Related papers: First-Order Logic in Finite Domains: Where Semanti…

Blocked clauses provide the basis for powerful reasoning techniques used in SAT, QBF, and DQBF solving. Their definition, which relies on a simple syntactic criterion, guarantees that they are both redundant and easy to find. In this paper,…

Traditional evaluation metrics for textual and visual question answering, like ROUGE, METEOR, and Exact Match (EM), focus heavily on n-gram based lexical similarity, often missing the deeper semantic understanding needed for accurate…

This paper shows how to harness existing theorem provers for first-order logic to automatically verify safety properties of imperative programs that perform dynamic storage allocation and destructive updating of pointer-valued structure…

Current end-to-end semantic role labeling is mostly accomplished via graph-based neural models. However, these all are first-order models, where each decision for detecting any predicate-argument pair is made in isolation with local…

Evaluating the capabilities and risks of foundation models is paramount, yet current methods demand extensive domain expertise, hindering their scalability as these models rapidly evolve. We introduce SKATE: a novel evaluation framework in…

We investigate the quantifier alternation hierarchy in first-order logic on finite words. Levels in this hierarchy are defined by counting the number of quantifier alternations in formulas. We prove that one can decide membership of a…

Semantic role labeling (SRL) identifies predicate-argument structure(s) in a given sentence. Although different languages have different argument annotations, polyglot training, the idea of training one model on multiple languages, has…

This paper investigates the satisfiability problem for Separation Logic, with unrestricted nesting of separating conjunctions and implications, for prenex formulae with quantifier prefix in the language $\exists^*\forall^*$, in the cases…

Logic has proved essential for formally modeling software based systems. Such formal descriptions, frequently called specifications, have served not only as requirements documentation and formalisation, but also for providing the…

This paper deals with a problem from discrete-time robust control which requires the solution of constraints over the reals that contain both universal and existential quantifiers. For solving this problem we formulate it as a program in a…

Semiring semantics for first-order logic provides a way to trace how facts represented by a model are used to deduce satisfaction of a formula. Team semantics is a framework for studying logics of dependence and independence in diverse…

Optimization is central to both modern machine learning (ML) and scientific machine learning (SciML), yet the structure of the underlying optimization problems differs substantially across these domains. Classical ML typically relies on…

Recent advances in reinforcement learning (RL) have led to substantial improvements in the mathematical reasoning abilities of LLMs, as measured by standard benchmarks. Yet these gains often persist even when models are trained with flawed…

We provide a novel computer-assisted technique for systematically analyzing first-order methods for optimization. In contrast with previous works, the approach is particularly suited for handling sublinear convergence rates and stochastic…

Mathematical reasoning is a hallmark of human intelligence, and whether large language models (LLMs) can meaningfully perform it remains a central question in artificial intelligence and cognitive science. As LLMs are increasingly…

Logical reasoning with large language models (LLMs) has received growing attention. One mainstream approach translates natural language into formal logic and then applies symbolic solvers for deduction. While effective in many tasks, these…

Natural language understanding applications such as interactive planning and face-to-face translation require extensive inferencing. Many of these inferences are based on the meaning of particular open class words. Providing a…

Multimodal Large Language Models (MLLMs) pose critical safety challenges, as they are susceptible not only to adversarial attacks such as jailbreaking but also to inadvertently generating harmful content for benign users. While internal…

Symmetry in finite model finding problems of many-sorted first-order logic (MSFOL) can be exploited to reduce the number of interpretations considered during search, thereby improving solver performance. In this thesis, we situate symmetry…

We propose a new calculus SCL(EQ) for first-order logic with equality that only learns non-redundant clauses. Following the idea of CDCL (Conflict Driven Clause Learning) and SCL (Clause Learning from Simple Models) a ground literal model…