An approach to information visualization based on algebraic semiotics is introduced, and illustrated with examples. Semiotics is the general theory of signs, and algebraic semiotics is a new approach combining algebraic abstract data type theory with a grounding in social reality. The most important new ideas are to use semiotic spaces for systems of related signs, semiotic morphisms for representations of signs, and preservation orderings for the quality of representations.

This paper studies the composition of modules that can hide information, over a very general class of logical systems called inclusive institutions. Two semantics are given for composition of such modules using five familiar operations, and a property called conservativity is shown necessary and sufficient for these semantics to agree. The first semantics extracts the visible properties of the result of composing the visible and hidden parts of modules, while the second uses only the visible properties of the components; the semantics agree when the visible consequences of hidden information are enough to determine the result of the composition. A number of "laws of software composition" are proved relating the composition operations. Inclusive institutions simplify many proofs.

: We describe some tools to support distributed cooperative design and validation of software systems. Workers at different sites can collaborate on tasks including specification, refinement, validation, verification, and documentation. A distributed database supports alternative and incomplete activities, and can be read using any web browser; remote proof execution, animation, and informal explanation are supported, and results are broadcast by a protocol that prevents inconsistencies. The Kumo tool assists with validations and generates documentation websites. A range of formality is supported, from full mechanical proofs to informal "back of envelope" arguments, using a fuzzy logic for confidence levels. Some conclusions drawn from experiments are reported. 1 Introduction Software engineering is very difficult. Typical projects have multiple workers, often at multiple sites with different schedules; then it is difficult to share information and coordinate tasks; documentation may...

: We describe a new approach to interface design called algebraic semiotics, combining semiotics with algebraic specification to give a rigorous theory of representation quality, and we apply it to the tatami distributed cooperative proving project. This project uses standard html, Java, etc. for remote proof browsing, servers for remote proof execution, a protocol to maintain truth of distributed cooperative proofs, and a tool combining proof assistance with website editing. Its proof paradigm reduces theorems to problems solvable by proof servers. ProofWebs integrate browsing, execution, animation, and informal explanation with formal proofs, and their design has been driven by semiotic ideas. 1 Introduction The landscape of theorem proving can be seen as two main peaks with a great plane between. These peaks represent fully automatic theorem provers and proof checking theorem provers; the plane represents the difficulty of combining their virtues. The peaks are steep and dark bec...

We provide a semantic basis for heterogeneous specifications that not only involve different logics, but also different kinds of translations between these. We show that Grothendieck institutions based on spans of (co)morphisms can serve as a unifying framework providing a simple but powerful semantics for heterogeneous specification.

theory, categorical logic. model theory that emerged in computer science studies of software specification and semantics. To handle proof theory, our institutions use an extension of traditional categorical logic with sets of sentences as objects instead of single sentences, and with morphisms representing proofs as usual. A natural equivalence relation on institutions is defined such that its equivalence classes are logics. Several invariants are defined for this equivalence, including a Lindenbaum

Colimits are a useful tool for the combination of specifications and logical theories. We generalize the notion of colimit to a heterogeneous multi-logic setting. For practically realistic cases, the notion has to be weakened. We describe an algorithm that approximates the weaker notion but obtains a colimit whenever possible. This algorithm is being implemented as part of the Heterogeneous Tool Set HETS.

: This paper describes some tools to support formal methods, and conversely some formal methods for developing such tools. We focus on distributed cooperative proving over the web. Our tools include a proof editor /assistant, servers for remote proof execution, a distributed truth protocol, an editor generator, and a new method for interface design called algebraic semiotics, which combines semiotics with algebraic specification. Some examples are given. 1. Introduction Formal methods have been used to prove correctness of software, but this task is known to be difficult, for various reasons [5, 13]. New technologies -- the internet, the web, multimedia, applets, etc. -- offer exciting opportunities to reduce this difficulty that have not yet been much explored. We seek to build industrial strength formal method tools for distributed work by ordinary software engineers over the web, especially for concurrent systems. This involves several challenging subtasks, including a practical ...

Nearly all listeners consider the subjective aspects of music, such as its emotional tone, to have primary importance. But contemporary philosophers often downplay, ignore, or even deny such aspects of experience. Moreover, traditional philosophies of music try to decontextualize it. Using music as an example, this paper explores the structure of qualitative experience, demonstrating that it is multi-layer emergent, non-compositional, enacted, and situation dependent, among other non-Cartesian properties.

CafeOBJ is an executable industrial strength multi-logic algebraic speci cation language which is a modern successor of OBJ and incorporates several new algebraic speci cation paradigms.