Francesco Belardinelli

Algebraic aspects of cut elimination

We will give here a purely algebraic proof of the cut elimination theorem for various sequent systems. Our basic idea is to introduce mathematical structures, called Gentzen structures, for a given sequent system without cut, and then to show the completeness of the sequent system without cut with respect to the class of algebras for the sequent system with cut, by using the quasi-completion of these Gentzen structures. It is shown that the quasi-completion is a generalization of the MacNeille completion. Moreover, the finite model property is obtained for many cases, by modifying our completeness proof. This is an algebraic presentation of the proof of the finite model property discussed by Lafont [12] and Okada-Terui [17].

Verification of deployed artifact systems via data abstraction

Artifact systems are a novel paradigm for specifying and implementing business processes described in terms of interacting modules called artifacts. Artifacts consist of data and lifecycle models, accounting for the relational structure of the artifact state and its possible evolutions over time. We consider the problem of verifying artifact systems against specifications expressed in quantified temporal logic. This problem is in general undecidable. However, when artifact systems are deployed, their states can contain only a bounded number of elements. We exploit this fact to develop an abstraction technique that enables us to verify deployed artifact systems by model checking their bounded abstraction.

Quantified epistemic logics for reasoning about knowledge in multi-agent systems

We introduce quantified interpreted systems, a semantics to reason about knowledge in multi-agent systems in a first-order setting. Quantified interpreted systems may be used to interpret a variety of first-order modal epistemic languages with global and local terms, quantifiers, and individual and distributed knowledge operators for the agents in the system. We define first-order modal axiomatisations for different settings, and show that they are sound and complete with respect to the corresponding semantical classes. The expressibility potential of the formalism is explored by analysing two MAS scenarios: an infinite version of the muddy children problem, a typical epistemic puzzle, and a version of the battlefield game. Furthermore, we apply the theoretical results here presented to the analysis of message passing systems [R. Fagin, J. Halpern, Y. Moses, M. Vardi, Reasoning about Knowledge, MIT Press, 1995; L. Lamport, Time, clocks, and the ordering of events in a distributed system, Communication of the ACM 21 (7) (1978) 558-565], and compare the results obtained to their propositional counterparts. By doing so we find that key known meta-theorems of the propositional case can be expressed as validities on the corresponding class of quantified interpreted systems.

Interactions between knowledge and time in a first-order logic for multi-agent systems: completeness results

We investigate a class of first-order temporal-epistemic logics for reasoning about multiagent systems. We encode typical properties of systems including perfect recall, synchronicity, no learning, and having a unique initial state in terms of variants of quantified interpreted systems, a first-order extension of interpreted systems. We identify several monodic fragments of first-order temporal-epistemic logic and show their completeness with respect to their corresponding classes of quantified interpreted systems.

A computationally-grounded semantics for artifact-centric systems and abstraction results

We present a formal investigation of artifact-based systems, a relatively novel framework in service oriented computing, aimed at laying the foundations for verifying these systems through model checking. We present an infinite-state, computationally grounded semantics for these systems that allows us to reason about temporal-epistemic specifications. We present abstraction techniques for the semantics that guarantee transfer of satisfaction from the abstract system to the concrete one.

First-Order Linear-time Epistemic Logic with Group Knowledge: An Axiomatisation of the Monodic Fragment

We investigate quantified interpreted systems, a computationally grounded semantics for a first-order temporal epistemic logic on linear time. We report a completeness result for the monodic fragment of a language that includes LTL modalities as well as distributed and common knowledge. We exemplify possible uses of the formalism by analysing message passing systems, a typical framework for distributed systems, in a first-order setting.

Model Checking Temporal-Epistemic Logic Using Alternating Tree Automata

We introduce a novel automata-theoretic approach for the verification of multi-agent systems. We present epistemic alternating tree automata, an extension of alternating tree automata, and use them to represent specifications in the temporal-epistemic logic CTLK. We show that model checking a memory-less interpreted system against a CTLK property can be reduced to checking the language non-emptiness of the composition of two epistemic tree automata. We report on an experimental implementation and discuss preliminary results. We evaluate the effectiveness of the technique using two real-life scenarios: a gossip protocol and the train gate controller.

A quantified epistemic logic for reasoning about multiagent systems

We investigate quantified interpreted systems, a semantics for multiagent systems in which agents can reason about individuals, their properties, and the relationships among them. We analyse a first-order epistemic language interpreted on this semantics and show soundness and completeness of Q.S5n, an axiomatisation for these structures.

A Complete Quantified Epistemic Logic for Reasoning about Message Passing Systems

We investigate quantified interpreted systems, a semantics to model multi-agent systems in which the agents can reason about individuals, their properties, and relationships among them. The semantics naturally extends interpreted systems to first-order by introducing a domain of individuals. We present a first-order epistemic language interpreted on this semantics and prove soundness and completeness of the quantified modal system

Verification of Broadcasting Multi-Agent Systems against an Epistemic Strategy Logic

QS5^{D}_n