arXiv subjects
Publications and source records attributed to Davide Catta.
IMITATOR4AMAS supports model checking and synthesis of memoryless imperfect information strategies for STCTL, interpreted over networks of parametric timed automata with asynchronous execution. While extending the verifier IMITATOR, IMITATOR4AMAS is the first tool for strategy synthesis in this setting. Our experimental results show a substantial speedup over previous approaches.
In recent years, there has been growing interest in logics that formalise strategic reasoning about agents capable of modifying the structure of a given model. This line of research has been motivated by applications where a modelled system evolves over time, such as communication networks, security protocols, and multi-agent planning. In this paper, we introduce three logics for reasoning about strategies that modify the topology of weighted graphs. In Strategic Deconstruction Logic, a destructive agent (the demon) removes edges up to a certain cost. In Strategic Construction Logic, a constructive agent (the angel) adds edges within a cost bound. Finally, Strategic Update Logic combines both agents, who may cooperate or compete. We study the expressive power of these logics and the complexity of their model checking problems.
We introduce First-Order Coalition Logic ($\mathsf{FOCL}$), which combines key intuitions behind Coalition Logic ($\mathsf{CL}$) and Strategy Logic ($\mathsf{SL}$). Specifically, $\mathsf{FOCL}$ allows for arbitrary quantification over actions of agents. $\mathsf{FOCL}$ is interesting for several reasons. First, we show that $\mathsf{FOCL}$ is strictly more expressive than existing coalition logics. Second, we provide a sound and complete axiomatisation of $\mathsf{FOCL}$, which, to the best of our knowledge, is the first axiomatisation of any variant of $\mathsf{SL}$ in the literature. Finally, while discussing the satisfiability problem for $\mathsf{FOCL}$, we reopen the question of the recursive axiomatisability of $\mathsf{SL}$.
In this paper, we propose to connect Prawitz's theory of grounds with Girard's Ludics. This connection is carried out on two levels. On a more philosophical one, we highlight some differences between Prawitz's and Girard's approaches, but we also argue that they share some basic ideas about proofs and deduction. On a more formal one, we sketch an indicative translation of Prawitz's theory grounds into Girard's Ludics relative to the implicational fragment of propositional intuitionistic logic. This may allow for a dialogical reading of Prawitz's ground-theoretic approach. Moreover, it becomes possible to provide a formal definition of a notion of ground-candidate introduced by Cozzo.
In this paper, we define an intuitionistic version of Computation Tree Logic. After explaining the semantic features of intuitionistic logic, we examine how these characteristics can be interesting for formal verification purposes. Subsequently, we define the syntax and semantics of our intuitionistic version of CTL and study some simple properties of the so obtained logic. We conclude by demonstrating that some fixed-point axioms of CTL are not valid in the intuitionistic version of CTL we have defined.
In this paper we investigate the Curry-Howard correspondence for constructive modal logic in light of the gap between the proof equivalences enforced by the lambda calculi from the literature and by the recently defined winning strategies for this logic. We define a new lambda-calculus for a minimal constructive modal logic by enriching the calculus from the literature with additional reduction rules and we prove normalization and confluence for our calculus. We then provide a typing system in the style of focused proof systems allowing us to provide a unique proof for each term in normal form, and we use this result to show a one-to-one correspondence between terms in normal form and winning innocent strategies.
In this paper we provide two new semantics for proofs in the constructive modal logics CK and CD. The first semantics is given by extending the syntax of combinatorial proofs for propositional intuitionistic logic, in which proofs are factorised in a linear fragment (arena net) and a parallel weakening-contraction fragment (skew fibration). In particular we provide an encoding of modal formulas by means of directed graphs (modal arenas), and an encoding of linear proofs as modal arenas equipped with vertex partitions satisfying topological criteria. The second semantics is given by means of winning innocent strategies of a two-player game over modal arenas. This is given by extending the Heijltjes-Hughes-Straßburger correspondence between intuitionistic combinatorial proofs and winning innocent strategies in a Hyland-Ong arena. Using our first result, we provide a characterisation of winning strategies for games on a modal arena corresponding to proofs with modalities.
In this chapter, we introduce a new dialogical system for first order classical logic which is close to natural language argumentation, and we prove its completeness with respect to usual classical validity. We combine our dialogical system with the Grail syntactic and semantic parser developed by the second author in order to address automated textual entailment, that is, we use it for deciding whether or not a sentence is a consequence of a short text. This work-which connects natural language semantics and argumentation with dialogical logic-can be viewed as a step towards an inferentialist view of natural language semantics.