Abstract. Development graphs are a tool for dealing with structured specifications in a formal program development in order to ease the management of change and reusing proofs. Often, different aspects of a software system have to be specified in different logics, since the construction of a huge logic covering all needed features would be too complex to be feasible. Therefore, we introduce heterogeneous development graphs as a means to cope with heterogeneous specifications. We cover both the semantics and the proof theory of heterogeneous development graphs. A proof calculus can be obtained either by combining proof calculi for the individual logics, or by representing these in some “universal ” logic like higher-order logic in a coherent way and then “borrowing” its calculus for the heterogeneous language. 1

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.

Abstract. We present a semantics for architectural specifications in Casl, including an extended static analysis compatible with modeltheoretic requirements. The main obstacle here is the lack of amalgamation for Casl models. To circumvent this problem, we extend the Casl logic by introducing enriched signatures, where subsort embeddings form a category rather than just a preorder. The extended model functor has amalgamation, which makes it possible to express the amalgamability conditions in the semantic rules in static terms. Using these concepts, we develop the semantics at various levels in an institution-independent fashion.

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.

Abstract. We connect the algebraic specification language Casl with a variety of automated first-order provers. The heart of this connection is an institution comorphism from Casl to SoftFOL (softly typed firstorder logic); the latter is then translated to the provers ’ input syntaxes. We also describe a GUI integrating the translations and the provers into the Heterogeneous Tool Set. We report on experiences with provers, which led to fine-tuning of the translations. This framework can also be used for checking consistency of specifications. 1

The status of the Common Framework Initiative (CoFI) and the Common Algebraic Specification Language (Casl) are briefly presented.

The specification language Csp-Casl allows one to model processes as well as data of distributed systems within one framework. In our paper, we describe how a combination of the existing tools Hets and Csp-Prover can solve the challenges that Csp-Casl raises on integrated theorem proving for processes and data. For building this new tool, the automated generation of theorems and their proofs in Isabelle/HOL plays a fundamental role. A case study of industrial strength demonstrates that our approach scales up to complex problems. Keywords:

We present an overview of the landscape of ontology languages, mostly pertaining to the first-order paradigm. In particular, we present a uniform formalisation of these languages based on the institution theoretical framework, allowing a systematic treatment and analysis of the translational relationships between the various languages and a general analysis of properties of such translations. We also discuss the importance of language translation from the point of view of ontological modularity and logical pluralism, and for the borrowing of tools and reasoners between languages.

Abstract. We describe a way to make the static analysis for the inthe-large part of the Common Algebraic Specification Language (Casl) independent of the underlying logic that is used for specification in-thesmall. The logic here is formalized as an institution with some extra components. Following the institution independent semantics of Casl in-the-large, we thus get an institution independent static analysis for Casl in-the-large. With this, it is possible to re-use the Casl static analysis for extensions of Casl, or even completely different logics. One only has to provide a static analysis for specifications in-the-small for the given logic. This then can be plugged into the generic static analysis for Casl in-the-large. 1

Abstract. The specification language Csp-Casl allows one to model data as well as processes of distributed systems within one framework. In our paper, we describe how a combination of the existing tools HETS and Csp-Prover can solve the challenges that Csp-Casl raises on integrated theorem proving for processes and data. For building this new tool, the automated generation of theorems and their proofs in Isabelle/HOL plays a fundamental role. A case study of industrial strength demonstrates that our approach scales up to complex problems. 1