Jaime Ramos

Combining Logics: Parchments Revisited

In the general context of the theory of institutions, several notions of parchment and parchment morphism have been proposed as the adequate setting for combining logics. However, so far, they seem to lack one of the main advantages of the combination mechanism known as fibring: general results of transference of important logical properties from the logics being combined to the resulting fibred logic. Herein, in order to bring fibring to the institutional setting, we propose to work with the novel notion of c-parchment. We show how both free and constrained fibring can be characterized as colimits of c-parchments, and illustrate both the construction and its preservation capabilities by exploring the idea of obtaining partial equational logic by fibring equational logic with a suitable logic of partiality. Last but not least, in the restricted context of propositional based, we state and prove a collection of meaningful soundness and completeness preservation results for fibring, with respect to Hilbert-like proof-calculi.

Distributed temporal logic for the analysis of security protocol models

The distributed temporal logic DTL is an expressive logic, well suited for formalizing properties of concurrent, communicating agents. We show how DTL can be used as a metalogic to reason about and relate different security protocol models. This includes reasoning about model simplifications, where models are transformed to have fewer agents or behaviors, and verifying model reductions, where to establish the validity of a property it suffices to consider its satisfaction on only a subset of models. We illustrate how DTL can be used to formalize security models, protocols, and properties, and then present three concrete examples of metareasoning. First, we prove a general theorem about sufficient conditions for data to remain secret during communication. Second, we prove the equivalence of two models for guaranteeing message-origin authentication. Finally, we relate channel-based and intruder-centric models, showing that it is sufficient to consider models in which the intruder completely controls the network. While some of these results belong to the folklore or have been shown, mutatis mutandis, using other formalisms, DTL provides a uniform means to prove them within the same formalism. It also allows us to clarify subtle aspects of these model transformations that are often neglected or cannot be specified in the first place.

Labelled Tableaux for Distributed Temporal Logic

The distributed temporal logic DTL is a logic for reasoning about temporal properties of discrete distributed systems from the local point of view of the systems agents, which are assumed to execute sequentially and to interact by means of synchronous event sharing. We present a sound and complete labelled tableaux system for full DTL. To achieve this, we first formalize a labelled tableaux system for reasoning locally at each agent and afterwards we combine the local systems into a global one by adding rules that capture the distributed nature of DTL. We also provide examples illustrating the use of DTL and our tableaux system.

From Fibring to Cryptofibring. A Solution to the Collapsing Problem

Abstract.The semantic collapse problem is perhaps the main difficulty associated to the very powerful mechanism for combining logics known as fibring. In this paper we propose cryptofibred semantics as a generalization of fibred semantics, and show that it provides a solution to the collapsing problem. In particular, given that the collapsing problem is a special case of failure of conservativeness, we formulate and prove a sufficient condition for cryptofibring to yield a conservative extension of the logics being combined. For illustration, we revisit the example of combining intuitionistic and classical propositional logics.

Evolving logical specification in information systems

Traditional logic-based specification approaches fix the structure and the dynamics of an object system at specification time. Information systems are applications with a very long life-time. Therefore, object and specification evolution is needed to react to changing requirements. Hence, this is a relevant aspect of describing information systems as object societies.

A Linear Temporal Logic Approach to Objects with Transactions

Our concern is the high level specification of reactive software systems such as information systems. We adopt an object oriented, temporal logic based approach to specification. The notion of transaction incorporates various application domains, for instance transactions as abstractions from processes as known from refinement theory, transactions as abstractions from business processes as known in business process modelling or database transactions. In this paper we investigate object specifications with transactions. We illustrate the use of transactions by examples given in an object oriented style and introduce a linear temporal logic with transactions (Tosl) which serves as denotional model for such object specifications with transactions. We explain how Tosl is semantically defined in terms of life cycles and illustrate by example the translation of object specifications to Tosl. Using Tosl for system specification results in sets of formulae which are independent from the level of granularity.

A temporal logic approach to object certification

A brief overview is made of the use of temporal logic formalisms for specifying and verifying concurrent systems in general and information systems in particular. The requirements imposed by object-orientation on such formalisms are examined. A logic is proposed fulfilling those requirements (except concerning non-monotonic features), allowing the uniform treatment of both local and global properties of systems with concurrent, interacting components organized in classes, and supporting specialization. A semantics and a calculus (following an axiomatic, Hilbert style) are presented in detail. The calculus includes rules for the sound inheritance and reflection of theorems between classes. Practical aspects of the usage of such a logic for both specification and verification are considered. To this end a set of metatheorems is provided for expediting the proof of invariants. Finally, the need and availability of automatic theorem proving for systems querying is briefly discussed.

The robust minimal controllability problem

In this paper, we address two minimal controllability problems, where the goal is to determine a minimal subset of state variables in a linear time-invariant system to be actuated to ensure controllability under additional constraints. First, we study the problem of characterizing the sparsest input matrices that assure controllability when the autonomous dynamics matrix is simple. Secondly, we build upon these results to describe the solutions to the robust minimal controllability problem, where the goal is to determine the sparsest input matrix ensuring controllability when specified number of inputs fail. Both problems are NP-hard, but under the assumption that the dynamics matrix is simple, we show that it is possible to reduce these two problems to set multi-covering problems. Consequently, these problems share the same computational complexity, i.e., they are NP-complete, but polynomial algorithms to approximate the solutions of a set multi-covering problem can be leveraged to obtain close-to-optimal solutions to either of the minimal controllability problems.

Cryptomorphisms at work

We show that the category proposed in [5] of logic system presentations equipped with cryptomorphisms gives rise to a category of parchments that is both complete and translatable to the category of institutions, improving on previous work [15]. We argue that limits in this category of parchments constitute a very powerful mechanism for combining logics.

A model checking framework for linear time invariant switching systems using structural systems analysis

This paper introduces the concept of structural hybrid systems to address, as a particular case, the model checking problem of switching (possible large scale) linear time invariant systems. Within the proposed setup, we provide necessary conditions to ensure properties such as controllability, at each time. We show that such model checking controllability properties can be implemented using efficient algorithms (with polynomial complexity). An example, based on the IEEE 5-bus power system, is presented which illustrates our model checking and design methodologies.