Related papers: The Ramified Analytical Hierarchy using Extended L…

The finite satisfiability problem for the two-variable fragment of first-order logic interpreted over trees was recently shown to be ExpSpace-complete. We consider two extensions of this logic. We show that adding either additional binary…

Graph Neural Networks (GNNs) are deep learning models that take graph data as inputs, and they are applied to various tasks such as traffic prediction and molecular property prediction. However, owing to the complexity of the GNNs, it has…

We introduce infinitary action logic with exponentiation -- that is, the multiplicative-additive Lambek calculus extended with Kleene star and with a family of subexponential modalities, which allows some of the structural rules…

We introduce a family of interpretable machine learning models, with two broad additions: Linearised Additive Models (LAMs) which replace the ubiquitous logistic link function in General Additive Models (GAMs); and SubscaleHedge, an expert…

Motivated by team semantics and existential second-order logic, we develop a model-theoretic framework for studying second-order objects such as sets and relations. We introduce a notion of abstract elementary team categories that…

In a classical Hamiltonian theory with second class constraints the phase space functions on the constraint surface are observables. We give general formulas for extended observables, which are expressions representing the observables in…

We define a semantics for first-order logic with generalized quantifiers based on double teams. We also define and investigate a notion of a generalized atom. Such atoms can be used in order to define extensions of first-order logic with a…

This paper introduces Logical Credal Networks, an expressive probabilistic logic that generalizes many prior models that combine logic and probability. Given imprecise information represented by probability bounds and conditional…

Characterizations of semi-stable and stage extensions in terms of 2-valued logical models are presented. To this end, the so-called GL-supported and GL-stage models are defined. These two classes of logical models are logic programming…

We propose a novel framework that leverages large language models (LLMs) to guide the rank selection in tensor network models for higher-order data analysis. By utilising the intrinsic reasoning capabilities and domain knowledge of LLMs,…

We investigate the decidability of the definability problem for fragments of first order logic over finite words enriched with modular predicates. Our approach aims toward the most generic statements that we could achieve, which…

While it was defined long ago, the extension of CTL with quantification over atomic propositions has never been studied extensively. Considering two different semantics (depending whether propositional quantification refers to the Kripke…

Over the past decade a considerable amount of research has been done to expand logic programming languages to handle incomplete information. One such language is the language of epistemic specifications. As is usual with logic programming…

Definite descriptions are first-order expressions that denote unique objects. In this paper, we propose a second-order counterpart, designed to refer to unique relations between objects. We investigate this notion within the framework of…

The celebrated Kleene fixed point theorem is crucial in the mathematical modelling of recursive specifications in Denotational Semantics. In this paper we discuss whether the hypothesis of the aforementioned result can be weakened. An…

Classical results in computability theory, notably Rice's theorem, focus on the extensional content of programs, namely, on the partial recursive functions that programs compute. Later and more recent work investigated intensional…

This paper explores the intricate relationship between interpretability and robustness in deep learning models. Despite their remarkable performance across various tasks, deep learning models often exhibit critical vulnerabilities,…

The formal construction of the second-order logic or predicate calculus essentially adds quantifiers to propositional logic. Why second-order logic cannot be reduced to that of the first order? How to demonstrate that certain predicates are…

When proving theorems from large sets of logical assertions, it can be helpful to restrict the search for a proof to those assertions that are relevant, that is, closely related to the theorem in some sense. For example, in the Watson…

We prove a Kleene theorem for higher-dimensional automata. It states that the languages they recognise are precisely the rational subsumption-closed sets of finite interval pomsets. The rational operations on these languages include a…