Francesco Santini

Marco Baioletti, Francesco Santini

In this paper, we develop a way to encode several NP-Complete problems in Abstract Argumentation to Quadratic Unconstrained Binary Optimization (QUBO) problems. In this form, a solution for a QUBO problem involves minimizing a quadratic function over binary variables (0/1), where the coefficients can be represented by a symmetric square matrix (or an equivalent upper triangular version). With the QUBO formulation, exploiting new computing architectures, such as Quantum and Digital Annealers, is possible. A more conventional approach consists of developing approximate solvers, which, in this case, are used to tackle the intrinsic complexity. We performed tests to prove the correctness and applicability of classical problems in Argumentation and enforcement of argument sets. We compared our approach to two other approximate solvers in the literature during tests. In the final experimentation, we used a Simulated Annealing algorithm on a local machine. Also, we tested a Quantum Annealer from the D-Wave Ocean SDK and the Leap Quantum Cloud Service.

Ryuta Arisaka, Stefano Bistarelli, Francesco Santini

We contemplate a higher-level bipolar abstract argumentation for non-elementary arguments such as: X argues against Ys sincerity with the fact that Y has presented his argument to draw a conclusion C, by omitting other facts which would not have validated C. Argumentation involving such arguments requires us to potentially consider an argument as a coherent block of argumentation, i.e. an argument may itself be an argumentation. In this work, we formulate block argumentation as a specific instance of Dung-style bipolar abstract argumentation with the dual nature of arguments. We consider internal consistency of an argument(ation) under a set of constraints, of graphical (syntactic) and of semantic nature, and formulate acceptability semantics in relation to them. We discover that classical acceptability semantics do not in general hold good with the constraints. In particular, acceptability of unattacked arguments is not always warranted. Further, there may not be a unique minimal member in complete semantics, thus sceptic (grounded) semantics may not be its subset. To retain set-theoretically minimal semantics as a subset of complete semantics, we define semi-grounded semantics. Through comparisons, we show how the concept of block argumentation may further generalise structured argumentation.

Stefano Bistarelli, Francesco Santini, Carlo Taticchi

We study invariant local expansion operators for conflict-free and admissible sets in Abstract Argumentation Frameworks (AFs). Such operators are directly applied on AFs, and are invariant with respect to a chosen "semantics" (that is w.r.t. each of the conflict free/admissible set of arguments). Accordingly, we derive a definition of robustness for AFs in terms of the number of times such operators can be applied without producing any change in the chosen semantics.

Fabio Martinelli, Ilaria Matteucci, Francesco Santini

Our goal is to provide different semiring-based formal tools for the specification of security requirements: we quantitatively enhance the open-system approach, according to which a system is partially specified. Therefore, we suppose the existence of an unknown and possibly malicious agent that interacts in parallel with the system. Two specification frameworks are designed along two different (but still related) lines. First, by comparing the behaviour of a system with the expected one, or by checking if such system satisfies some security requirements: we investigate a novel approximate behavioural-equivalence for comparing processes behaviour, thus extending the Generalised Non Deducibility on Composition (GNDC) approach with scores. As a second result, we equip a modal logic with semiring values with the purpose to have a weight related to the satisfaction of a formula that specifies some requested property. Finally, we generalise the classical partial model-checking function, and we name it as quantitative partial model-checking in such a way to point out the necessary and sufficient conditions that a system has to satisfy in order to be considered as secure, with respect to a fixed security/functionality threshold-value.