Uwe Reyle

This paper proposes a method for computing the temporal aspects of the interpretations of a variety of Germa sentences. The method is strictly modular in the sense that it allows each meaning-bearing sentence constituent to make its own, separate, contribution to the semantic representation of any sentence containing it. The semantic representation of a sentence is reached in several stages. First, an ‘initial semantic representation’ is constructed, using a syntactic analysis of the sentence as input. This initial representation is then transformed into the definitive representation by a series of transformations which reflect the ways in which the contributions from different constituents of the sentence interact. Since the different constituents which make their respective contributions to the meaning of the sentence are in most instances ambiguous, the initial representations are typically of a high degree of underspecification.

This paper presents a sound and complete proof system for the first order fragment of Discourse Representation Theory. Since the inferences that human language users draw from the verbal input they receive for the most transcend the capacities of such a system, it can be no more than a basis on which more powerful systems, which are capable of producing those inferences, may then be built. Nevertheless, even within the general setting of first order logic the structure of the formulas of DRS-languages, i.e. of the Discourse Representation Structures suggest for the components of such a system inference rules that differ somewhat from those usually found in proof systems for the first order predicate calculus and which are, we believe, more in keeping with inference patterns that are actually employed in common sense reasoning.This is why we have decided to publish the present exercise, in spite of the fact that it is not one for which a great deal of originality could be claimed. In fact, it could be argued that the problem addressed in this paper was solved when Gödel first established the completeness of the system of Principia Mathematica for first order logic. For the DRS-languages we consider here are straightforwardly intertranslatable with standard formulations of the predicate calculus; in fact the translations are so straightforward that any sound and complete proof system for first order logic can be used as a sound and complete proof system for DRSs: simply translate the DRSs into formulas of predicate logic and then proceed as usual. As a matter of fact, this is how one has chosen to proceed in some implementations of DRT, which involve inferencing as well as semantic representation; an example is the Lex system developed jointly by IBM and the University of Tübingen )

th This volume is dedicated to Dov Gabbay who celebrated his 50 birthday in October 1995. Dov is one of the most outstanding and most productive researchers we have ever met. He has exerted a profound influence in major fields of logic, linguistics and computer science. His contributions in the areas of logic, language and reasoning are so numerous that a comprehensive survey would already fill half of this book. Instead of summarizing his work we decided to let him speak for himself. Sitting in a car on the way to Amsterdam airport he gave an interview to Jelle Gerbrandy and Anne-Marie Mineur. This recorded conversation with him, which is included gives a deep insight into his motivations and into his view of the world, the Almighty and, of course, the role of logic. In addition, this volume contains a partially annotated bibliography of his main papers and books. The length of the bibliography and the broadness of the topics covered there speaks for itself.

Resolution is an effective deduction procedure for classical logic. There is no similar "resolution" system for non-classical logics (though there are various automated deduction systems). The paper presents resolution systems for intuistionistic predicate logic as well as for modal and temporal logics within the framework of labelled deductive systems. Whereas in classical predicate logic resolution is applied to literals, in our system resolution is applied to L(abelled) R(epresentation) S(tructures). Proofs are discovered by a refutation procedure defined on LRSs, that imposes a hierarchy on clause sets of such structures together with an inheritance discipline. This is a form of Theory Resolution. For intuitionistic logic these structures are called I(ntuitionistic) R(epresentation) S(tructures). Their hierarchical structure allows the restriction of unification of individual variables and/or constants without using Skolem functions. This structures must therefore be preserved when we consider other (non-modal) logics. Variations between different logics are captured by fine tuning of the inheritance properties of the hierarchy. For modal and temporal logics IRS's are extended to structures that represent worlds and/or times. This enables us to consider all kinds of combined logics.