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Machine learning models are increasingly being trained across multiple GPUs and servers. In this setting, data is transferred between GPUs using communication collectives such as AlltoAll and AllReduce, which can become a significant…

First-order logic (FOL) can represent the logical entailment semantics of natural language (NL) sentences, but determining natural language entailment using FOL remains a challenge. To address this, we propose the Entailment-Preserving FOL…

The Univalent Foundations requires a logic that allows us to define structures on homotopy types, similar to how first-order logic with equality ($\text{FOL}_=$) allows us to define structures on sets. We develop the syntax, semantics and…

We investigate graph transformations, defined using Datalog-like rules based on acyclic conjunctive two-way regular path queries (acyclic C2RPQs), and we study two fundamental static analysis problems: type checking and equivalence of…

We study the problem of finding flows in undirected graphs so as to minimize the weighted $p$-norm of the flow for any $p > 1$. When $p=2$, the problem is that of finding an electrical flow, and its dual is equivalent to solving a Laplacian…

The Semantic Web ontology language OWL 2 DL comes with a variety of language features that enable sophisticated and practically useful modeling. However, the use of these features has been severely restricted in order to retain decidability…

Work on knowledge graphs and graph-based data management often focus either on declarative graph query languages or on frameworks for graph analytics, where there has been little work in trying to combine both approaches. However, many…

Education in the practical applications of logic and proving such as the formal specification and verification of computer programs is substantially hampered by the fact that most time and effort that is invested in proving is actually…

We recently proposed Acceleration Driven Clause Learning (ADCL), a novel calculus to analyze satisfiability of Constrained Horn Clauses (CHCs). Here, we adapt ADCL to disprove termination of transition systems, and we evaluate its…

Constrained Reinforcement Learning (CRL) is a subset of machine learning that introduces constraints into the traditional reinforcement learning (RL) framework. Unlike conventional RL which aims solely to maximize cumulative rewards, CRL…

This work deals with the presence of topological structures in models of two real scalar fields in the two-dimensional spacetime. The subject concerns the presence of a geometric constriction, which appears with a modification of the…

The overall goal of this paper is to investigate the theoretical foundations of algorithmic verification techniques for first order linear logic specifications. The fragment of linear logic we consider in this paper is based on the linear…

Formalisms based on temporal logics interpreted over finite strict linear orders, known in the literature as finite traces, have been used for temporal specification in automated planning, process modelling, (runtime) verification and…

Formulating optimization problems for industrial applications demands significant manual effort and domain expertise. While Large Language Models (LLMs) show promise in automating this process, evaluating their performance remains difficult…

Satisfiability of boolean formulae (SAT) has been a topic of research in logic and computer science for a long time. In this paper we are interested in understanding the structure of satisfiable and unsatisfiable sentences. In previous work…

Many languages and algebras have been proposed in recent years for the specification of authorization policies. For some proposals, such as XACML, the main motivation is to address real-world requirements, typically by providing a complex…

Techniques for runtime verification often utilise specification languages that are (i) reasonably expressive, and (ii) relatively abstract (i.e. they operate on a level of abstraction that separates them from the system being monitored).…

Real-world robotic tasks often require agents to achieve sequences of goals while respecting time-varying safety constraints. However, standard Reinforcement Learning (RL) paradigms are fundamentally limited in these settings. A natural…

In this paper, we study a class of stochastic and finite-sum convex optimization problems with deterministic constraints. Existing methods typically aim to find an $\epsilon$-$expectedly\ feasible\ stochastic\ optimal$ solution, in which…

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…