Related papers: State Representation and Termination for Recursive…
Large Reasoning Models (LRMs) exhibit remarkable reasoning abilities but rely primarily on parametric knowledge, limiting factual accuracy. While recent works equip reinforcement learning (RL)-based LRMs with retrieval capabilities, they…
We consider a model where an agent is must choose between alternatives that each provide only an imprecise description of the world (e.g. linguistic expressions). The set of alternatives is closed under logical conjunction and disjunction,…
Causal reasoning in relational domains is fundamental to studying real-world social phenomena in which individual units can influence each other's traits and behavior. Dynamics between interconnected units can be represented as an…
We combine Recurrent Neural Networks with Tensor Product Representations to learn combinatorial representations of sequential data. This improves symbolic interpretation and systematic generalisation. Our architecture is trained end-to-end…
Neither the classical nor intuitionistic logic traditions are perfectly-aligned with the purpose of reasoning about computation, in that neither tradition can permit unconstrained recursive definitions without inconsistency: recursive…
Probabilistic logical rule learning has shown great strength in logical rule mining and knowledge graph completion. It learns logical rules to predict missing edges by reasoning on existing edges in the knowledge graph. However, previous…
This paper presents Abduction and Argumentation as two principled forms for reasoning, and fleshes out the fundamental role that they can play within Machine Learning. It reviews the state-of-the-art work over the past few decades on the…
Modeling the structure of coherent texts is a key NLP problem. The task of coherently organizing a given set of sentences has been commonly used to build and evaluate models that understand such structure. We propose an end-to-end…
Transformers encode structure in sequences via an expanding contextual history. However, their purely feedforward architecture fundamentally limits dynamic state tracking. State tracking -- the iterative updating of latent variables…
Large Reasoning Models (LRMs) employ reasoning to address complex tasks. Such explicit reasoning requires extended context lengths, resulting in substantially higher resource consumption. Prior work has shown that adversarially crafted…
Renewal processes are broadly used to model stochastic behavior consisting of isolated events separated by periods of quiescence, whose durations are specified by a given probability law. Here, we identify the minimal sufficient statistic…
In many instances in first order logic or computable algebra, classical theorems show that many problems are undecidable for general structures, but become decidable if some rigidity is imposed on the structure. For example, the set of…
Reasoning is fundamental to human intelligence, and critical for problem-solving, decision-making, and critical thinking. Reasoning refers to drawing new conclusions based on existing knowledge, which can support various applications like…
We define the syntax and reduction relation of a recursively typed lambda calculus with a parallel case-function (a parallel conditional). The reduction is shown to be confluent. We interpret the recursive types as information systems in a…
Legal reasoning requires both precise interpretation of statutory language and consistent application of complex rules, presenting significant challenges for AI systems. This paper introduces a modular multi-agent framework that decomposes…
Retrieval-Augmented Generation (RAG) grounds language models in external evidence, but multi-hop question answering remains difficult because iterative pipelines must control what to retrieve next and when the available evidence is…
We establish a recursive representation that fully decouples jumps from a large class of multivariate inhomogeneous stochastic differential equations with jumps of general time-state dependent unbounded intensity, not of L\'evy-driven type…
Think-Answer reasoners such as DeepSeek-R1 have made notable progress by leveraging interpretable internal reasoning. However, despite the frequent presence of self-reflective cues like "Oops!", they remain vulnerable to output errors…
This paper offers an approach to extensible knowledge representation and reasoning for a family of formalisms known as Description Logics. The approach is based on the notion of adding new concept constructors, and includes a heuristic…
Cyclic proof theory breaks tradition by allowing certain infinite proofs: those that can be represented by a finite graph, while satisfying a soundness condition. We reconcile cyclic proofs with traditional finite proofs: we extend abstract…