Related papers: Problem solving in ID-logic with aggregates: some …

The logics of knowledge are modal logics that have been shown to be effective in representing and reasoning about knowledge in multi-agent domains. Relatively few computational frameworks for dealing with computation of models and useful…

With sound unification, Definite Clause Grammars and compact expression of combinatorial generation algorithms, logic programming is shown to conveniently host a declarative playground where interesting properties and behaviors emerge from…

Higher-level cognition includes logical reasoning and the ability of question answering with common sense. The RatioLog project addresses the problem of rational reasoning in deep question answering by methods from automated deduction and…

Our position is that logic programming is not programming in the Horn clause sublogic of classical logic, but programming in a logic of (inductive) definitions. Thus, the similarity between prototypical Prolog programs (e.g., member,…

We propose abstract compilation for precise static type analysis of object-oriented languages based on coinductive logic programming. Source code is translated to a logic program, then type-checking and inference problems amount to queries…

Problem-solving has been a fundamental driver of human progress in numerous domains. With advancements in artificial intelligence, Large Language Models (LLMs) have emerged as powerful tools capable of tackling complex problems across…

The goal of inductive logic programming (ILP) is to search for a hypothesis that generalises training examples and background knowledge (BK). To improve performance, we introduce an approach that, before searching for a hypothesis, first…

Given the emergent reasoning abilities of large language models, information retrieval is becoming more complex. Rather than just retrieve a document, modern information retrieval systems advertise that they can synthesize an answer based…

Large language models (LLMs) are increasingly used for program verification, and yet little is known about \emph{how} they reason about program semantics during this process. In this work, we focus on abstract interpretation based-reasoning…

This paper describes a system, called PLP, for compiling ordered logic programs into standard logic programs under the answer set semantics. In an ordered logic program, rules are named by unique terms, and preferences among rules are given…

We propose ILP-CoT, a method that bridges Inductive Logic Programming (ILP) and Multimodal Large Language Models (MLLMs) for abductive logical rule induction. The task involves both discovering logical facts and inducing logical rules from…

Large Language Models (LLMs) have succeeded remarkably in various natural language processing (NLP) tasks, yet their reasoning capabilities remain a fundamental challenge. While LLMs exhibit impressive fluency and factual recall, their…

We extend the {\lambda}-calculus with constructs suitable for relational and functional-logic programming: non-deterministic choice, fresh variable introduction, and unification of expressions. In order to be able to unify…

We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…

The Abstraction and Reasoning Corpus (ARC) is a general artificial intelligence benchmark that is currently unsolvable by any Machine Learning method, including Large Language Models (LLMs). It demands strong generalization and reasoning…

This article describes an evaluation of Automated Theorem Proving (ATP) systems on problems taken from the QMLTP library of first-order modal logic problems. Principally, the problems are translated to both typed first-order and…

Inductive logic programming is a type of machine learning in which logic programs are learned from examples. This learning typically occurs relative to some background knowledge provided as a logic program. This dissertation introduces…

This paper describes experiments on learning Dutch phonotactic rules using Inductive Logic Programming, a machine learning discipline based on inductive logical operators. Two different ways of approaching the problem are experimented with,…

First-order logic (FOL) reasoning, which involves sequential deduction, is pivotal for intelligent systems and serves as a valuable task for evaluating reasoning capabilities, particularly in chain-of-thought (CoT) contexts. Existing…

Benchmarking automated theorem proving (ATP) systems using standardized problem sets is a well-established method for measuring their performance. However, the availability of such libraries for non-classical logics is very limited. In this…