidly transformed the landscape of artificial intelligence, enabling natural language interfaces and dynamic orchestration of software components. However, their reliance on probabilistic inference limits…

Class incremental learning (CIL) algorithms aim to continually learn new object classes from incrementally arriving data while not forgetting past learned classes. The common evaluation protocol for CIL algorithms is to measure the average…

We focus on the problem of inducing logic programs that explain models learned by the support vector machine (SVM) algorithm. The top-down sequential covering inductive logic programming (ILP) algorithms (e.g., FOIL) apply hill-climbing…

Inductive logic programming, or relational learning, is a powerful paradigm for machine learning or data mining. However, in order for ILP to become practically useful, the efficiency of ILP systems must improve substantially. To this end,…

Mixed Integer Linear Programs (MILPs) are highly flexible and powerful tools for modeling and solving complex real-world combinatorial optimization problems. Recently, machine learning (ML)-guided approaches have demonstrated significant…

Generating rational and generally accurate responses to tasks, often accompanied by example demonstrations, highlights Large Language Model's (LLM's) remarkable In-Context Learning (ICL) capabilities without requiring updates to the model's…

Certain constructs allowed in Mizar articles cannot be represented in first-order logic but can be represented in higher-order logic. We describe a way to obtain higher-order theorem proving problems from Mizar articles that make use of…

We propose a new formal language for the expressive representation of probabilistic knowledge based on Answer Set Programming (ASP). It allows for the annotation of first-order formulas as well as ASP rules and facts with probabilities and…

Combining machine learning with logic-based expert systems in order to get the best of both worlds are becoming increasingly popular. However, to what extent machine learning can already learn to reason over rule-based knowledge is still an…

Cutting planes (cuts) are important for solving mixed-integer linear programs (MILPs), which formulate a wide range of important real-world applications. Cut selection -- which aims to select a proper subset of the candidate cuts to improve…

We introduce an extension of first-order logic that comes equipped with additional predicates for reasoning about an abstract state. Sequents in the logic comprise a main formula together with pre- and postconditions in the style of Hoare…