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Giuseppe Filippone

Publications and source records attributed to Giuseppe Filippone.

7 recordsLinked to original sources
arXiv2026

Fuzzy OWL 2 Reasoning: A Re-Engineered Python Framework

In many real-world domains, knowledge is inherently vague or imprecise - features that classical ontology languages, based on crisp Description Logics (DLs), are unable to capture. This shortcoming poses particular challenges for applications in the Semantic Web and Explainable Artificial Intelligence (XAI), where robust reasoning over graded information is essential. Fuzzy ontologies address this limitation by enriching DLs with fuzzy logic, enabling the expression of partial truth and supporting more nuanced modelling of real-world knowledge. We present fuzzy-dl-owl2, a complete re-engineering in Python of the fuzzyDL reasoner and the Fuzzy OWL 2 framework. The former is an expressive fuzzy DL reasoner, while the latter allows for defining fuzzy ontologies within OWL 2. Our contribution addresses several shortcomings of the original software, including semantic inconsistencies, rigid architectural design, and limited solver integration. The re-implementation features a modular class hierarchy tailored for extensibility, supports a broader range of Mixed-Integer Linear Programming (MILP) solvers (including open-source alternatives), and corrects IRI ambiguities arising from overlapping ontological elements. Furthermore, a dedicated Python library (pyowl2) has also been developed to handle OWL 2 annotations in a standards-compliant manner, improving interoperability with existing Semantic Web tooling and resolving IRI ambiguities. The resulting framework offers a portable, extensible, and theoretically grounded platform for reasoning with fuzzy ontologies, suitable for both research and deployment in vague-aware systems. Performance tests have also been conducted that show improved execution times w.r.t. the original Java implementation. The source code and full documentation are publicly available to facilitate community adoption and further development.

math.GM↗
arXiv2024

On the number of small Steiner triple systems with Veblen points

The concept of Schreier extensions of loops was introduced in the general case in [11] and, more recently, it has been explored in the context of Steiner loops in [6]. In the latter case, it gives a powerful method for constructing Steiner triple systems containing Veblen points. Counting all Steiner triple systems of order v is an open problem for v>21. In this paper, we investigate the number of Steiner triple systems of order 19, 27 and 31 containing Veblen points and we present some examples.

math.CO↗
arXiv2023

On the Discrete Logarithm Problem for elliptic curves over local fields

The Discrete Logarithm Problem (DLP) for elliptic curves has been extensively studied since, for instance, it is the core of the security of cryptosystems like Elliptic Curve Cryptography (ECC). In this paper, we present an attack to the DLP for elliptic curves based on its connection to the problem of lifting, by using the exponential map for elliptic curves and its inverse over $ \mathbb{Z} / p^k \mathbb{Z} $. Additionally, we show that hyperelliptic curves are resistant to this attack, meaning that these latter curves offer a higher level of security compared to the classic elliptic curves used in cryptography.

math.AG↗
arXiv2023

Exp function for Edwards curves over local fields

We extend the map Exp for elliptic curves in short Weierstrass form over $ \mathbb{C} $ to Edwards curves over local fields. Subsequently, we compute the map Exp for Edwards curves over the local field $ \mathbb{Q}_{p} $ of $ p $-adic numbers.

math.NT↗
arXiv2023

Mumford representation and Riemann Roch space of a divisor on a hyperelliptic curve

For an (imaginary) hyperelliptic curve $ \mathcal{H} $ of genus $g$, with a Weierstrass point $\Omega$, taken as the point at infinity, we determine a basis of the Riemann-Roch space $\mathcal{L}(\Delta + m \Omega)$, where $\Delta$ is of degree zero, directly from the Mumford representation of $\Delta$. This provides in turn a generating matrix of a Goppa code.

math.AG↗
arXiv2023

Goppa codes over Edwards curves

Given an Edwards curve, we determine a basis for the Riemann-Roch space of any divisor whose support does not contain any of the two singular points. This basis allows us to compute a generating matrix for an algebraic-geometric Goppa code over the Edwards curve.

math.AG↗