Language uses location description with respect to spatial reference frames. For the transformation from a visual perception to the relative expression the reference frames must fix three parameters: . origin (e.g., the speaker, an object, another person), . orientation (e.g., the axial frame of the speakers, of the addressee, of another object), . handedness of the coordinate system (same as a person's or inverse).

. This paper describes the concept of higher order quotients and an implementation in Isabelle. Higher order quotients are a generalization of quotients. They use partial equivalence relations (PERs) instead of equivalence relations to group together different elements. This makes them applicable to arbitrary function spaces. Higher order quotients are conservatively implemented in the Isabelle logic HOL with a type constructor and a type class for PERs. Ordinary quotients are a special case of higher order quotients. An example shows how they can be used in Isabelle. 1 Introduction Quotients are used in mathematics to group together different elements. This is done by defining an equivalence relation relating different elements. The quotient is a structure (type) consisting of groups (sets) of equivalent elements, called equivalence classes. Equivalent elements are in the same equivalence class. In formal system and software engineering quotients are used in many ways. For e...

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In this paper we present a case study on Auto-Focus, a tool prototype for the development of distributed and concurrent systems based on the concepts of the formal method Focus. We develop (specify, consistency-check and simulate) the controller of a pedestrian traffic light using different graphical description techniques to illustrate an engineering process for concurrent systems.

The thesis describes the production of a large prototype proof system for Z, and a tactic language in which the proof tactics used in a wide range of systems (including the system described here) can be discussed. The details of the construction of the tool---using the W logic for Z, and implemented in 2OBJ---are presented, along with an account of some of the proof tactics which enable W to be applied to typical proofs in Z. A case study gives examples of such proofs. Special attention is paid to soundness concerns, since it is considerably easier to check that a program such as this one produces sound proofs, than to check that each of the impenetrable proofs which it creates is indeed sound. As the first such encoding of W, this helped to find bugs in the published presentations of W, and to demonstrate that W makes proof in Z tractable. The second part of the thesis presents a tactic language, with a formal semantics (independent of any particular tool) and a set of rules for reasoning about tactics written in this language. A small set of these rules is shown to be complete for the finite (nonrecursive)

The formal specification of spatial objects and spatial relations is at the core of geographic data exchange and interoperability for geographic information systems (GIS). It is necessary that the representation of such objects and relations comes close to how people use them in their everyday lives, i.e., that these specifications are built upon elements of human spatial cognition. Image schemata have been suggested as highly abstract and structured mental patterns to capture spatial and similar physical as well as metaphorical relations between objects in the experiential world. We assume that image-schematic details for large-scale (geographic) space are potentially different from image-schematic details for small-scale (table-top) space. This paper reviews methods for the formal description of spatial relations, integrates them in a categorical view, and applies the methods arrived at to formally specify image schemata for large-scale (LOCATION, PATH, REGION, and BOUNDARY) as well ...

of the Thesis Presented in Partial Fulfillment of the Requirements for the Degree of Master of Science (in Spatial Information Science and Engineering) December, 1997 Wayfinding is a basic activity that people do throughout their entire lives as they navigate from one place to another. Many theories of spatial cognition have been developed to account for this behavior. But most of the computational models focus on knowledge representation (e.g., cognitive maps) and do not consider the process of structuring wayfinding tasks and space. This thesis presents a methodology based on image schemata to structure people's wayfinding tasks. Image schemata are recurring mental patterns (e.g., the CONTAINER or PATH schema) that people use to understand a spatial situation. They are highly structured and grounded in people's experience. The area of our attention is airport space which is used as a case study. Many airports are badly designed and passengers are often unfamiliar with the parti...

DataTypes : : : : : : : : : : : : : : : : : : : : : : : : : 40 4.2 PolymorphicDataTypes : : : : : : : : : : : : : : : : : : : : : : : 40 vi 4.3 Existential DataTypes : : : : : : : : : : : : : : : : : : : : : : : : 41 4.4 DynamicTypes : : : : : : : : : : : : : : : : : : : : : : : : : : : : 43 4.5 Dynamic Semantics : : : : : : : : : : : : : : : : : : : : : : : : : : 45 5 A Tiny Programming Language 48 5.1 Tiny Layout Conventions : : : : : : : : : : : : : : : : : : : : : : 48 5.2 Existential Type Variables : : : : : : : : : : : : : : : : : : : : : : 50 5.3 Type Signatures withHoles : : : : : : : : : : : : : : : : : : : : : 50 5.4 PolymorphicAbstractions : : : : : : : : : : : : : : : : : : : : : : 51 5.5 Top-Level Function Signatures : : : : : : : : : : : : : : : : : : : : 53 5.6 AlgebraicDataTypes : : : : : : : : : : : : : : : : : : : : : : : : 54 5.7 Restricted Type Synonyms and Newtype : : : : : : : : : : : : : : 55 5.8 Summary of Type System : : : : : : : : : : : : : : : : : : : : : : 56 5.9 DynamicTypes : : : : : : : : : : : : : : : : : : : : : : : : : : : : 57 6 Systems Programming with Dynamic Types 59 6.1 Error Handling : : : : : : : : : : : : : : : : : : : : : : : : : : : : 59 6.2 Inter-Process Communication : : : : : : : : : : : : : : : : : : : : 62 6.3 A Simple Address Server : : : : : : : : : : : : : : : : : : : : : : : 64 6.4 A Simple File Server : : : : : : : : : : : : : : : : : : : : : : : : : 66 6.5 A Capability System : : : : : : : : : : : : : : : : : : : : : : : : : 69 6.6 Distributed Inter-Process Communication : : : : : : : : : : : : : 75 6.7 A Compiler Interface : : : : : : : : : : : : : : : : : : : : : : : : : 78 6.8 AFunctional Compiler Interface : : : : : : : : : : : : : : : : : : 81 7 Dynamic Overloading 83 7.1 Dynamically Resolved Overloading : : ...

Modeling and documentation are two essential ingredients for the engineering discipline of software development. During the last twenty years a wide variety of description and modeling techniques as well as document formats has been proposed. However, often these are not integrated into a coherent methodology with well-defined dependencies between the models and documentations. This hampers focused software development as well as the provision of powerful tool-support. In this paper we present the main issues and outline solutions in the direction of a unified, formal basis for software and system modeling.

The tool we use influences the product. This paper demonstrates that higher order functions are a necessary tool for research in the GIS area, because higher order functions permit to separate the treatment of attribute data from the organisation of processing in data structures. Higher order functions are functions which have functions as arguments. A function to traverse a data structure can thus have as an argument a function to perform specific operations with the attribute data stored. This is crucial in the GIS arena, where complex spatial data structures are necessary. Higher order functions were tacitly assumed for Tomlin's Map Algebra. The lack of higher order functions in the design stage of GIS and in the implementation is currently most felt for visualization, where the problems of the interaction between the generic computer graphics solutions and the particulars of the application area preclude advanced solutions, which combine the best results from both worlds. Similar ...