Constraint Design Rewriting

We propose an algebraic approach to the design and transformation of constraint networks, inspired by Architectural Design Rewriting. The approach can be understood as (i) an extension of ADR with constraints, and (ii) an application of ADR to the design of reconfigurable constraint networks. The main idea is to consider classes of constraint networks as algebras whose operators are used to denote constraint networks with terms. Constraint network transformations such as constraint propagations are specified with rewrite rules exploiting the network’s structure provided by terms

Qualitative Spatial Configuration Queries Towards Next Generation Access Methods for GIS

For a long time survey, management, and provision of geographic information in Geographic Information Systems (GIS) have mainly had an authoritative nature. Today the trend is changing and such an authoritative geographic information source is now accompanied by a public and freely available one which is usually referred to as Volunteered Geographic Information (VGI). Actually, the term VGI does not refer only to the mere geographic information, but, more generally, to the whole process which assumes the engagement of volunteers to collect and maintain such information in freely accessible GIS. The quick spread of VGI gives new relevance to a well-known challenge: developing new methods and techniques to ease down the interaction between users and GIS. Indeed, in spite of continuous improvements, GIS mainly provide interfaces tailored for experts, denying the casual user usually a non-expert the possibility to access VGI information. One main obstacle resides in the different ways GIS and humans deal with spatial information: GIS mainly encode spatial information in a quantitative format, whereas human beings typically prefer a qualitative and relational approach. For example, we use expressions like the lake is to the right-hand side of the wood or is there a supermarket close to the university? which qualitatively locate a spatial entity with respect to another. Nowadays, such a gap in representation has to be plugged by the user, who has to learn about the system structure and to encode his requests in a form suitable to the system. Contrarily, enabling gis to explicitly deal with qualitative spatial information allows for shifting the translation effort to the system side. Thus, to facilitate the interaction with human beings, GIS have to be enhanced with tools for efficiently handling qualitative spatial information. The work presented in this thesis addresses the problem of enabling Qualitative Spatial Configuration Queries (QSCQs) in GIS. A QSCQ is a spatial database query which allows for an automatic mapping of spatial descriptions produced by humans: A user naturally expresses his request of spatial information by drawing a sketch map or producing a verbal description. The qualitative information conveyed by such descriptions is automatically extracted and encoded into a QSCQ. The focus of this work is on two main challenges: First, the development of a framework that allows for managing in a spatial database the variety of spatial aspects that might be enclosed in a spatial description produced by a human. Second, the conception of Qualitative Spatial Access Methods (QSAMs): algorithms and data structures tailored for efficiently solving QSCQs. The main objective of a QSAM is that of countering the exponential explosion in terms of storage space occurring when switching from a quantitative to a qualitative spatial representation while keeping query response time acceptable

A universe of processes and some of its guises

Our starting point is a particular `canvas' aimed to `draw' theories of physics, which has symmetric monoidal categories as its mathematical backbone. In this paper we consider the conceptual foundations for this canvas, and how these can then be converted into mathematical structure. With very little structural effort (i.e. in very abstract terms) and in a very short time span the categorical quantum mechanics (CQM) research program has reproduced a surprisingly large fragment of quantum theory. It also provides new insights both in quantum foundations and in quantum information, and has even resulted in automated reasoning software called `quantomatic' which exploits the deductive power of CQM. In this paper we complement the available material by not requiring prior knowledge of category theory, and by pointing at connections to previous and current developments in the foundations of physics. This research program is also in close synergy with developments elsewhere, for example in representation theory, quantum algebra, knot theory, topological quantum field theory and several other areas.Comment: Invited chapter in: "Deep Beauty: Understanding the Quantum World through Mathematical Innovation", H. Halvorson, ed., Cambridge University Press, forthcoming. (as usual, many pictures

Connector algebras for C/E and P/T nets interactions

A quite fourishing research thread in the recent literature on component based system is concerned with the algebraic properties of different classes of connectors. In a recent paper, an algebra of stateless connectors was presented that consists of five kinds of basic connectors, namely symmetry, synchronization, mutual exclusion, hiding and inaction, plus their duals and it was shown how they can be freely composed in series and in parallel to model sophisticated "glues". In this paper we explore the expressiveness of stateful connectors obtained by adding one-place buffers or unbounded buffers to the stateless connectors. The main results are: i) we show how different classes of connectors exactly correspond to suitable classes of Petri nets equipped with compositional interfaces, called nets with boundaries; ii) we show that the difference between strong and weak semantics in stateful connectors is reflected in the semantics of nets with boundaries by moving from the classic step semantics (strong case) to a novel banking semantics (weak case), where a step can be executed by taking some "debit" tokens to be given back during the same step; iii) we show that the corresponding bisimilarities are congruences (w.r.t. composition of connectors in series and in parallel); iv) we show that suitable monoidality laws, like those arising when representing stateful connectors in the tile model, can nicely capture concurrency aspects; and v) as a side result, we provide a basic algebra, with a finite set of symbols, out of which we can compose all P/T nets, fulfilling a long standing quest

Description Logic for Scene Understanding at the Example of Urban Road Intersections

Understanding a natural scene on the basis of external sensors is a task yet to be solved by computer algorithms. The present thesis investigates the suitability of a particular family of explicit, formal representation and reasoning formalisms for this task, which are subsumed under the term Description Logic

A graphical approach to relational reasoning

Relational reasoning is concerned with relations over an unspecified domain of discourse. Two limitations to which it is customarily subject are: only dyadic relations are taken into account; all formulas are equations, having the same expressive power as first-order sentences in three variables. The relational formalism inherits from the Peirce-Schröder tradition, through contributions of Tarski and many others. Algebraic manipulation of relational expressions (equations in particular) is much less natural than developing inferences in first-order logic; it may in fact appear to be overly machine-oriented for direct hand-based exploitation. The situation radically changes when one resorts to a convenient representation of relations based on labeled graphs. The paper provides details of this representation, which abstracts w.r.t. inessential features of expressions. Formal techniques illustrating three uses of the graph representation of relations are discussed: one technique deals with translating first-order specifications into the calculus of relations; another one, with inferring equalities within this calculus with the aid of convenient diagram-rewriting rules; a third one with checking, in the specialized framework of set theory, the definability of particular set operations. Examples of use of these techniques are produced; moreover, a promising approach to mechanization of graphical relational reasoning is outlined

Acyclic Solos and Differential Interaction Nets

We present a restriction of the solos calculus which is stable under reduction and expressive enough to contain an encoding of the pi-calculus. As a consequence, it is shown that equalizing names that are already equal is not required by the encoding of the pi-calculus. In particular, the induced solo diagrams bear an acyclicity property that induces a faithful encoding into differential interaction nets. This gives a (new) proof that differential interaction nets are expressive enough to contain an encoding of the pi-calculus. All this is worked out in the case of finitary (replication free) systems without sum, match nor mismatch