Christoph Beierle

Methoden wissensbasierter Systeme

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Refining Abstract Machine Specifications of the Steam Boiler Control to Well Documented Executable Code

We use the steam boiler control specification problem to illustrate how the evolving algebra approach to the specification and the verification of complex systems can be exploited for a reliable and well documented development of executable, but formally inspectable and systematically modifiable code. A hierarchy of stepwise refined abstract machine models is developed, the ground version of which can be checked for whether it faithfully reflects the informally given problem. The sequence of machine models yields various abstract views of the system, making the various design decisions transparent, and leads to a C++ program. This program has been demonstrated during the Dagstuhl-Meeting on Methods for Semantics and Specification, in June 1995, to control the Karlsruhe steam boiler simulator satisfactorily.

Modelling conditional knowledge discovery and belief revision by abstract state machines

We develop a high-level ASM specification for the CONDOR system that provides powerful methods and tools for managing knowledge represented by conditionals. Thereby, we are able to elaborate crucial interdependencies between different aspects of knowledge representation, knowledge discovery, and belief revision. Moreover, this specification provides the basis for a stepwise refinement development process of the CONDOR system based on the ASM methodology.

Logic programming with typed unification and its realization on an abstract machine

Logic programming can benefit from a typing concept which supports many software engineering principles such as data abstraction, modularization, etc. From a computational point of view, the use of types can drastically reduce the search space. Starting from these observations, this paper gives a survey of many-sorted, order-sorted, and polymorphic approaches to type concepts in logic programming. The underlying unification procedures for ordinary term unification, order-sorted unification, and in particular for polymorphic order-sorted unification are given in the style of solving a set of equations, giving a common basis for comparing them. In addition, the realization of these unification procedures on a Warren Abstract Machine-like architecture is described. Special emphasis is placed on the abstract machine developed for PROTOS-L, a logic programming language based on polymorphic order-sorted unification.

Correctness Proof For the WAM with Types

We provide a mathematical specification of an extension of Warrens Abstract Machine for executing Prolog to type-constraint logic programming and prove its correctness. In this paper, we keep the notion of types and dynamic type constraints rather abstract to allow applications to different constraint formalisms like Prolog III or CLP(R). This generality permits us to introduce modular extensions of Borgers and Rosenzweigs formal derivation of the WAM. Starting from type-constraint Prolog algebras that are derived from Borgers standard Prolog algebras, the specification of the type-constraint WAM extension is given by a sequence of evolving algebras, each representing a refinement level. For each refinement step a correctness proof is given. Thus, we obtain the theorem that for every such abstract type-constraint logic programming system L and for every compiler satisfying the specified conditions, the WAM extension with an abstract notion of types is correct w.r.t. L. This is a first step towards our aim to provide a full specification and correctness proof of a concrete system, the PROTOS Abstract Machine (PAM), an extension of the WAM by polymorphic order-sorted unification as required by the logic programming language PROTOS-L.

Using equivalences of worlds for aggregation semantics of relational conditionals

For relational probabilistic conditionals, the so-called aggregation semantics has been proposed recently. Applying the maximum entropy principle for reasoning under aggregation semantics requires solving a complex optimization problem. Here, we improve an approach to solving this optimization problem by Generalized Iterative Scaling (GIS). After showing how the method of Lagrange multipliers can also be used for aggregation semantics, we exploit that possible worlds are structurally equivalent with respect to a knowledge base

An Algebraic Characterization of STUF

\mathcal R

Skeptical Inference Based on C-Representations and Its Characterization as a Constraint Satisfaction Problem

if they have the same verification and falsification properties. We present a GIS algorithm operating on the induced equivalence classes of worlds; its implementation yields significant performance improvements.

Defining Standard Prolog in Rewriting Logic

Unification-based grammar formalisms rest on the representation of linguistic entities in terms of feature-value structures. Lexical entries, grammar rules, phrases, and sentences are represented by complex feature structures enriched with equality. Speaking of feature structures as linguistic types suggests to look at other areas where types have been studied for a long time: the world of abstract data type specifications. One immediately observes a number of similarities between feature types and data types. The major link is the concept of equality which plays a central role in both approaches. Taking this as the starting point, we employ the algebraic machinery known from abtract data type specifications to the Stuttgart Type Unification Formalism (STUF). STUF provides a powerful notation for handling feature graphs, and the algebraic characterization of STUF we present here contributes to the formal understanding of the formalism. By translating feature graphs into algebraic data type specifications we are able to define an algebraic semantics for feature graphs. The algebraic framework also provides simple and precise definitions of operations of STUF graphs such as unification, subsumption and equivalence. Moreover, by employing the Knuth-Bendix Algorithm, a well-known tool for normalizing systems of equations, the various consistency concepts used for feature graph descriptions can be described and tested easily.

Specification and correctness proof of a WAM extension with abstract type constraints

The axiomatic system P is an important standard for plausible, nonmonotonic inferences that is, however, known to be too weak to solve benchmark problems like irrelevance, or subclass inheritance so-called Drowning Problem. Spohns ranking functions which provide a semantic base for system P have often been used to design stronger inference relations, like Pearls system Z, or c-representations. While each c-representation shows excellent inference properties and handles particularly irrelevance and subclass inheritance properly, it is still an open problem which c-representation is the best. In this paper, we focus on the generic properties of c-representations and consider the skeptical inference relation c-inference that is obtained by taking all c-representations of a given knowledge base into account. In particular, we show that c-inference preserves the properties of solving irrelevance and subclass inheritance which are met by every single c-representation. Moreover, we characterize skeptical c-inference as a constraint satisfaction problem so that constraint solvers can be used for its implementation.