Dynamic Tracing: a graphical language for rewriting protocols

The category Set* of sets and partial functions is well-known to be traced monoidal, meaning that a partial function S+U -/-> T+U can be coherently transformed into a partial function S -/-> T. This transformation is generally described in terms of an implicit procedure that must be run. We make this procedure explicit by enriching the traced category in Cat#, the symmetric monoidal category of categories and cofunctors: each hom-category has such procedures as objects, and advancement through the procedures as arrows. We also generalize to traced Kleisli categories beyond Set*, providing a conjectural trace operator for the Kleisli category of any polynomial monad of the form t+1. The main motivation for this work is to give a formal and graphical syntax for performing sophisticated computations powered by graph rewriting, which is itself a graphical language for data transformation

Incremental syntax generation with tree adjoining grammars

With the increasing capacity of AI systems the design of human--computer interfaces has become a favorite research topic in AI. In this paper we focus on aspects of the output of a computer. The architecture of a sentence generation component -- embedded in the WIP system -- is described. The main emphasis is laid on the motivation for the incremental style of processing and the encoding of adequate linguistic units as rules of a Lexicalized Tree Adjoining Grammar with Unification

Modular Grammars and Splitting of Catamorphisms

An abstract context-free grammar can be viewed as a system of polynomial functors. The initial algebra of this functor coincides with its least fixed-point; and this fixed-point can be computed by a method of substitution using Bek\`{\i}c theorem. By doing so the system of polynomial functors is transformed into a related system of regular functors. We introduce a splitting operation on algebras producing an algebra for the resulting system of regular functors from an algebra of the original system of polynomial functors. This transformation preserves the interpretation function (catamorphism). The end result is a class of (extended) abstract context-free grammars, associated with regular functors. This class seems to be well-adapted to the modular design of domain-specific embedded languages

Unification in monoidal theories is solving linear equations over semirings

Although for numerous equational theories unification algorithms have been developed there is still a lack of general methods. In this paper we apply algebraic techniques to the study of a whole class of theories, which we call monoidal. Our approach leads to general results on the structure of unification algorithms and the unification type of such theories. An equational theory is monoidal if it contains a binary operation which is associative and commutative, an identity for the binary operation, and an arbitrary number of unary symbols which are homomorphisms for the binary operation and the identity. Monoidal theories axiomatize varieties of abelian monoids. Examples are the theories of abelian monoids (AC), idempotent abelian monoids (ACI), and abelian groups. To every monoidal theory we associate a semiring. Intuitively, semirings are rings without subtraction. We show that every unification problem in a monoidal theory can be translated into a system of linear equations over the corresponding semiring. More specifically, problems without free constants are translated into homogeneous equations. For problems with free constants inhomogeneous equations have to be solved in addition. Exploiting the correspondence between unification and linear algebra we give algebraic characterizations of the unification type of a theory. In particular, we show that with respect to unification without constants monoidal theories are either unitary or nullary. Applying Hilbert\u27s Basis Theorem we prove that theories of groups with commuting homomorphisms are unitary with respect to unification with and without constants

Constraint-basierte Verarbeitung graphischen Wissens

Bei der Entwicklung neuerer intelligenter Benutzerschnittstellen, die wie im Beispiel des multimodalen Präsentationssystems WIP natürliche Sprache und Graphik kombinieren, spielt insbesondere die wissensbasierte Gestaltung des Layouts multimodaler Dokumente eine wichtige Rolle. Am Beispiel des Layout-Managers in WIP soll gezeigt werden, wie aufgrund der von einem Präsentationsplaner spezifizierten semantischen und pragmatischen Relationen, die von den media-spezifischen Generatoren erzeugten Graphik- und Textfragmente in einem Dokument automatische arrangiert werden können. Dabei wird das Layoutproblem als Constraint-Satisfaction-Problem behandelt. Es wird hier gezeigt, wie der Constraint-Ansatz sowohl zur Repräsentation von graphischem Wissen, als auch zur Berechnung der Platzierung der Layoutobjekte auf einem Design-Grid verwendet werden kann. So werden semantische Kohärenzrelationen wie etwa "sequence" oder "contrast" durch entsprechende Design-Constraints reflektiert, die perzeptuelle Kriterien (Alignierung, Gruppierung, Symmetrie, etc.) spezifizieren. Zur Realisierung wird in WIP ein mehrschichtiger inkrementeller Constraint-Solver mit lokaler Propagierung verwendet, der es erlaubt, Constraints dynamisch zu generieren

PIM : planning in manufacturing using skeletal plans and features

In order to create a production plan from product model data, a human expert thinks in a special terminology with respect to the given work piece and its production plan: He recognizes certain features and associates fragments of a production plan. By combining these skeletal plans he generates the complete production plan. We present a set of representation formalisms suitable for the modelling of this approach. When an expert\u27s knowledge has been represented using these formalisms, the generation of a production plan can be achieved by a sequence of abstraction, selection and refinement. This is demonstrated in the CAPP-system PIM, which is currently developed as a prototype. The close modelling of the knowledge of the concrete expert (or the accumulated know-how of a concrete factory) facilitate the development of planning systems which are especially tailored to the concrete manufacturing environment and optimally use the expert\u27s knowledge and should also lead to improved acceptance of the system