Adding homomorphisms to commutative/monoidal theories or : how algebra can help in equational unification

Two approaches to equational unification can be distinguished. The syntactic approach relies heavily on the syntactic structure of the identities that define the equational theory. The semantic approach exploits the structure of the algebras that satisfy the theory. With this paper we pursue the semantic approach to unification. We consider the class of theories for which solving unification problems is equivalent to solving systems of linear equations over a semiring. This class has been introduced by the authors independently of each other as commutative theories (Baader) and monoidal theories (Nutt). The class encompasses important examples like the theories of abelian monoids, idempotent abelian monoids, and abelian groups. We identify a large subclass of commutative/monoidal theories that are of unification type zero by studying equations over the corresponding semiring. As a second result, we show with methods from linear algebra that unitary and finitary commutative/monoidal theories do not change their unification type when they are augmented by a finite monoid of homomorphisms, and how algorithms for the extended theory can be obtained from algorithms for the basic theory. The two results illustrate how using algebraic machinery can lead to general results and elegant proofs in unification theory

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

Residuation and guarded rules for constraint logic programming

A major difficulty with logic programming is combinatorial explosion: since goals are solved with possibly indeterminate (i.e., branching) reductions, the resulting search trees may grow wildly. Constraint logic programming systems try to avoid combinatorial explosion by building in strong determinate (i.e., non-branching) reduction in the form of constraint simplification. In this paper we present two concepts, residuation and guarded rules, for further strengthening determinate reduction. Both concepts apply to constraint logic programming in general and yield an operational semantics that coincides with the declarative semantics. Residuation is a control strategy giving priority to determinate reductions. Guarded rules are logical consequences of programs adding otherwise unavailable determinate reductions

Integrated plan generation and recognition : a logic-based approach

The work we present in this paper is settled within the field of intelligent help systems. Intelligent help systems aim at supporting users of application systems by the achievements of qualified experts. In order to provide such qualified support our approach is based on the integration of plan generation and plan recognition components. Plan recognition in this context serves to identify the users goals and so forms the basis for an active user support. The planning component dynamically generates plans which are proposed for the user to reach her goal. We introduce a logic-based approach where plan generation and plan recognition is done on a common logical basis and both components work in some kind of cross-talk

Relfun/X : an experimental prolog implementation of Relfun

Relfun/X is an experimental implementation of Relfun, a relational and functional language developed by Harold Boley at Kaiserslautern University. It is totally implemented in Prolog; additionally, the Relfun/X programs are compiled into Prolog programs (i.e. "consulted" analogously to the ordinary consulting scheme of Prolog). While Relfun/X does not provide all the features of the Lisp-based Relfun implementation, it is the first running version supporting Relfun´s multi-footed clauses

Towards the integration of functions, relations and types in an AI programming language

This paper describes the design and implementation of the programming language PC-Life. This language integrates the functional and the Logic-oriented programming style and feature types supporting inheritance. This combination yields a language particularly suited to knowledge representation, especially for application in computational linguistics

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

The complexity of existential quantification in concept languages

Much of the research on concept languages, also called terminological languages, has focused on the computational complexity of subsumption. The intractability results can be divided into two groups. First, it has been shown that extending the basic language FL- with constructs containing some form of logical disjunction leads to co-NP-hard subsumption problems. Second, adding negation to FL- makes subsumption PSPACE-complete. The main result of this paper is that extending FL- with unrestricted existential quantification makes subsumption NP-complete. This is the first proof of intractability for a concept language containing no construct expressing disjunction--whether explicitly or implicitly. Unrestricted existential quantification is therefore, alongside disjunction, a source of computational complexity in concept languages

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

Using pattern-action rules for the generation of GPSG structures from separate semantic representations

In many tactical NL generators the semantic input structure is taken for granted. In this paper, a new approach to multilingual, tactical generation is presented that keeps the syntax separate from the semantics. This allows for the system to be directly adapted to application-dependent representations. In the case at hand, the semantics is specifically designed for sentence-semantic transfer in a machine translation system. The syntax formalism used is Generalized Phrase Structure Grammar (GPSG). The mapping from semantic onto syntactic structures is performed by a set of pattern-action rules. Each rule matches a piece of the input structure and guides the GPSG structure-building process by telling it which syntax rule(s) to apply. The scope of each pattern-action rule is strictly local, the actions are primitive, and rules can not call each other. These restrictions render the production rule approach both highly modular and transparent