This paper is a contribution to the theoretical foundations of strategies. We first present a general definition of abstract strategies which is extensional in the sense that a strategy is defined explicitly as a set of derivations of an abstract reduction system. We then move to a more intensional definition supporting the abstract view but more operational in the sense that it describes a mea...

We describe a logic language to formally express interdependencies between classes belonging to different schemas, the socalled interschema knowledge. These interdependencies allow a designer of a multidatabase (MDB) to establish relationships between both the intensional definition and the set of instances of classes represented in different schemas. These assertions form the „backbone“ of the...

My discussion will be focussed on the notion of a property. I first present the standard intensional definition of a property, which is formulated in terms of possible worlds, and outline some of the philosophical problems this definition leads to. Then I introduce the notion of a conceptual space and show how such spaces can be used as a basis for a new criterion of what a property is. This cr...

In this paper we present an extensional higher-order resolution calculus that is complete relative to Henkin model semantics. The treatment of the extensionality principles – necessary for the completeness result – by specialized (goal-directed) inference rules is of practical applicability, as an implentation of the calculus in the Leo-System shows. Furthermore, we prove the long-standing conj...

We show the existence of an infinitary confluent and normalising extension of the finite extensional lambda calculus with beta and eta. Besides infinite beta reductions also infinite eta reductions are possible in this extension, and terms without head normal form can be reduced to bottom. As corollaries we obtain a simple, syntax based construction of an extensional Böhm model of the finite la...

We propose a natural syntactic account of extensional equality in type theory. Starting from the classical definition of extensional equality by induction on type structure, we show how the logical relation can be internalized in a way that covers all higher dimensions simultaneously. The result is a type theory in which every type has a (nontruncated) globular structure with degeneracy maps. S...

Inspired by recent work on normalisation by evaluation for sums, we propose a normalising and confluent extensional rewriting theory for the simply-typed λ-calculus extended with sum types. As a corollary of confluence we obtain decidability for the extensional equational theory of simply-typed λ-calculus extended with sum types. Unlike previous decidability results, which rely on advanced rewr...

The German mathematician and one of the founding fathers of modern logic, Gottlob Frege (1848-1925), was the first to clearly realize that semantics has little to do with psychology, and that it could be usefully explicated in mathematical terms (see Dummett, 1973; 1981). His depsychologization of semantics followed from his depsychologization of logic. Frege understood how crucial it was for t...