arXiv subjects

Francesco A. Genco

Publications and source records attributed to Francesco A. Genco.

11 recordsLinked to original sources

arXiv2026

A Strongly Normalising System of Dependent Types for Transparent and Opaque Probabilistic Computation

We define an extension of lambda-calculus with dependents types that enables us to encode transparent and opaque probabilistic programs and prove a strong normalisation result for it by a reducibility technique. While transparent nondeterministic programs are formalised by rather usual techniques, opaque nondeterministic programs are formalised by introducing in the syntax oracle constants, the behaviour of which is governed by oracular functions. The generality of these functions and the fact that their values are determined by the form of the whole term inside which the relative oracle occurs also enable us to simulate learning-like behaviours. We then extend the calculus in order to define a computational trustworthiness predicate. The extension of the calculus does not only enable us to precisely formalise a notion of trustworthiness and to encode the procedures required to test it on programs, but also to reason, by means of the type system, on the behaviour of programs with respect to trustworthiness.

cs.LO↗

arXiv2025

A Logic of Knowledge and Justifications, with an Application to Computational Trust

We present a logical framework that enables us to define a formal theory of computational trust in which this notion is analysed in terms of epistemic attitudes towards the possible objects of trust and in relation to existing evidence in favour of the trustworthiness of these objects. The framework is based on a quantified epistemic and justification logic featuring a non-standard handling of identities. Thus, the theory is able to account for the hyperintensional nature of computational trust. We present a proof system and a frame semantics for the logic, we prove soundness and completeness results and we introduce the syntactical machinery required to define a theory of trust.

cs.LO↗

arXiv2025

A Direct Characterisation of Logical Grounds and a Decidability Proof

We present a standard calculus for logical grounding based on well-established grounding principles [Schnieder, 2011, Fine, 2012, Correia, 2014, Correia, 2024] and provide a very direct characterisation of the provable grounding claims exclusively relying on the syntactic tree of the grounded formula. The technical features of the characterisation imply that the grounding relation induced by the calculus is decidable.

math.LO↗

arXiv2025

A Typed Lambda-Calculus for Establishing Trust in Probabilistic Programs

The extensive deployment of probabilistic algorithms has radically changed our perspective on several well-established computational notions. Correctness is probably the most basic one. While a typical probabilistic program cannot be said to compute the correct result, we often have quite strong expectations about the frequency with which it should return certain outputs. In these cases, trust as a generalisation of correctness fares better. One way to understand it is to say that a probabilistic computational process is trustworthy if the frequency of its outputs is compliant with a probability distribution which models its expected behaviour. We present a formal computational framework that formalises this idea. In order to do so, we define a typed lambda-calculus that features operators for conducting experiments at runtime on probabilistic programs and for evaluating whether they compute outputs as determined by a target probability distribution. After proving some fundamental computational properties of the calculus, such as progress and termination, we define a static notion of confidence that allows to prove that our notion of trust behaves correctly with respect to the basic tenets of probability theory.

cs.LO↗

arXiv2024

Evaluating AI fairness in credit scoring with the BRIO tool

We present a method for quantitative, in-depth analyses of fairness issues in AI systems with an application to credit scoring. To this aim we use BRIO, a tool for the evaluation of AI systems with respect to social unfairness and, more in general, ethically undesirable behaviours. It features a model-agnostic bias detection module, presented in \cite{DBLP:conf/beware/CoragliaDGGPPQ23}, to which a full-fledged unfairness risk evaluation module is added. As a case study, we focus on the context of credit scoring, analysing the UCI German Credit Dataset \cite{misc_statlog_(german_credit_data)_144}. We apply the BRIO fairness metrics to several, socially sensitive attributes featured in the German Credit Dataset, quantifying fairness across various demographic segments, with the aim of identifying potential sources of bias and discrimination in a credit scoring model. We conclude by combining our results with a revenue analysis.

cs.AI↗

arXiv2023

Grounding Operators: Transitivity and Trees, Logicality and Balance

We formally investigate immediate and mediate grounding operators from an inferential perspective. We discuss the differences in behaviour displayed by several grounding operators and consider a general distinction between grounding and logical operators. Without fixing a particular notion of grounding or grounding relation, we present inferential rules that define, once a base grounding calculus has been fixed, three grounding operators: an operator for immediate grounding, one for mediate grounding (corresponding to the transitive closure of the immediate grounding one) and a grounding tree operator, which enables us to internalise chains of immediate grounding claims without loosing any information about them. We then present an in-depth proof-theoretical study of the introduced rules by focusing, in particular, on the question whether grounding operators can be considered as logical operators and whether balanced rules for grounding operators can be defined.

math.LO↗

arXiv2020

A typed parallel λ-calculus via 1-depth intermediate proofs

We introduce a Curry-Howard correspondence for a large class of intermediate logics characterized by intuitionistic proofs with non-nested applications of rules for classical disjunctive tautologies (1-depth intermediate proofs). The resulting calculus, we call it $λ_{\parallel}$, is a strongly normalizing parallel extension of the simply typed $λ$-calculus. Although simple, the $λ_{\parallel}$ reduction rules can model arbitrary process network topologies, and encode interesting parallel programs ranging from numeric computation to algorithms on graphs.

cs.LO↗

arXiv2019

$\unicode{8523}$ means Parallel: Multiplicative Linear Logic Proofs as Concurrent Functional Programs

Along the lines of the Abramsky ``Proofs-as-Processes'' program, we present an interpretation of multiplicative linear logic as typing system for concurrent functional programming. In particular, we study a linear multiple-conclusion natural deduction system and show it is isomorphic to a simple and natural extension of $λ$-calculus with parallelism and communication primitives, called $λ_{\unicode{8523}}$. We shall prove that $λ_{\unicode{8523}}$ satisfies all the desirable properties for a typed programming language: subject reduction, progress, strong normalization and confluence.

cs.LO↗

arXiv2018

Hypersequents and Systems of Rules: Embeddings and Applications

We define a bi-directional embedding between hypersequent calculi and a subclass of systems of rules (2-systems). In addition to showing that the two proof frameworks have the same expressive power, the embedding allows for the recovery of the benefits of locality for 2-systems, analyticity results for a large class of such systems, and a rewriting of hypersequent rules as natural deduction rules.

math.LO↗

arXiv2017

Gödel Logic: from Natural Deduction to Parallel Computation

Propositional Gödel logic extends intuitionistic logic with the non-constructive principle of linearity $A\rightarrow B\ \lor\ B\rightarrow A$. We introduce a Curry-Howard correspondence for this logic and show that a particularly simple natural deduction calculus can be used as a typing system. The resulting functional language enriches the simply typed lambda calculus with a synchronous communication mechanism between parallel processes. Our normalization proof employs original termination arguments and sophisticated proof transformations with a meaningful computational reading. Our results provide a computational interpretation of Gödel logic as a logic of communicating parallel processes, thus proving Avron's 1991 conjecture.

cs.LO↗

arXiv2017

Mīmā\d{m}sā deontic logic: proof theory and applications

Starting with the deontic principles in M\=ımā\d{m}sā texts we introduce a new deontic logic. We use general proof-theoretic methods to obtain a cut-free sequent calculus for this logic, resulting in decidability, complexity results and neighbourhood semantics. The latter is used to analyse a well known example of conflicting obligations from the Vedas.

cs.LO↗