stonian p ortholattices a new approach to the mereotopology rt0 this paper gives an algebraic representation of the subtheories rt rt e c and rt of asher and vieu s first order ontology of mereotopology rt 0 it corrects and extends previous work on the representation of these mereotopologies we develop the theory of p ortholattices lattices that are both orthocomplemented and pseudocomplemented and show that together with the stone identity x y x y or equivalent definitions the natural class of stonian p ortholattices can be defined the main contribution of the paper consists of a representation theorem for rt as stonian p ortholattices moreover it is shown that the class of models of rt e c is isomorphic to the non distributive stonian p ortholattices and a characterization of rt is given by a set of four algebras of which one need to be a subalgebra of the present lattice model as corollary we obtain that axiom a11 existence of two externally connected regions is in fact a theorem of the remaining axioms of rt

constants and finite unary relations in qualitative constraint reasoning extending qualitative csps with the ability of restricting selected variables to finite sets of possible values has been proposed as an interesting research direction with important applications c

a nonlinear filtering approach to changepoint detection problems direct and differential geometric methods a benchmark change detection problem is considered which involves the detection of a change of unknown size at an unknown time both unknown quantities are modelled by stochastic variables which allows the problem to be formulated within a bayesian framework it turns out that the resulting nonlinear filtering problem is much harder than the well known detection problem for known sizes of the change and in particular that it can no longer be solved in a recursive manner an approximating recursive filter is therefore proposed which is designed using differential geometric methods in a suitably chosen space of unnormalized probability densities the new nonlinear filter can be interpreted as an adaptive version of the celebrated shiryayev wonham equation for the detection of a priori known changes combined with a modified kalman filter structure to generate estimates of the unknown size of the change this intuitively appealing interpretation of the nonlinear filter and its excellent performance in simulation studies indicate that it may be of practical use in realistic change detection problems

a relation algebraic approach to the region connection calculus abstract we explore the relation algebraic aspects of the region connection calculus rcc of randell et al proceedings of the cade vol 11 pp 786 790 springer berlin 1992a in particular we present a refinement of the rcc8 table which shows that the axioms provide for more relations than are listed in the present table we also show that each rcc model leads to a boolean algebra finally we prove that a refined version of the rcc5 table has as models all atomless boolean algebras b with the natural ordering as the part of relation and that the table is closed under first order definable relations iff b is homogeneous

realizing rcc8 networks using convex regions rcc8 is a popular fragment of the region connection calculus in which qualitative spatial relations between regions such as adjacency overlap and parthood can be expressed while rcc8 is essentially dimensionless most current applications are confined to reasoning about two dimensional or three dimensional physical space in this paper however we are mainly interested in conceptual spaces which typically are high dimensional euclidean spaces in which the meaning of natural language concepts can be represented using convex regions the aim of this paper is to analyze how the restriction to convex regions constrains the realizability of networks of rcc8 relations first we identify all ways in which the set of rcc8 base relations can be restricted to guarantee that consistent networks can be convexly realized in respectively 1d 2d 3d and 4d most surprisingly we find that if the relation partially overlaps is disallowed all consistent atomic rcc8 networks can be convexly realized in 4d if instead refinements of the relation part of are disallowed all consistent atomic rcc8 relations can be convexly realized in 3d we furthermore show among others that any consistent rcc8 network with 2 n 1 variables can be realized using convex regions in the n dimensional euclidean space

region connection calculus its models and composition table originating in allen s analysis of temporal relations the notion of composition table has become a key technique in providing an efficient inference mechanism for a wide class of theories in the field artificial intelligence this paper is mainly about the consistency based composition table rcc8 ct of the region connection calculus rcc raised by randell cui and cohn first we show each rcc model is a consistent model of the rcc8 ct then after an exhaustive analysis we show that no rcc model can be interpreted extensionally anyway and hence give a negative answer to a conjecture raised by bennett all these results are given in an extensional rcc8 composition table where we attach to each cell entry in the rcc8 ct a superscript to indicate in what circumstances an extensional interpretation is possible

recursive nonlinear estimation geometry of a space of posterior densities the paper establishes a geometric formulation for nonlinear parameter estimation using reduced statistics if a reduced rather than sufficient statistic is used in estimation an equivalence class of densities p t rather than the true posterior density p t is determined two questions arise in this connection 1 what kind of a reduced statistic allows recursive computations 2 what is the appropriate representative p t of the equivalence class p t typically the first question is not posed at all and the second one is resolved by heuristic considerations the present paper attempts to cast the problem into a solid mathematical structure it closely follows the differential geometric approach suggested in kulhav automatica 26 545 555 1990 but goes into more detail roughly admissible statistics are characterized here as homomorphisms of a group containing all possible likelihoods a representative of the pertinent equivalence class is constructed by a projection along this class onto an orthogonal submanifold going through a prespecified density p and imbedded in the manifold of possible posteriors the obtained projection p t has attractive extremal properties it minimizes the kullback leibler distance from the reference point p and at the same time the dual kullback leibler distance from the true point p t

rcc8 binary constraint network can be consistently extended the rcc8 constraint language developed by randell et al has been popularly adopted by the qualitative spatial reasoning and gis communities the recent observation that rcc8 composition table describes only weak composition instead of composition raises questions about renz and nebel s maximality results about the computational complexity of reasoning with rcc8 this paper shows that any consistent rcc8 binary constraint network rcc8 network for short can be consistently extended given an rcc8 network and z a fresh variable suppose xty and t is contained in the weak composition of r and s this means that we can add two new constraints xrz and zsy to without changing the consistency of the network the result guarantees the applicability to rcc8 of one key technique theorem 5 of j renz b nebel on the complexity of qualitative spatial reasoning a maximal tractable fragment of the region connection calculus artificial intelligence 108 1999 69 123 which allows the transfer of tractability of a set of rcc8 relations to its closure under composition intersection and converse

boolean connection algebras a new approach to the region connection calculus abstract the region connection calculus rcc is a well established formal system for qualitative spatial reasoning it provides an axiomatization of space which takes regions as primitive rather than as constructions from sets of points the paper introduces boolean connection algebras bcas and proves that these structures are equivalent to models of the rcc axioms bcas permit a wealth of results from the theory of lattices and boolean algebras to be applied to rcc this is demonstrated by two theorems which provide constructions for bcas from suitable distributive lattices it is already well known that regular connected topological spaces yield models of rcc but the theorems in this paper substantially generalize this result additionally the lattice theoretic techniques used provide the first proof of this result which does not depend on the existence of points in regions

combining topological and size information for spatial reasoning information about the size of spatial regions is often easily accessible and when combined with other types of spatial information it can be practically very useful in this paper we introduce four classes of qualitative and metric size constraints and we study their integration with the region connection calculus rcc 8 a well known approach to qualitative spatial reasoning with topological relations we propose a new path consistency algorithm for combining rcc 8 relations and qualitative size relations the algorithm is complete for deciding satisfiability of an input set of topological constraints over one of the three maximal tractable subclasses of rcc 8 containing all the basic relations moreover its time complexity is cubic and is the same as the complexity of the best known method for deciding satisfiability when only these topological relations are considered we also provide results on finding a consistent scenario in cubic time for these combined classes regarding metric size constraints we first study their combination with rcc 8 and we show that deciding satisfiability for the combined sets of constraints is np hard even when only the rcc 8 basic relations are used then we introduce rcc 7 a subalgebra of rcc 8 that can be used for applications where spatial regions cannot partially overlap we show that reasoning with the seven rcc 7 basic relations and the universal relation is intractable but that reasoning with the rcc 7 basic relations combined with metric size information is tractable finally we give a polynomial algorithm for the latter case and a backtracking algorithm for the general case

a differential geometric approach to nonlinear filtering the projection filter this paper presents a new and systematic method of approximating exact nonlinear filters with finite dimensional filters using the differential geometric approach to statistics the projection filter is defined rigorously in the case of exponential families a convenient exponential family is proposed which allows one to simplify the projection filter equation and to define an a posteriori measure of the local error of the projection filter approximation finally simulation results are discussed for the cubic sensor problem

a representation theorem for boolean contact algebras we prove a representation theorem for boolean contact algebras which implies that the axioms for the region connection calculus rcc d a randell a g cohn z cui computing transitivity tables a challenge for automated theorem provers in d kapur ed proceedings of the 11th international conference on automated deduction cade 11 lecture notes in artificial intelligence vol 607 springer saratoga springs ny 1992 pp 786 790 are complete for the class of subalgebras of the algebras of regular closed sets of weakly regular connected t1 spaces

gaussian approximation in recursive estimation of multiple state of nonlinear wiener systems abstract the paper concerns recursive state estimation in wiener systems where the output is a scalar weighted sum of multiple states a gaussian approximation to the computed conditional probability distribution for the scalar sum of states is shown to lead to a practicable numerical algorithm for estimating the multiple states this algorithm mimics the kalman filter simulations show the method giving good performance when the nonlinearity is severe quantization

deformations of calabi yau hypersurfaces arising from deformations of toric varieties one can deform the complex structure of calabi yau hypersurfaces in toric varieties by changing the coefficients of the defining polynomial however there must also exist non polynomial deformations of the calabi yau hypersurfaces which cannot be realized inside the ambient toric variety in this paper we have constructed the missing non polynomial deformations which are induced by an automorphism on the open part of the ambient toric variety

differential geometry of curved exponential families curvatures and information loss the differential geometrical framework is given for analyzing statistical problems related to multi parameter families of distributions the dualistic structures of the exponential families and curved exponential families are elucidated from the geometrical viewpoint the duality connected by the legendre transformation is thus extended to include two kinds of affine connections and two kinds of curvatures the second order information loss is calculated for fisher efficient estimators and is decomposed into the sum of two non negative terms one is related to the exponential curvature of the statistical model and the other is related to the mixture curvature of the estimator only the latter term depends on the estimator and vanishes for the maximum likelihood estimator a set of statistics which recover the second order information loss are given the second order efficiency also is obtained the differential geometry of the function space of distributions is discussed

on binary constraint problems the concepts of binary constraint satisfaction problems can be naturally generalized to the relation algebras of tarski the concept of path consistency plays a central role algorithms for path consistency can be implemented on matrices of relations and on matrices of elements from a relation algebra we give an example of a 4 by 4 matrix of infinite relations on which on iterative local path consistency algorithm terminates we give a class of examples over a fixed finite algebra on which all iterative local algorithms whether parallel or sequential must take quadratic time specific relation algebras arising from interval constraint problems are also studied the interval algebra the point algebra and the containment algebra

rudiments of rough sets abstract worldwide there has been a rapid growth in interest in rough set theory and its applications in recent years evidence of this can be found in the increasing number of high quality articles on rough sets and related topics that have been published in a variety of international journals symposia workshops and international conferences in recent years in addition many international workshops and conferences have included special sessions on the theory and applications of rough sets in their programs rough set theory has led to many interesting applications and extensions it seems that the rough set approach is fundamentally important in artificial intelligence and cognitive sciences especially in research areas such as machine learning intelligent systems inductive reasoning pattern recognition mereology knowledge discovery decision analysis and expert systems in the article we present the basic concepts of rough set theory and point out some rough set based research directions and applications

a logic for rough sets abstract the collection of all subsets of a set forms a boolean algebra under the usual set theoretic operations while the collection of rough sets of an approximation space is a regular double stone algebra pomykala and pomykala 1988 the appropriate class of algebras for classical propositional logic are boolean algebras and it is reasonable to assume that regular double stone algebras are a class of algebras appropriate for a logic of rough sets using the representation theorem for these algebras by katrinak 1974 we present such a logic for rough sets and its algebraic semantics in the spirit of andreka and nemeti 1994

generalized region connection calculus the region connection calculus rcc is one of the most widely referenced system of high level qualitative spatial reasoning rcc assumes a continuous representation of space this contrasts sharply with the fact that spatial information obtained from physical recording devices is nowadays invariably digital in form and therefore implicitly uses a discrete representation of space recently galton developed a theory of discrete space that parallels rcc but question still lies in that can we have a theory of qualitative spatial reasoning admitting models of discrete spaces as well as continuous spaces in this paper we aim at establishing a formal theory which accommodates both discrete and continuous spatial information and a generalization of region connection calculus is introduced grcc the new theory takes two primitives the mereological notion of part and the topological notion of connection rcc and galton s theory for discrete space are both extensions of grcc the relation between continuous models and discrete ones is also clarified by introducing some operations on models of grcc in particular we propose a general approach for constructing countable rcc models as direct limits of collections of finite models compared with standard rcc models given rise from regular connected spaces these countable models have the nice property that each region can be constructed in finite steps from basic regions two interesting countable rcc models are also given one is a minimal rcc model the other is a countable sub model of the continuous space r 2

reasoning about cardinal directions between extended objects direction relations between extended spatial objects are important commonsense knowledge recently goyal and egenhofer proposed a relation model known as the cardinal direction calculus cdc for representing direction relations between connected plane regions the cdc is perhaps the most expressive qualitative calculus for directional information and has attracted increasing interest from areas such as artificial intelligence geographical information science and image retrieval given a network of cdc constraints the consistency problem is deciding if the network is realizable by connected regions in the real plane this paper provides a cubic algorithm for checking the consistency of complete networks of basic cdc constraints and proves that reasoning with the cdc is in general an np complete problem for a consistent complete network of basic cdc constraints our algorithm returns a canonical solution in cubic time this cubic algorithm is also adapted to check the consistency of complete networks of basic cardinal constraints between possibly disconnected regions

on redundant topological constraints redundancy checking is an important task in the research of knowledge representation and reasoning in this paper we consider redundant qualitative constraints for a set of qualitative constraints we say a constraint x r y in is redundant if it is entailed by the rest of a prime subnetwork of is a subset of which contains no redundant constraints and has the same solution set as it is natural to ask how to compute such a prime subnetwork and when it is unique we show that this problem is in general intractable but becomes tractable if is over a tractable subalgebra s of a qualitative calculus furthermore if s is a subalgebra of the region connection calculus rcc8 in which weak composition distributes over nonempty intersections then has a unique prime subnetwork which can be obtained in cubic time by removing all redundant constraints simultaneously from as a by product we show that any path consistent network over such a distributive subalgebra is minimal and globally consistent in a qualitative sense a thorough empirical analysis of the prime subnetwork upon real geographical data sets demonstrates the approach is able to identify significantly more redundant constraints than previously proposed algorithms especially in constraint networks with larger proportions of partial overlap relations