Related papers: "ReLIC: Reduced Logic Inference for Composition" f…
For performance and verification in machine learning, new methods have recently been proposed that optimise learning systems to satisfy formally expressed logical properties. Among these methods, differentiable logics (DLs) are used to…
Atomic decomposition -- breaking a candidate answer into claims before verifying each against a reference -- is a widely adopted design for LLM-based reference-grounded judges. However, atomic prompts are typically richer and longer, making…
We propose a new cyclic proof system for automated, equational reasoning about the behaviour of pure functional programs. The key to the system is the way in which cyclic proof and equational reasoning are mediated by the use of contextual…
Typically, a practical algorithm of hardware verification obtains a semantic result by being applied to a particular formula $F$. That is, although this algorithm uses the specifics of $F$ (sometimes inadvertently), its result holds for all…
We introduce a synthetic dataset called Sentences Involving Complex Compositional Knowledge (SICCK) and a novel analysis that investigates the performance of Natural Language Inference (NLI) models to understand compositionality in logic.…
In this report, we study partial quantifier elimination (PQE) for propositional CNF formulas. PQE is a generalization of quantifier elimination where one can limit the set of clauses taken out of the scope of quantifiers to a small subset…
Relativistic corrections to the evolution of structure can be used to test general relativity on cosmological scales. They are also a well-known systematic contamination in the search for a primordial non-Gaussian signal. We present a…
Let $\mathcal{L}_{\mathcal{X}}$ be the language of first-order, decidable theory $\mathcal{X}$. Consider the language, $\mathcal{L}_{\mathcal{RQ}}(\mathcal{X})$, that extends $\mathcal{L}_{\mathcal{X}}$ with formulas of the form $\forall x…
Semantic ID (SID)-based recommendation is a promising paradigm for scaling sequential recommender systems, but existing methods largely follow a semantic-centric pipeline: item embeddings are learned from foundation models and discretized…
Compositional Reasoning (CR) entails grasping the significance of attributes, relations, and word order. Recent Vision-Language Models (VLMs), comprising a visual encoder and a Large Language Model (LLM) decoder, have demonstrated…
Language models (LMs) can perform complex reasoning either end-to-end, with hidden latent state, or compositionally, with transparent intermediate state. Composition offers benefits for interpretability and safety, but may need workflow…
Logical reasoning, i.e., deductively inferring the truth value of a conclusion from a set of premises, is an important task for artificial intelligence with wide potential impacts on science, mathematics, and society. While many…
We propose a method for compositional verification to address the state space explosion problem inherent to model-checking timed systems with a large number of components. The main challenge is to obtain pertinent global timing constraints…
This thesis introduces the "method of structural refinement", which serves as a means of transforming the relational semantics of a modal and/or constructive logic into an 'economical' proof system by connecting two proof-theoretic…
Quantum error correction (QEC) is fundamental for suppressing noise in quantum hardware and enabling fault-tolerant quantum computation. In this paper, we propose an efficient verification framework for QEC programs. We define an assertion…
Entity Linking (EL) and Relation Extraction (RE) are fundamental tasks in Natural Language Processing, serving as critical components in a wide range of applications. In this paper, we propose ReLiK, a Retriever-Reader architecture for both…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
We present a logic named L_{LF} whose intended use is to formalize properties of specifications developed in the dependently typed lambda calculus LF. The logic is parameterized by the LF signature that constitutes the specification. Atomic…
LLM-based formal proof assistants (e.g., in Lean) hold great promise for automating mathematical discovery. But beyond syntactic correctness, do these systems truly understand mathematical structure as humans do? We investigate this…
We report on the development of an optimized and verified decision procedure for orthologic equalities and inequalities. This decision procedure is quadratic-time and is used as a sound, efficient and predictable approximation to classical…