Lars Hallnäs’s research while affiliated with University of Borås and other places

MedView is a joint project with participants from oral medicine and computer science. The aim of the project is to build a large database from patient examinations and produce computerized tools to extend, view, and analyze the contents of the database. The contents of the data base is based on a formalization of health-care processes and clinical knowledge in oral medicine harmonized within the network SOMNET. We give an overview of the current status of the MedView project and discuss background and future directions.

Informative art is computer augmented, or amplified, works of art that not only are aesthetical objects but also information displays, in as much as they dynamically reflect information about their environment. Informative art can be seen as a kind of slow technology, i.e. a technology that promotes moments of concentration and reflection. Our aim is to present the design space of informative art. We do so by discussing its properties and possibilities in relation to work on information visualisation, novel information display strategies, as well as art. A number of examples based on different kinds of mapping relations between information and the properties of the composition of an artwork are described.

Primitive recursion can be seen as the computational interpretation of induction through the Curry-Howard interpretation of propositions-as-types. In the present paper we discuss what happens if we apply this idea to possible non monotone inductive definitions. We start with a logical interpretation of a class of inductive definitions, thepartial inductive definitions. Then we internalise induction over such definitions as a rule of inference and consider a Curry-Howard interpretation of these definitions as type systems. As a basic example we discuss what meaning this interpretation gives to primitive recursion on a definition likeN=N→N.

We introduce a definitional extension of logic programming by means of an inference schema (Ph), which, in acertain sense, is dual to the (1-P) schema of rule application discussed in Part I. In the operational semantics, this schema is dual to the resolution principle. We prove soundness and completeness for the extended system, discuss the computation of substitutions that this new schema gives rise to, and also consider the notion of negation intrinsic to the system and its relation to negation by failure.

An attempt to consider partial definitions of semantically oriented data types will be described. We will in a certain sense think of such data types as inductively defined. A class of inductive definitions will be interpreted as partial definitions: partial inductive definitions. The presentation of such a definition is in itself elementary and the true complexity of the definition will show itself in questions concerning the isolation of totally defined objects. It is the same situation as in the case of partial recursive functions.The basic aim is to investigate the possibility to give direct inductive definitions of semantical notions exploring, so to speak, the structure of the given notion rather than to think of such notions as indirectly presented by a formal system or given by a definition, together with a proof of its correctness, in terms of recursion on some well-founded structure.

Without Abstract

In this paper definite Horn clause programs are investigated within a proof-theoretic framework; program clauses being considered rules of a formal system. Based on this approach, the soundness and completeness of SLD-resolution is established by purely proof-theoretic methods. Extended Horn clauses are defined as rules of higher levels and related to an approach based on implication formulae in the bodies of clauses. In a further extension, which is treated in Part II of this series, program clauses are viewed as clauses in inductive definitions of atoms, justifying an additional inference schema: a reflection principle that roughly corresponds to interpreting the program clauses as introduction rules in the sense of natural deduction. The evaluation procedures for queries with respect to the defined extensions of definite Horn clause programs are shown to be sound and complete. The sequent calculus with the general elimination schema even permits the introduction of a genuine notion of falsity which is not defined via a meta-rule.

We present a logic programming language, GCLA*** (Generalized horn Clause LAnguage), that is based on a generalization of Prolog. This generalization is unusual in that it takes a quite different view of the meaning of a logic program—a “definitional” view rather than the traditional logical view. GCLA has a number of noteworthy properties, for instance hypothetical and non-monotonic reasoning. This makes implementation of reasoning in knowledge-based systems more direct in GCLA than in Prolog. GCLA is also general enough to incorporate functional programming as a special case. GCLA and its syntax and semantics are described. The use of various language constructs are illustrated with several examples.