Related papers: The Imandra Automated Reasoning System (system des…

This paper presents a language, Alda, that supports all of logic rules, sets, functions, updates, and objects as seamlessly integrated built-ins. The key idea is to support predicates in rules as set-valued variables that can be used and…

Most deep learning recommendation models operate as black boxes, relying on latent representations that obscure their decision process. This lack of intrinsic interpretability raises concerns in applications that require transparency and…

This thesis concerns the implementation of Lambda Prolog, a higher-order logic programming language that supports the lambda-tree syntax approach to representing and manipulating formal syntactic objects. Lambda Prolog achieves its…

We introduce a non-wellfounded proof system for intuitionistic logic extended with inductive and co-inductive definitions, based on a syntax in which fixpoint formulas are annotated with explicit variables for ordinals. We explore the…

Higher-order logic HOL offers a very simple syntax and semantics for representing and reasoning about typed data structures. But its type system lacks advanced features where types may depend on terms. Dependent type theory offers such a…

We present a generic framework that facilitates object level reasoning with logics that are encoded within the Higher Order Logic theorem proving environment of HOL Light. This involves proving statements in any logic using intuitive…

Table reasoning requires models to jointly perform comprehensive semantic understanding and precise numerical operations. Although recent large language model (LLM)-based methods have achieved promising results, most of them still rely on a…

Prompting large language models has enabled significant recent progress in multi-step reasoning over text. However, when applied to text generation from semi-structured data (e.g., graphs or tables), these methods typically suffer from low…

Large Language Models (LLMs) are widely used as judges to evaluate response quality, providing a scalable alternative to human evaluation. However, most LLM judges operate solely on intrinsic text-based reasoning, limiting their ability to…

Tabular foundation models are becoming increasingly popular for low-resource tabular problems. These models make up for small training datasets by pretraining on large volumes of synthetic data. The prior knowledge obtained via pretraining…

When humans face problems beyond their immediate capabilities, they rely on tools, providing a promising paradigm for improving visual reasoning in multimodal large language models (MLLMs). Effective reasoning, therefore, hinges on knowing…

In this work, we introduce Contextual Analog Logic with Multimodality (CALM). CALM unites symbolic reasoning with neural generation, enabling systems to make context-sensitive decisions grounded in real-world multi-modal data. Background:…

The vast quantity of data generated and captured every day has led to a pressing need for tools and processes to organize, analyze and interrelate this data. Automated reasoning and optimization tools with inherent support for data could…

Motivated by algorithmic information theory, the problem of program discovery can help find candidates of underlying generative mechanisms of natural and artificial phenomena. The uncomputability of such inverse problem, however,…

Large foundation models enable powerful reasoning for autonomous systems, but mapping semantic intent to reliable real-time control remains challenging. Existing approaches either (i) let Large Language Models (LLMs) generate trajectories…

Multimodal Large Language Models (MLLMs) have made remarkable progress in multimodal perception and reasoning by bridging vision and language. However, most existing MLLMs perform reasoning primarily with textual CoT, which limits their…

In this work we present a computation paradigm based on a concurrent and incremental construction of proof nets (de-sequentialized or graphical proofs) of the pure multiplicative and additive fragment of Linear Logic, a resources conscious…

The sequential process of conceptualization and instantiation is essential to generalizable commonsense reasoning as it allows the application of existing knowledge to unfamiliar scenarios. However, existing works tend to undervalue the…

This work explores the integration of ontology-based reasoning and Machine Learning techniques for explainable value classification. By relying on an ontological formalization of moral values as in the Moral Foundations Theory, relying on…

Recent advances in deep thinking models have demonstrated remarkable reasoning capabilities on mathematical and coding tasks. However, their effectiveness in embodied domains which require continuous interaction with environments through…