Nominal Abstraction

Recursive relational specifications are commonly used to describe the computational structure of formal systems. Recent research in proof theory has identified two features that facilitate direct, logic-based reasoning about such descriptions: the interpretation of atomic judgments through recursive definitions and an encoding of binding constructs via generic judgments. However, logics encompassing these two features do not currently allow for the definition of relations that embody dynamic aspects related to binding, a capability needed in many reasoning tasks. We propose a new relation between terms called nominal abstraction as a means for overcoming this deficiency. We incorporate nominal abstraction into a rich logic also including definitions, generic quantification, induction, and co-induction that we then prove to be consistent. We present examples to show that this logic can provide elegant treatments of binding contexts that appear in many proofs, such as those establishing properties of typing calculi and of arbitrarily cascading substitutions that play a role in reducibility arguments.Comment: To appear in the Journal of Information and Computatio

Communicating Finite-State Machines and Two-Variable Logic

Communicating finite-state machines are a fundamental, well-studied model of finite-state processes that communicate via unbounded first-in first-out channels. We show that they are expressively equivalent to existential MSO logic with two first-order variables and the order relation

Datalog and Constraint Satisfaction with Infinite Templates

On finite structures, there is a well-known connection between the expressive power of Datalog, finite variable logics, the existential pebble game, and bounded hypertree duality. We study this connection for infinite structures. This has applications for constraint satisfaction with infinite templates. If the template Gamma is omega-categorical, we present various equivalent characterizations of those Gamma such that the constraint satisfaction problem (CSP) for Gamma can be solved by a Datalog program. We also show that CSP(Gamma) can be solved in polynomial time for arbitrary omega-categorical structures Gamma if the input is restricted to instances of bounded treewidth. Finally, we characterize those omega-categorical templates whose CSP has Datalog width 1, and those whose CSP has strict Datalog width k.Comment: 28 pages. This is an extended long version of a conference paper that appeared at STACS'06. In the third version in the arxiv we have revised the presentation again and added a section that relates our results to formalizations of CSPs using relation algebra

Verification of Agent-Based Artifact Systems

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 lifecycles, accounting respectively for the relational structure of the artifacts' states and their possible evolutions over time. In this paper we put forward artifact-centric multi-agent systems, a novel formalisation of artifact systems in the context of multi-agent systems operating on them. Differently from the usual process-based models of services, the semantics we give explicitly accounts for the data structures on which artifact systems are defined. We study the model checking problem for artifact-centric multi-agent systems against specifications written in a quantified version of temporal-epistemic logic expressing the knowledge of the agents in the exchange. We begin by noting that the problem is undecidable in general. We then identify two noteworthy restrictions, one syntactical and one semantical, that enable us to find bisimilar finite abstractions and therefore reduce the model checking problem to the instance on finite models. Under these assumptions we show that the model checking problem for these systems is EXPSPACE-complete. We then introduce artifact-centric programs, compact and declarative representations of the programs governing both the artifact system and the agents. We show that, while these in principle generate infinite-state systems, under natural conditions their verification problem can be solved on finite abstractions that can be effectively computed from the programs. Finally we exemplify the theoretical results of the paper through a mainstream procurement scenario from the artifact systems literature

Certainty Closure: Reliable Constraint Reasoning with Incomplete or Erroneous Data

Constraint Programming (CP) has proved an effective paradigm to model and solve difficult combinatorial satisfaction and optimisation problems from disparate domains. Many such problems arising from the commercial world are permeated by data uncertainty. Existing CP approaches that accommodate uncertainty are less suited to uncertainty arising due to incomplete and erroneous data, because they do not build reliable models and solutions guaranteed to address the user's genuine problem as she perceives it. Other fields such as reliable computation offer combinations of models and associated methods to handle these types of uncertain data, but lack an expressive framework characterising the resolution methodology independently of the model. We present a unifying framework that extends the CP formalism in both model and solutions, to tackle ill-defined combinatorial problems with incomplete or erroneous data. The certainty closure framework brings together modelling and solving methodologies from different fields into the CP paradigm to provide reliable and efficient approches for uncertain constraint problems. We demonstrate the applicability of the framework on a case study in network diagnosis. We define resolution forms that give generic templates, and their associated operational semantics, to derive practical solution methods for reliable solutions.Comment: Revised versio

A compositional monitoring framework for hard real-time systems

Runtime Monitoring of hard real-time embedded systems is a promising technique for ensuring that a running system respects timing constraints, possibly combined with faults originated by the software and/or hardware. This is particularly important when we have real-time embedded systems made of several components that must combine different levels of criticality, and different levels of correctness requirements. This paper introduces a compositional monitoring framework coupled with guarantees that include time isolation and the response time of a monitor for a predicted violation. The kind of monitors that we propose are automatically generated by synthesizing logic formulas of a timed temporal logic, and their correctness is ensured by construction.This work was partially supported by National Funds through FCT (Portuguese Foundation for Science and Technology) and by ERDF (European Regional Development Fund) through COMPETE (Operational Programme ’Thematic Factors of Competitiveness’), within projects Ref. FCOMP-01-0124-FEDER-022701 (CISTER), FCOMP-01-0124- FEDER-015006 (VIPCORE) and FCOMP-01-0124-FEDER-020486 (AVIACC)