Spatial Logics for Bigraphs

Bigraphs are emerging as an interesting model for concurrent calculi, like CCS, pi-calculus, and Petri nets. Bigraphs are built orthogonally on two structures: a hierarchical place graph for locations and a link (hyper-)graph for connections. With the aim of describing bigraphical structures, we introduce a general framework for logics whose terms represent arrows in monoidal categories. We then instantiate the framework to bigraphical structures and obtain a logic that is a natural composition of a place graph logic and a link graph logic. We explore the concepts of separation and sharing in these logics and we prove that they generalise some known spatial logics for trees, graphs and tree contexts

Separability in the Ambient Logic

The \it{Ambient Logic} (AL) has been proposed for expressing properties of process mobility in the calculus of Mobile Ambients (MA), and as a basis for query languages on semistructured data. We study some basic questions concerning the discriminating power of AL, focusing on the equivalence on processes induced by the logic $(=_L>)$. As underlying calculi besides MA we consider a subcalculus in which an image-finiteness condition holds and that we prove to be Turing complete. Synchronous variants of these calculi are studied as well. In these calculi, we provide two operational characterisations of $_=L$: a coinductive one (as a form of bisimilarity) and an inductive one (based on structual properties of processes). After showing $_=L$ to be stricly finer than barbed congruence, we establish axiomatisations of $_=L$ on the subcalculus of MA (both the asynchronous and the synchronous version), enabling us to relate $_=L$ to structural congruence. We also present some (un)decidability results that are related to the above separation properties for AL: the undecidability of $_=L$ on MA and its decidability on the subcalculus.Comment: logical methods in computer science, 44 page

Model Checking Dynamic-Epistemic Spatial Logic

In this paper we focus on Dynamic Spatial Logic, the extension of Hennessy-Milner logic with the parallel operator. We develop a sound complete Hilbert-style axiomatic system for it comprehending the behavior of spatial operators in relation with dynamic/temporal ones. Underpining on a new congruence we define over the class of processes - the structural bisimulation - we prove the finite model property for this logic that provides the decidability for satisfiability, validity and model checking against process semantics. Eventualy we propose algorithms for validity, satisfiability and model checking

An observational model for spatial logics

Spatiality is an important aspect of distributed systems because their computations depend both on the dynamic behaviour and on the structure of their components. Spatial logics have been proposed as the formal device for expressing spatial properties of systems. We define CCS∥, a CCS-like calculus whose semantics allows one to observe spatial aspects of systems on the top of which we define models of the spatial logic. Our alternative definition of models is proved equivalent to the standard one. Furthermore, logical equivalence is characterized in terms of the bisimilarity of CCS∥

Logics for Unranked Trees: An Overview

Labeled unranked trees are used as a model of XML documents, and logical languages for them have been studied actively over the past several years. Such logics have different purposes: some are better suited for extracting data, some for expressing navigational properties, and some make it easy to relate complex properties of trees to the existence of tree automata for those properties. Furthermore, logics differ significantly in their model-checking properties, their automata models, and their behavior on ordered and unordered trees. In this paper we present a survey of logics for unranked trees

Towards the Knowledge in Coalgebraic Model of IDS

In the last decades linear logic became a useful logical system for various usage in computer science. Its ability to handle resources and its competence to describe dynamics of processes predetermine it for describing behaviour of programs and program systems. Linear logic can be apprehended as a multiplicative and additive extension of usual logic. We show the possibilities how these fragments can be enriched to describe behaviour and to achieve knowledge on an example of simplified Intrusion Detection System (IDS). We construct Kripke model over a coalgebra of modal linear logic for pursuing observable behaviour of IDS. Using the same Kripke frame we show how knowledge and belief in the terms of epistemic linear logic can be achieved

Theories of Meaning for the Internet of Things

In this chapter, we consider the theoretical foundations for representing knowledge in the Internet of Things context. Specifically, we consider (1) the model-theoretic semantics (i.e., extensional semantics), (2) the possible-world semantics (i.e., intensional semantics), (3) the situation semantics, and (4) the cognitive/distributional semantics. Given the peculiarities of the Internet of Things, we pay particular attention to (a) perception (i.e., how to establish a connection to the world), (b) intersubjectivity (i.e., how to align world representations), and (c) the dynamics of world knowledge (i.e., how to model events). We come to the conclusion that each of the semantic theories helps in modeling specific aspects, but does not sufficiently address all three aspects simultaneously

05081 Abstracts Collection -- Foundations of Global Computing

From 20.02.05 to 25.02.05, the Dagstuhl Seminar 05081 on ``Foundations of Global Computing\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available