Propositional dynamic logic for searching games with errors

We investigate some finitely-valued generalizations of propositional dynamic logic with tests. We start by introducing the (n+1)-valued Kripke models and a corresponding language based on a modal extension of {\L}ukasiewicz many-valued logic. We illustrate the definitions by providing a framework for an analysis of the R\'enyi - Ulam searching game with errors. Our main result is the axiomatization of the theory of the (n+1)-valued Kripke models. This result is obtained through filtration of the canonical model of the smallest (n+1)-valued propositional dynamic logic

Deciding regular grammar logics with converse through first-order logic

We provide a simple translation of the satisfiability problem for regular grammar logics with converse into GF2, which is the intersection of the guarded fragment and the 2-variable fragment of first-order logic. This translation is theoretically interesting because it translates modal logics with certain frame conditions into first-order logic, without explicitly expressing the frame conditions. A consequence of the translation is that the general satisfiability problem for regular grammar logics with converse is in EXPTIME. This extends a previous result of the first author for grammar logics without converse. Using the same method, we show how some other modal logics can be naturally translated into GF2, including nominal tense logics and intuitionistic logic. In our view, the results in this paper show that the natural first-order fragment corresponding to regular grammar logics is simply GF2 without extra machinery such as fixed point-operators.Comment: 34 page

FAST : a fault detection and identification software tool

The aim of this work is to improve the reliability and safety of complex critical control systems by contributing to the systematic application of fault diagnosis. In order to ease the utilization of fault detection and isolation (FDI) tools in the industry, a systematic approach is required to allow the process engineers to analyze a system from this perspective. In this way, it should be possible to analyze this system to find if it provides the required fault diagnosis and redundancy according to the process criticality. In addition, it should be possible to evaluate what-if scenarios by slightly modifying the process (f.i. adding sensors or changing their placement) and evaluating the impact in terms of the fault diagnosis and redundancy possibilities. Hence, this work proposes an approach to analyze a process from the FDI perspective and for this purpose provides the tool FAST which covers from the analysis and design phase until the final FDI supervisor implementation in a real process. To synthesize the process information, a very simple format has been defined based on XML. This format provides the needed information to systematically perform the Structural Analysis of that process. Any process can be analyzed, the only restriction is that the models of the process components need to be available in the FAST tool. The processes are described in FAST in terms of process variables, components and relations and the tool performs the structural analysis of the process obtaining: (i) the structural matrix, (ii) the perfect matching, (iii) the analytical redundancy relations (if any) and (iv) the fault signature matrix. To aid in the analysis process, FAST can operate stand alone in simulation mode allowing the process engineer to evaluate the faults, its detectability and implement changes in the process components and topology to improve the diagnosis and redundancy capabilities. On the other hand, FAST can operate on-line connected to the process plant through an OPC interface. The OPC interface enables the possibility to connect to almost any process which features a SCADA system for supervisory control. When running in on-line mode, the process is monitored by a software agent known as the Supervisor Agent. FAST has also the capability of implementing distributed FDI using its multi-agent architecture. The tool is able to partition complex industrial processes into subsystems, identify which process variables need to be shared by each subsystem and instantiate a Supervision Agent for each of the partitioned subsystems. The Supervision Agents once instantiated will start diagnosing their local components and handle the requests to provide the variable values which FAST has identified as shared with other agents to support the distributed FDI process.Per tal de facilitar la utilització d'eines per la detecció i identificació de fallades (FDI) en la indústria, es requereix un enfocament sistemàtic per permetre als enginyers de processos analitzar un sistema des d'aquesta perspectiva. D'aquesta forma, hauria de ser possible analitzar aquest sistema per determinar si proporciona el diagnosi de fallades i la redundància d'acord amb la seva criticitat. A més, hauria de ser possible avaluar escenaris de casos modificant lleugerament el procés (per exemple afegint sensors o canviant la seva localització) i avaluant l'impacte en quant a les possibilitats de diagnosi de fallades i redundància. Per tant, aquest projecte proposa un enfocament per analitzar un procés des de la perspectiva FDI i per tal d'implementar-ho proporciona l'eina FAST la qual cobreix des de la fase d'anàlisi i disseny fins a la implementació final d'un supervisor FDI en un procés real. Per sintetitzar la informació del procés s'ha definit un format simple basat en XML. Aquest format proporciona la informació necessària per realitzar de forma sistemàtica l'Anàlisi Estructural del procés. Qualsevol procés pot ser analitzat, només hi ha la restricció de que els models dels components han d'estar disponibles en l'eina FAST. Els processos es descriuen en termes de variables de procés, components i relacions i l'eina realitza l'anàlisi estructural obtenint: (i) la matriu estructural, (ii) el Perfect Matching, (iii) les relacions de redundància analítica, si n'hi ha, i (iv) la matriu signatura de fallades. Per ajudar durant el procés d'anàlisi, FAST pot operar aïlladament en mode de simulació permetent a l'enginyer de procés avaluar fallades, la seva detectabilitat i implementar canvis en els components del procés i la topologia per tal de millorar les capacitats de diagnosi i redundància. Per altra banda, FAST pot operar en línia connectat al procés de la planta per mitjà d'una interfície OPC. La interfície OPC permet la possibilitat de connectar gairebé a qualsevol procés que inclogui un sistema SCADA per la seva supervisió. Quan funciona en mode en línia, el procés està monitoritzat per un agent software anomenat l'Agent Supervisor. Addicionalment, FAST té la capacitat d'implementar FDI de forma distribuïda utilitzant la seva arquitectura multi-agent. L'eina permet dividir sistemes industrials complexes en subsistemes, identificar quines variables de procés han de ser compartides per cada subsistema i generar una instància d'Agent Supervisor per cadascun dels subsistemes identificats. Els Agents Supervisor un cop activats, començaran diagnosticant els components locals i despatxant les peticions de valors per les variables que FAST ha identificat com compartides amb altres agents, per tal d'implementar el procés FDI de forma distribuïda.Postprint (published version

Kleene algebra with domain

We propose Kleene algebra with domain (KAD), an extension of Kleene algebra with two equational axioms for a domain and a codomain operation, respectively. KAD considerably augments the expressiveness of Kleene algebra, in particular for the specification and analysis of state transition systems. We develop the basic calculus, discuss some related theories and present the most important models of KAD. We demonstrate applicability by two examples: First, an algebraic reconstruction of Noethericity and well-foundedness; second, an algebraic reconstruction of propositional Hoare logic.Comment: 40 page

A Canonical Model Construction for Iteration-Free PDL with Intersection

We study the axiomatisability of the iteration-free fragment of Propositional Dynamic Logic with Intersection and Tests. The combination of program composition, intersection and tests makes its proof-theory rather difficult. We develop a normal form for formulae which minimises the interaction between these operators, as well as a refined canonical model construction. From these we derive an axiom system and a proof of its strong completeness.Comment: In Proceedings GandALF 2016, arXiv:1609.0364

Parametrised Complexity of Model Checking and Satisfiability in Propositional Dependence Logic

In this paper, we initiate a systematic study of the parametrised complexity in the field of Dependence Logics which finds its origin in the Dependence Logic of V\"a\"an\"anen from 2007. We study a propositional variant of this logic (PDL) and investigate a variety of parametrisations with respect to the central decision problems. The model checking problem (MC) of PDL is NP-complete. The subject of this research is to identify a list of parametrisations (formula-size, treewidth, treedepth, team-size, number of variables) under which MC becomes fixed-parameter tractable. Furthermore, we show that the number of disjunctions or the arity of dependence atoms (dep-arity) as a parameter both yield a paraNP-completeness result. Then, we consider the satisfiability problem (SAT) showing a different picture: under team-size, or dep-arity SAT is paraNP-complete whereas under all other mentioned parameters the problem is in FPT. Finally, we introduce a variant of the satisfiability problem, asking for teams of a given size, and show for this problem an almost complete picture.Comment: Update includes refined result

Separation of Test-Free Propositional Dynamic Logics over Context-Free Languages

For a class L of languages let PDL[L] be an extension of Propositional Dynamic Logic which allows programs to be in a language of L rather than just to be regular. If L contains a non-regular language, PDL[L] can express non-regular properties, in contrast to pure PDL. For regular, visibly pushdown and deterministic context-free languages, the separation of the respective PDLs can be proven by automata-theoretic techniques. However, these techniques introduce non-determinism on the automata side. As non-determinism is also the difference between DCFL and CFL, these techniques seem to be inappropriate to separate PDL[DCFL] from PDL[CFL]. Nevertheless, this separation is shown but for programs without test operators.Comment: In Proceedings GandALF 2011, arXiv:1106.081