Spatial and Epistemic Modalities in Constraint-Based Process Calculi

Abstract

Abstract. We introduce spatial and epistemic process calculi for reasoning about spatial information and knowledge distributed among the agents of a system. We introduce domain-theoretical structures to represent spatial and epistemic information. We provide operational and denotational techniques for reasoning about the potentially infinite behaviour of spatial and epistemic processes. We also give compact representations of infinite objects that can be used by processes to simulate announcements of common knowledge and global information.Introduction. 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 [16] 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.Epistemic concepts were crucial in distributed computing as was realized in the mid 1980s with Halpern and Moses' groundbreaking paper on common knowledge [13]. This led to a flurry of activity in the next few years [11] with many distributed protocols being understood from an epistemic point of view. The impact of epistemic ideas in the concurrency theory community was slower in coming. In an invited talk by one of us [20] at a joint PODC-CONCUR conference in 2008, this point was emphasized and a plea was made for epistemic ideas to be exploited more by concurrency theorists.The goal of the present paper is simple: to put epistemic concepts in the hands of programmers rather than just appearing in post-hoc theoretical analyses. One could imagine the incorporation of these ideas in a variety of process algebraic settings -and indeed we expect that such formalisms will appear in due course -but what is particularly appealing about the concurrent constraint programming (ccp) paradigm [24,25] is that it was designed to give programmers explicit access to the concept of partial information and, as such, had close ties with logic [21,18]. This makes it ideal for the incorporation of epistemic concepts by expanding the logical connections to include modal logic [15]. In particular, agents posting and querying information in the presence of spatial hierarchies for sharing information and knowledge, e.g. friend circles and

Efficient computation of program equivalence for confluent concurrent constraint programming

“…The challenge would be to find a more efficient version of =⇒ that can still be used for deciding≈ sb and so it can be adapted to the case of the full ccp. Finally, we plan to investigate how the procedures here defined can be extended to different versions of ccp where the summation operator is not present, for instance timed ccp (tcc) [25], universal temporal ccp (utcc) [21] and epistemic ccp (eccp) [17]). …”

“…Ccp is parametric in a constraint system indicating interdependencies (entailment) between partial information and providing for the specification of data types and other rich structures. The above features have attracted a renewed attention as witnessed by the works [23,11,7,6,17] on calculi exhibiting data-types, logic assertions as well as tell and ask operations. A compelling example of the kind of system ccp can model involves users interacting by posting and querying information in a social network [17].…”

Models and emerging trends of concurrent constraint programming

“…Semiringbased constraints [25] allowed to define Soft Concurrent Constraint Programming [29] where agents can post and ask soft constraints in order to express preferences, fuzziness, probabilities, etc. Moreover, by adding space functions into the structure of the constraint system, CCP calculi devised for epistemic and spatial reasoning where studied in [124]. We will come back to these definitions in Section 3 where we give an account of different CCP-based calculi.…”

“…This operator can also be interpreted as an epistemic construction to specify that the information computed by a process will be known to a given agent. It is worth noticing that the CCP concept of local variables cannot faithfully model local spaces since in the spatial constraint systems defined in [124], it is possible to have inconsistent local stores without propagating their inconsistencies towards the global store.…”

“…In [124] the authors enhance and generalize the theory of CCP for systems with spatial distribution of information. More precisely, the underlying theory of constraint systems is extended by adding space functions to their structure.…”