In this paper, we present a dynamic logic with parallel operators for the formal verification of authenticity and safety properties of cryptographic protocols. The logic incorporates communication actions and is specifically designed to reason about protocol executions in adversarial environments. We extend an existing dynamic logic with parallel operators by introducing concepts derived from the Dolev-Yao intruder model. As the underlying logic is completely axiomatizable, we obtain a complete axiomatization for the extended system. Furthermore, we develop a tableau calculus for the proposed logic and prove its termination, soundness, and completeness.

Guarded Kleene Algebra with Tests (GKAT) was presented as a fragment of KAT to abstract imperative programming languages, where only if-then-else and while-do statements are allowed in the language. The loss of expressiveness is, nevertheless, compensated by a clear advantage over KAT: it allows almost linear decidability of program equivalence. In this work, we give the first step to optimizing the complexity of dynamic logic equivalence, which is EXPTIME-complete in propositional dynamic logic (PDL). First, and based on strict deterministic PDL, we present guarded propositional dynamic logic (GPDL), a fragment of PDL where programs correspond to GKAT terms. It comes embedded, as expected, with a semantics over relational models and a sound axiomatisation. Then, we present a Natural Deduction system for GPDL, proving its soundness and completeness, concerning the axiomatisation. Based on Smolka et al. (2019, Proceedings of the ACM Programming Language 4), we obtain the main result of this work-the equivalence of GPDL programs can be established in almost linear time.

This paper introduces two logic frameworks for the study of SIR (Susceptible-Infected-Recovered) and SIRS compartmental epidemic models, one based on Linear Temporal Logic and the other on Computation Tree Logic. We provide a short literature overview on compartmental models and other related works using logics, and then define our logics with their respective axiomatizations, and demonstrate their soundness and completeness proofs.

Given the increasing importance of security protocols in our daily activities and communication via internet, the efforts to develop mechanisms and models for verification of such protocols are always relevant. In this work, we explore the Dolev-Yao Multi-Agent Epistemic Logic by providing a tableaux method for it. This logic is an extension of Multi-Agent Epistemic Logic, aimed to verify authenticity and safety in communication protocols and inspired by the Dolev-Yao model, a seminal work in formal cryptography.

This work introduces a new fuzzy epistemic logic with public announcement with fuzzyness on both transitions and propositions. The interpretation of the connectives is done over the Gödel algebra and the interpretation of public announcements in this logic generalises the traditional update one. The core idea is that, the effect of a public announcement is reflected on the transitions degrees of the models. The update takes in account not only the truth degree of the announcement, at a target state, but also the degree of the transitions reaching that state. We prove the soundness of all axioms of the multi-agent epistemic logic with public announcements with respect to this graded semantics. Finally, we introduce the notion of bisimulation and prove the modal invariance property for our logic.

This paper introduces a logic with a class of social network models that is based on standard Linear Temporal Logic (LTL), leveraging the power of existing model checkers for the analysis of social networks. We provide a short literature overview, and then define our logic and its axiomatization, present some simple motivational examples of both models and formulas, and show its soundness and completeness via a translation into propositional formulas. Lastly, we briefly discuss model checking and time complexity analysis.

Dynamic Epistemic Logic (DEL) is used in the analysis of a wide class of application scenarios involving multi-agents systems with local perceptions of information and knowledge. In its classical form, the knowledge of epistemic states is represented by sets of propositions. However, the complexity of the current systems, requires other richer structures, than sets of propositions, to represent knowledge on their epistemic states. Algebras, graphs or distributions are examples of useful structures for this end. Based on this observation, we introduced a parametric method to build dynamic epistemic logics on-demand, taking as parameter the specific knowledge representation framework (e.g., propositional, equational or even a modal logic) that better fits the problems in hand. In order to use the built logics in practices, tools support is needed. Based on this, we extended our previous method with a parametric construction of complete proof calculi. The complexity of the model checking and satisfiability problems for the achieved logics are provided.

This paper presents an on going work on Propositional Dynamic Logic PDL in which atomic programs are STRIPS actions. We think that this new framework is appropriate to reasoning about actions and plans when dealing with planning problem. Unlike, PDL atomic programs, STRIPS actions have pre-conditions and post-conditions. We propose a novel operator of action composition that takes in account the features of STRIPS actions. We propose an axiomatization and prove its soundness. Completeness, decidability and computational complexity are left as future work.

Populational Announcement Logic (PPAL), is a variant of the standard Public Announcement Logic (PAL) with a fuzzy-inspired semantics, where instead of specific agents we have populations and groups. The semantics and the announcement logic are defined, and an example is provided. We show validities analogous to PAL axioms and their proofs, and also provide a proof of decidability. We briefly talk about model checking and compare the framework against probabilistic logic. We conclude that the main advantage of PPAL over PAL is the flexibility to work with previously defined agents.

The DALI 2017 proceedings book is focusing on the theoretical relevance and practical potential of dynamic logic.

This work proposes a Dynamic Epistemic Logic with Communication Actions that can be performed concurrently. Unlike Concurrent Epistemic Action Logic introduced by Ditmarsch, Hoek and Kooi [van Ditmarsch, H., W. van der Hoek and B. Kooi, “Concurrent Dynamic Epistemic Logic,” Kluwer, Ed. V.F. Hendricks et al., vol. 322, 2003], where the concurrency mechanism is the so called true concurrency, here we use an approach based on process calculus, like CCS and CSP, and Action Models Logic. Our approach makes possible the proof of soundness, completeness and decidability, different from the others approaches. We present an axiomatisation and show that the proof of soundness, completeness and decidability can be done using a reduction method.

Petri nets play a central role in the formal modelling of a wide range of complex systems and scenarios. Their ability to handle with both concurrency and resource awareness justifies their spread in the current formal development practices. On the logic side, Dynamic Logics are widely accepted as the de facto formalisms to reason about computational systems. However, as usual, the application to new situations raises new challenges and issues. The ubiquity of failures in the execution of current systems, interpreted in these models as triggered events that are not followed by the corresponding transition, entails not only the adjustment of these structures to deal with this reality, but also the introduction of new logics adequate to this emerging phenomenon. This paper contributes to this challenge by exploring a combination of two previous works of the authors, namely the Propositional Dynamic Logic for Petri Nets [ 1 ] and a parametric construction of multi-valued dynamic logics presented in [ 13 ]. This exercise results in a new family of Dynamic Logics for Petri Nets suitable to deal with firing failures.

Multi-agent Dynamic Epistemic Logic, as a suitable modal logic to reason about knowledge evolving systems, has emerged in a number of contexts and scenarios. The agents knowledge in this logic is simply characterised by valuations of propositions. This paper discusses the adoption of other richer structures to make these representations, as graphs, algebras or even epistemic models. This method of building epistemic logics over richer structures is called “Epistemisation”. On this view a parametric method to build such Epistemic Logics with Public Announcements is introduced. Moreover, a parametric notion of bisimulation is presented, and the modal invariance of the proposed logics, with respect to this relation, are proved. Some interesting application horizons opened with this construction are stated.

We introduce a general approach, based on diagrams, to the specification and construction of model checkers. This approach gives general model checkers that can be instantiated to a model checker for a specific modal logic with semantics described by graphical rules. This paper proposes a way of combining graphical and general approaches to model checking so that the instantiation to specific logics is user-friendly and natural.

Multi-Agent Epistemic Logic has been investigated in Computer Science [Fagin, R., J. Halpern, Y. Moses and M. Vardi, “Reasoning about Knowledge,” MIT Press, USA, 1995] to represent and reason about agents or groups of agents knowledge and beliefs. Some extensions aimed to reasoning about knowledge and probabilities [Fagin, R. and J. Halpern, Reasoning about knowledge and probability, Journal of the ACM 41 (1994), pp. 340–367] and also with a fuzzy semantics have been proposed [Fitting, M., Many-valued modal logics, Fundam. Inform. 15 (1991), pp. 235–254; Maruyama, Y., Reasoning about fuzzy belief and common belief: With emphasis on incomparable beliefs, in: IJCAI 2011, Proceedings of the 22nd International Joint Conference on Artificial Intelligence, Barcelona, Catalonia, Spain, July 16–22, 2011, 2011, pp. 1008–1013]. This paper introduces a parametric method to build graded epistemic logics inspired in the systematic method to build Multi-valued Dynamic Logics introduced in [Madeira, A., R. Neves and M. A. Martins, An exercise on the generation of many-valued dynamic logics, J. Log. Algebr. Meth. Program. 85 (2016), pp. 1011–1037. URL http://dx.doi.org/10.1016/j.jlamp.2016.03.004; Madeira, A., R. Neves, M. A. Martins and L. S. Barbosa, A dynamic logic for every season, in: C. Braga and N. Martí-Oliet, editors, Formal Methods: Foundations and Applications – 17th Brazilian Symposium, SBMF 2014, Maceió, AL, Brazil, September 29-October 1, 2014. Proceedings, Lecture Notes in Computer Science 8941 (2014), pp. 130–145. URL http://dx.doi.org/10.1007/978-3-319-15075-8_9]. The parameter in both methods is the same: an action lattice [Kozen, D., On action algebras, Logic and Information Flow (1994), pp. 78–88]. This algebraic structure supports a generic space of agent knowledge operators, as choice, composition and closure (as a Kleene algebra), but also a proper truth space for possible non bivalent interpretation of the assertions (as a residuated lattice).

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.

This work proposes a extension of dynamic epistemic logic to work with assignment. The difference between this work and others works, such as [7], is the use of actions models, from DEL, to make Boolean assignments to the propositions, instead of creating new mechanisms to make the assignments. We extend the definition of action model by creating the postcondition property of each state of the model, making it possible to assign Boolean values to the propositions.

In this work, we extend multi-agent epistemic logic for reasoning about properties in protocols. It is based on Dolev-Yao model and uses structured propositions, a new technique to deal with messages, keys and properties in security protocols in an uniform manner, keeping the logic propositional. In order to illustrate the applicability of this new logic, an example is presented.

We present a sound and complete graph calculus for modalities. This calculus is a general framework for expressing modal formulas and frame properties, with a rich repertoire of relations, and reasoning about them in a uniform manner. The calculus employs graphical interpretations of logical operators and builds graphical objects that represent conditions on Kripke structures.

In standard Propositional Dynamic Logic (PDL) literature, the semantics is given by Labeled Transition Systems, where for each program pi we associate a binary relation R-pi. Process Algebras also give semantics to process (terms) by means of Labeled Transition Systems. In both formalisms, PDL and Process Algebra, the key notion to compare processes is bisimulation. In PDL, we also have the notion of logic equivalence, that can be used to prove that two programs pi(1) and pi(2) are logically equivalent proves phi <-> phi. Unfortunately, logic equivalence and bisimulation do not match in PDL. Bisimilar programs are logic equivalent but the converse does not hold. This paper proposes a semantics and an axiomatization for PDL that makes logically equivalent programs also bisimilar.This allows for developing Dynamic Logics to reasoning about CCS specification. As in CCS the bisimulation is the main tool to establish equivalence of programs, it is very important that these two relations coincide. We propose a new Propositional Dynamic Logic with a new non-deterministic choice operator, PDL+. We prove its soundness, completeness, finite model property and EXPTIME-completeness for the satisfiability problem. We also add to PDL+ the parallel composition operator (PPDL+) and prove its soundness and completeness.We establish that the satisfiability problem for PPDL+ is in 2-EXPTIME. Finally, we define some fragments of PPDL+ and prove its EXPTIME-completeness. (C) 2017 Elsevier B.V. All rights reserved.