Related papers: Adding the Power-Set to Description Logics
One approach for interpreting black-box machine learning models is to find a global approximation of the model using simple interpretable functions, which is called a metamodel (a model of the model). Approximating the black-box with a…
Analogical reasoning is a hallmark of human intelligence, enabling us to solve new problems by transferring knowledge from one situation to another. Yet, developing artificial intelligence systems capable of robust human-like analogical…
$\omega$-regular languages are a natural extension of the regular languages to the setting of infinite words. Likewise, they are recognised by a host of automata models, one of the most important being Alternating Parity Automata (APAs), a…
Recent years have seen important advances in the building of interpretable models, machine learning models that are designed to be easily understood by humans. In this work, we show that large language models (LLMs) are remarkably good at…
Ontologies are a popular way of representing domain knowledge, in particular, knowledge in domains related to life sciences. (Semi-)automating the process of building an ontology has attracted researchers from different communities into a…
Non-classical generalizations of classical modal logic have been developed in the contexts of constructive mathematics and natural language semantics. In this paper, we discuss a general approach to the semantics of non-classical modal…
Understanding when linear immersions of nonlinear dynamical systems exist is important since such immersions allow us to leverage the rich tools of linear system theory to analyze nonlinear dynamics. Recently, Liu et al. (2023) showed that…
Writing temporal logic properties is often a challenging task for users of model-based development frameworks, particularly when translating informal requirements into formal specifications. In this paper, we explore the idea of integrating…
The term {\em meta-programming} refers to the ability of writing programs that have other programs as data and exploit their semantics. The aim of this paper is presenting a methodology allowing us to perform a correct termination analysis…
We introduce ontology-to-tools compilation as a proof-of-principle mechanism for coupling large language models (LLMs) with formal domain knowledge. Within The World Avatar (TWA), ontological specifications are compiled into executable tool…
Orbit-finite models of computation generalise the standard models of computation, to allow computation over infinite objects that are finite up to symmetries on atoms, denoted by $\mathbb{A}$. Set theory with atoms is used to reason about…
The ability of Large Language Models (LLMs) to perform reasoning tasks such as deduction has been widely investigated in recent years. Yet, their capacity to generate proofs-faithful, human-readable explanations of why conclusions…
Algebraic theories with dependency between sorts form the structural core of Martin-L\"of type theory and similar systems. Their denotational semantics are typically studied using categorical techniques; many different categorical…
OWL ontologies, whose formal semantics are rooted in Description Logic (DL), have been widely used for knowledge representation. Similar to Knowledge Graphs (KGs), ontologies are often incomplete, and maintaining and constructing them has…
Recent advancements in transformer-based models have initiated research interests in investigating their ability to learn to perform reasoning tasks. However, most of the contexts used for this purpose are in practice very simple: generated…
The recently introduced series of description logics under the common moniker DL-Lite has attracted attention of the description logic and semantic web communities due to the low computational complexity of inference, on the one hand, and…
In previous papers on this project a general static logical framework for formalizing and mechanizing set theories of different strength was suggested, and the power of some predicatively acceptable theories in that framework was explored.…
If $\mathcal{L}$ is an abstract logic (a.k.a. model theoretic logic), we can define the inner model $C(\mathcal{L})$ by replacing first order logic with $\mathcal{L}$ in G\"odel's definition of the inner model $L$ of constructible sets. Set…
Various topological concepts are often involved in the research of mathematical logic, and almost all of these concepts can be regarded as developing from the Stone representation theorem. In the Stone representation theorem, a Boolean…
This paper revisits the multi-agent epistemic logic presented in [10], where agents and sets of agents are replaced by abstract, intensional "names". We make three contributions. First, we study its model theory, providing adequate notions…