9 papers
A Linear Temporal Logic of Frequencies on Series of Events
Melissa Antonelli, Leonardo Ceragioli, Alessandro Giuseppe Buda +1
This paper introduces LTLF, a temporal logic designed to express the frequency properties of event series in a natural but rigorous manner. By introducing novel, measure-sensitive…
Counting Worlds Branching Time Semantics for post-hoc Bias Mitigation in generative AI
Alessandro G. Buda, Giuseppe Primiero, Leonardo Ceragioli +1
Generative AI systems are known to amplify biases present in their training data. While several inference-time mitigation strategies have been proposed, they remain largely empiric…
On Randomized Computational Models and Complexity Classes: a Historical Overview
Melissa Antonelli, Ugo Dal Lago, Paolo Pistone
Since their appearance in the 1950s, computational models capable of performing probabilistic choices have received wide attention and are nowadays pervasive in almost every areas…
Enumerating Error Bounded Polytime Algorithms Through Arithmetical Theories
Melissa Antonelli, Ugo Dal Lago, Davide Davoli +2
We consider a minimal extension of the language of arithmetic, such that the bounded formulas provably total in a suitably-defined theory à la Buss (expressed in this new language)…
An Arithmetic Theory for the Poly-Time Random Functions
Melissa Antonelli, Ugo Dal Lago, Davide Davoli +2
We introduce a new bounded theory RS^1_2 and show that the functions which are Sigma^b_1-representable in it are precisely random functions which can be computed in polynomial time…
Some Remarks on Counting Propositional Logic
Melissa Antonelli
Counting propositional logic was recently introduced in relation to randomized computation and shown able to logically characterize the full counting hierarchy. In this paper we ai…
Curry and Howard Meet Borel
Melissa Antonelli, Ugo Dal Lago, Paolo Pistone
We show that an intuitionistic version of counting propositional logic corresponds, in the sense of Curry and Howard, to an expressive type system for the probabilistic event lambd…
On Measure Quantifiers in First-Order Arithmetic (Long Version)
Melissa Antonelli, Ugo Dal Lago, Paolo Pistone
We study the logic obtained by endowing the language of first-order arithmetic with second-order measure quantifiers. This new kind of quantification allows us to express that the…
On Counting Propositional Logic
Melissa Antonelli, Ugo Dal Lago, Paolo Pistone
We study counting propositional logic as an extension of propositional logic with counting quantifiers. We prove that the complexity of the underlying decision problem perfectly ma…