Section: New Results

Foundations of Concurrency

Distributed systems have changed substantially in the recent past with the advent of phenomena like social networks and cloud computing. In the previous incarnation of distributed computing the emphasis was on consistency, fault tolerance, resource management and related topics; these were all characterized by interaction between processes. Research proceeded along two lines: the algorithmic side which dominated the Principles Of Distributed Computing conferences and the more process algebraic approach epitomized by CONCUR where the emphasis was on developing compositional reasoning principles. What marks the new era of distributed systems is an emphasis on managing access to information to a much greater degree than before.

Declarative Framework for Semantical Interpretations of Structured Information — An Applicative Approach.

Spatial constraint systems are algebraic structures from concurrent constraint programming to specify spatial and epistemic behavior in multi-agent system. In [21], [15] we studied the applicability of declarative models to encode and describe structured information by means of semantics. Specifically, we introduced D-SPACES, an implementation of constraint systems with space and extrusion operators. D-SPACES provides property-checking methods as well as an implementation of a specific type of constraint systems (a spatial boolean algebra). We showed the applicability of this framework with two examples; a scenario in the form of a social network where users post their beliefs and utter their opinions, and a semantical interpretation of a logical language to express time behaviors and properties.

Characterizing Right Inverses for Spatial Constraint Systems with Applications to Modal Logic

In [23] spatial constraint systems were used to give an abstract characterization of the notion of normality in modal logic and to derive right inverse/reverse operators for modal languages. In particular, a necessary and sufficient condition for the existence of right inverses was identified and the abstract notion of normality is shown to correspond to the preservation of finite suprema. Furthermore, a taxonomy of normal right inverses was provided, identifying the greatest normal right inverse as well as the complete family of minimal right inverses. These results were applied to existing modal languages such as the weakest normal modal logic, Hennessy-Milner logic, and linear-time temporal logic. Some implications of these results were also discussed in the context of modal concepts such as bisimilarity and inconsistency invariance.

Observational and Behavioural Equivalences for Soft Concurrent Constraint Programming

In citegadducci:hal-01675060 we presented a labelled semantics for Soft Concurrent Constraint Programming (SCCP), a meta-language where concurrent agents may synchronise on a shared store by either posting or checking the satisfaction of (soft) constraints. SCCP generalises the classical formalism by parametrising the constraint system over an order-enriched monoid, thus abstractly representing the store with an element of the monoid, and the standard unlabelled semantics just observes store updates. The novel operational rules were shown to offer a sound and complete co-inductive technique to prove the original equivalence over the unlabelled semantics. Based on this characterisation, we provided an axiomatisation for finite agents.

On the Expressiveness of Spatial Constraint Systems

The dissertation [11] focused on the expressiveness of spatial constraint systems in the broader perspective of modal and epistemic behaviour. It was shown that that spatial constraint systems are sufficiently robust to capture inverse modalities and to derive new results for modal logics. It was shown that one can use scs’s to express a fundamental epistemic behaviour such as knowledge. The dissertation also provided an algebraic characterization of the notion of distributed information by means of constructors over scs’s.