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In the course of classifying the homogeneous permutations, Cameron introduced the viewpoint of permutations as structures in a language of two linear orders, and this structural viewpoint is taken up here. The majority of this thesis is…
We construct extended TQFTs associated to Rozansky--Witten models with target manifolds $T^*\mathbb{C}^n$. The starting point of the construction is the 3-category whose objects are such Rozansky--Witten models, and whose morphisms are…
Transformer language models are state of the art in a multitude of NLP tasks. Despite these successes, their opaqueness remains problematic. Recent methods aiming to provide interpretability and explainability to black-box models primarily…
The stable model semantics had been recently generalized to non-Herbrand structures by several works, which provides a unified framework and solid logical foundations for answer set programming. This paper focuses on the expressiveness of…
The ability to interpret machine learning models has become increasingly important now that machine learning is used to inform consequential decisions. We propose an approach called model extraction for interpreting complex, blackbox…
The terms 'semantics' and 'ontology' are increasingly appearing together with 'explanation', not only in the scientific literature, but also in organizational communication. However, all of these terms are also being significantly…
This paper investigates the contingency of logic within the framework of possible world semantics. Possible world semantics captures the meaning of necessitation, i.e., a statement is necessarily true if it holds in all possible worlds.…
It is here proposed an analysis of symbolic and sub-symbolic models for studying cognitive processes, centered on emergence and logical openness notions.The Theory of Logical Openness connects the Physics of system/environment relationships…
We present a construction of nondeterministic semantics for some deontic logics based on the class of paraconsistent logics known as Logics of Formal Inconsistency (LFIs), for the first time combining swap structures and Kripke models…
In a series of papers, a many-minds interpretation of quantum theory has been developed. The aim in these papers is to present an explicit mathematical formalism which constitutes a complete theory compatible with relativistic quantum field…
We reformulate known exotic theories (including theories of fractons) on a Euclidean spacetime lattice. We write them using the Villain approach and then we modify them to a convenient range of parameters. The new lattice models are closer…
We systematically investigate the complexity of model checking the existential positive fragment of first-order logic. In particular, for a set of existential positive sentences, we consider model checking where the sentence is restricted…
This paper develops a categorical framework to clarify the relationship between the completeness and compactness theorems in classical first-order logic. Rather than claiming that different model constructions yield naturally isomorphic…
The paper proves finite model property and decidability for a family of modal logics. A binary relation $R$ is called pretransitive, if $R^*=\cup_{i\leq m} R^i$ for some $m\geq 0$, where $R^*$ is the transitive reflexive closure of $R$. By…
Uncertainty plays a crucial role in the machine learning field. Both model trustworthiness and performance require the understanding of uncertainty, especially for models used in high-stake applications where errors can cause cataclysmic…
Decomposition of text into atomic propositions is a flexible framework allowing for the closer inspection of input and output text. We use atomic decomposition of hypotheses in two natural language reasoning tasks, traditional NLI and…
Various research initiatives try to utilize the operational principles of organisms and brains to develop alternative, biologically inspired computing paradigms and artificial cognitive systems. This paper reviews key features of the…
In this contribution we revisit regular model checking, a powerful framework that has been successfully applied for the verification of infinite-state systems, especially parameterized systems (concurrent systems with an arbitrary number of…
We present a two-level theory to formalize constructive mathematics as advocated in a previous paper with G. Sambin. One level is given by an intensional type theory, called Minimal type theory. This theory extends the set-theoretic version…
(Pre)closure spaces are a generalization of topological spaces covering also the notion of neighbourhood in discrete structures, widely used to model and reason about spatial aspects of distributed systems. In this paper we introduce an…