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Joint logical-numerical reasoning remains a major challenge for language models, yet existing datasets rely on fixed rule sets and offer limited control over task complexity, constraining their generalizability for evaluation and training.…

$\{log\}$ is a programming language at the intersection of Constraint Logic Programming, set programming and declarative programming. But $\{log\}$ is also a satisfiability solver for a theory of finite sets and finite binary relations.…

We convert the DeepMind Mathematics Dataset into a reinforcement learning environment by interpreting it as a program synthesis problem. Each action taken in the environment adds an operator or an input into a discrete compute graph. Graphs…

While Large Language Models (LLMs) have demonstrated significant potential in natural language processing , complex general-purpose reasoning requiring multi-step logic, planning, and verification remains a critical bottleneck. Although…

Logic programming is a flexible programming paradigm due to the use of predicates without a fixed data flow. To extend logic languages with the compact notation of functional programming, there are various proposals to map evaluable…

When an evolving program is modified to address issues related to thread synchronization, there is a need to confirm the change is correct, i.e., it does not introduce unexpected behavior. However, manually comparing two programs to…

Enhancing the mathematical reasoning of large language models (LLMs) demands high-quality training data, yet conventional methods face critical challenges in scalability, cost, and data reliability. To address these limitations, we propose…

We present a new approach to termination analysis of numerical computations in logic programs. Traditional approaches fail to analyse them due to non well-foundedness of the integers. We present a technique that allows overcoming these…

Recent advances in neural symbolic learning, such as DeepProbLog, extend probabilistic logic programs with neural predicates. Like graphical models, these probabilistic logic programs define a probability distribution over possible worlds,…

Knowledge workers frequently encounter repetitive web data entry tasks, like updating records or placing orders. Web automation increases productivity, but translating tasks to web actions accurately and extending to new specifications is…

Synthesizing a program that realizes a logical specification is a classical problem in computer science. We examine a particular type of program synthesis, where the objective is to synthesize a strategy that reacts to a potentially…

Symbolic knowledge can provide crucial inductive bias for training neural models, especially in low data regimes. A successful strategy for incorporating such knowledge involves relaxing logical statements into sub-differentiable losses for…

This paper studies learning logic rules for reasoning on knowledge graphs. Logic rules provide interpretable explanations when used for prediction as well as being able to generalize to other tasks, and hence are critical to learn. Existing…

Application domains that require considering relationships among objects which have real-valued attributes are becoming even more important. In this paper we propose NeuralLog, a first-order logic language that is compiled to a neural…

We propose a framework that can incrementally expand the explanatory temporal logic rule set to explain the occurrence of temporal events. Leveraging the temporal point process modeling and learning framework, the rule content and weights…

The goal of inductive logic programming is to induce a logic program (a set of logical rules) that generalises training examples. Inducing programs with many rules and literals is a major challenge. To tackle this challenge, we introduce an…

While logical reasoning evaluation of Large Language Models (LLMs) has attracted significant attention, existing benchmarks predominantly rely on multiple-choice formats that are vulnerable to random guessing, leading to overestimated…

This paper describes a resolution based Description Logic reasoning system called DLog. DLog transforms Description Logic axioms into a Prolog program and uses the standard Prolog execution for efficiently answering instance retrieval…

The current paradigm of evaluating Large Language Models (LLMs) through static benchmarks comes with significant limitations, such as vulnerability to data contamination and a lack of adaptability to the evolving capabilities of LLMs.…

Synthesizing user-intended programs from a small number of input-output examples is a challenging problem with several important applications like spreadsheet manipulation, data wrangling and code refactoring. Existing synthesis systems…