In our paper we investigate the use of qualitative spatial representations (QSR) about relative direction and distance for shape representation. Our new approach has the advantage that we can generate prototypical shapes from our abstract representation in first-order predicate calculus. Using the conceptual neighborhood which is an established concept in QSR we can directly establish a concept...

Recently a new connection between proof theory and formal language theory was introduced. It was shown that the operation of cut elimination for proofs in first-order predicate logic involving Π1-cuts corresponds to computing the language of a particular class of regular tree grammars. The present paper expands this connection to the level of Π2-cuts. Given a proof π of a Σ1 formula with cuts o...

In this paper we introduce a conception of learning which is a natural extension of economists' representations of learning and which is natural to develop using KBS technology. In the particular form of KBS we use, rule conditions and actions are well formulated formulae of first-order predicate logic (FOPL). As a result, the simulation results obtained from these models are no less analytical...

This is a study on the truth-conditional semantics of propositional attitude attribution statements. It is suggested that attitude contents should be characterized in terms of abstract concepts, which are connected by way of a number of basic logical relations derived from a version of Quinean predicate-functor logic. This allows us to handle all logical relationships definable by first-order p...

Binary decision diagrams (BDDs) are known to be a very efficient technique to handle propositional formulas. We present an extension of BDDs such that they can be used for predicate logic. We define BDDs similar to Bryant [IEEE Trans. Comp. C-35 (1986) 677–691], but with the difference that we allow predicates as labels instead of proposition symbols. We present a sound and complete proof searc...

In this paper we present a powerful uniform first-order framework for representing and reasoning with complex forms of default knowledge. This is achieved by extending first-order predicate logic with a new generalized quantifier, anchored in the quasi-probabilistic ranking measure paradigm [Weydert 94], which subsumes and refines the original, propositional notion of a default conditional [Del...

There is a range of modelling notations, both textual and diagrammatic, whose semantics are based on first-order predicate logic. This paper presents a visual framework for organizing models of systems which allows a mixture of notations, diagrammatic or textbased, to be used. The framework is based on the use of templates for connective operations which can be nested and sometimes flattened. I...

We propose a new method of computing cohomology groups of spaces of knots in Rn, n ≥ 3, based on the topology of configuration spaces and twoconnected graphs, and calculate all such classes of order ≤ 3. As a byproduct we define the higher indices, which invariants of knots in R define at arbitrary singular knots. More generally, for any finite-order cohomology class of the space of knots we de...

We will provide an example of a p-group G which has elements of order p in some of its integral cohomology groups but which also has the property that p annihilates H̄(G;Z) for all sufficiently high i. This provides a counterexample to a conjecture of A. Adem which stated that if a finite group K has an element of order p in one of its integral cohomology groups then it has such an element in in...

— It is shown here that, for any finitely generated lattice r in certain semi simple groups over local fields of positive characteristics, H (r. Ad) is nonvanishing; this is in sharp contrast with the situation in characteristic zero. Let Kbe a local field (i. e. a non-discrete locally compact field), and let G be a connected semi simple algebraic group defined over K. Let G = G (K), and let r ...