Bruno Lopes

Propositional dynamic logic for Petri nets

Propositional Dynamic Logic (PDL) is a multi-modal logic used for specifying and reasoning on sequential programs. Petri Net is a widely used formalism to specify and to analyse concurrent programs with a very nice graphical representation. In this work, we propose a PDL to reasoning about Petri Nets. First we define a compositional encoding of Petri Nets from basic nets as terms. Second, we use these terms as PDL programs and provide a compositional semantics to PDL Formulas. Finally, we present an axiomatization and prove completeness w.r.t. our semantics. The advantage of our approach is that we can do reasoning about Petri Nets using our dynamic logic and we do not need to to translate it to other formalisms. Moreover our approach is compositional allowing for construction of complex nets using basic ones.

Reasoning about Multi-Agent Systems Using Stochastic Petri Nets

Multi-agent systems are composed by many independent agents where the task of some of them may depend on the task of others. In this work we present a generic Stochastic Petri Net model for agents and illustrate the usage of a sound, complete and decidable logic system to verify properties in multi-agent systems modelled as Stochastic Petri Nets: the \(\mathcal{DS}_3\) logic. This logic takes advantage of the intuitive graphical interpretation of Petri Nets, allowing the user to model the behaviour of agents and their interactions by means of nets (i.e. seen Petri Nets as graphs). Our approach leads not only to a usual place-transition connection provided by Petri-nets underlying graphs modelling, such as the verification of properties and validation of agents, but also regards the verification of properties concerning their behaviour inside an environment.

Towards Reasoning in Dynamic Logics with Rewriting Logic: The Petri-PDL Case

Safety is a desired property in software to ensure that no unforeseen scenarios will be achieved and in concurrent systems the variety of scenarios increase with complexity. Dynamic Logics (DL) present a large body of techniques to reason about and certify systems. Modelling and assessing concurrent systems with a formal semantics leads to the possibility of proving that they comply with their specification. Petri nets fulfill these requirements as a formal modelling language comprising a wide body of tools and an intuitive graphical interpretation. Petri-PDL puts together DL with Petri nets, providing a theoretical background to reason about Petri nets, inheriting their properties with all the techniques available for DL. This work presents a prototype implementation, in the Rewriting Logic language Maude, of a bounded model checker for Petri-PDL. The Petri-PDL model checker is formally designed following the representation of Kripke models as rewrite theories defined for the Linear Temporal Logic model checker available in the Maude system.

A Calculus for Automatic Verification of Petri Nets Based on Resolution and Dynamic Logics

Petri Nets are a widely used formalism to deal with concurrent systems. Dynamic Logics (DL) are a family of modal logics where each modality corresponds to a program. This works presents a resolution-based method for Petri-PDL, a DL where programs are replaced by Petri Nets. We present a procedure to convert any Petri-PDL formula into a normal form, a set of resolution-based inference rules, examples of application of the method, and discuss soundness and completeness.

Propositional Dynamic Logic for Petri Nets with Iteration

This work extends our previous work [20] with the iteration operator. This new operator allows for representing more general networks and thus enhancing the former propositional logic for Petri Nets. We provide an axiomatization and a new semantics and prove soundness and completeness with respect with its semantics. In order to illustrate its usage, we also provide some examples.

Towards reasoning about Petri nets: A Propositional Dynamic Logic based approach

Abstract This work extends our previous work [4] , [22] with the iteration operator. This new operator allows for representing more general networks and thus enhancing the former propositional logic for Petri nets. We provide an axiomatization and a new semantics, prove soundness and completeness with respect to its semantics and the EXPTIME-Hardness of its satisfiability problem, present a linear model checking algorithm and show that its satisfiability problem is in 2EXPTIME. In order to illustrate its usage, we also provide some examples.