Tractability Results in the Block Algebra

Balbiani, Philippe; Condotta, Jean‐François; Cerro, Luís Fariñas del

doi:10.1093/logcom/12.5.885

Cited by 31 publications

(28 citation statements)

References 17 publications

(15 reference statements)

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“…The set Cba of convex BArelations, together with the operations of intersection, composition and converse, is a sub algebra of BA [12]. A similar result holds for the set Cbcd of convex relations of the BCD calculus.…”

Section: The Tractability Of Convex Subalgebra Of the Bcd Calculusmentioning

confidence: 62%

“…All the convex relations in 2 B 3 are closed under the operations of intersection, converse and composition [12]. We show that the set of convex block cardinal direction relations of the BCD calculus is tractable by using this property.…”

Section: The Tractability Of Convex Subalgebra Of the Bcd Calculusmentioning

confidence: 94%

“…As we already know, the convex subset of the BA is tractable [12]. We now exploit the connection between the BA and BCD-calculus to show that the consistency and minimality problem of BCD network can be solved in polynomial time.…”

Section: The Tractability Of Convex Subalgebra Of the Bcd Calculusmentioning

confidence: 99%

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Reasoning with Cardinal Directions in 3D Space Based on Block Algebra

Hou¹,

Wu²,

Yang³

2017

dtcse

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Spatial relations have been studied in various interrelated areas such as qualitative spatial reasoning, geographic information science, image retrieval, and others. Direction as one of the most important spatial relations has received much attention. In this paper, we introduce a new formalism, we name BCD calculus, for qualitative spatial reasoning with block cardinal direction relations between blocks in 3D space. Based on the theory of block algebra, the correlations between block cardinal direction relations in 3D and block algebra are explained, and the tractable subset of convex block cardinal direction relations is identified. We show that the consistency problem for convex block cardinal direction network can be solved in polynomial time, by translating qualitative networks of BCD calculus to qualitative network of block algebra and applying a suitable adaption of path consistency algorithm.

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Section: The Tractability Of Convex Subalgebra Of the Bcd Calculusmentioning

confidence: 62%

Section: The Tractability Of Convex Subalgebra Of the Bcd Calculusmentioning

confidence: 94%

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Reasoning with Cardinal Directions in 3D Space Based on Block Algebra

Hou¹,

Wu²,

Yang³

2017

dtcse

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“…The region-level spatial constraints can be formalized using a block algebra [67], which is a spatial application of Allen's interval algebra [68]. The constraints on a HIT are shown in a matrix form in Table 1.…”

Section: Header Indexed Tables: Formal Characterizationmentioning

confidence: 99%

Converting heterogeneous statistical tables on the web to searchable databases

Embley

Krishnamoorthy

Nagy

et al. 2016

IJDAR

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Much of the world's quantitative data resides in scattered web tables. For a meaningful role in Big Data analytics, the facts reported in these tables must be brought into a uniform framework. Based on a formalization of header-indexed tables, we proffer an algorithmic solution to end-to-end table processing for a large class of humanreadable tables. The proposed algorithms transform headerindexed tables to a category table format that maps easily to a variety of industry-standard data stores for query processing. The algorithms segment table regions based on the unique indexing of the data region by header paths, classify table cells, and factor header category structures of two-dimensional as well as the less common multidimensional tables. Experimental evaluations substantiate the algorithmic approach to processing heterogeneous tables. As demonstrable results, the algorithms generate queryable relational database tables and semantic-web triple stores. Application of our algorithms to 400 web tables randomly selected from diverse sources shows that the algorithmic solution automates end-to-end table processing. document analysis table segmentation table analysis table header factoring end-to-end table processing· table headers queries over table data ___________________________________________ Keywords

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“…The projections are intervals and their relation can be described using Allen's interval relations. This approach is known as the block algebra [14] and illustrated in Figure 4. Moreover, there are several useful binary relations to describe point locations in two-dimensional space.…”

Section: Qualitative Representation Of Spacementioning

confidence: 99%

Leveraging Qualitative Reasoning to Learning Manipulation Tasks

Wolter

Kirsch

2015

Robotics

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Learning and planning are powerful AI methods that exhibit complementary strengths. While planning allows goal-directed actions to be computed when a reliable forward model is known, learning allows such models to be obtained autonomously. In this paper we describe how both methods can be combined using an expressive qualitative knowledge representation. We argue that the crucial step in this integration is to employ a representation based on a well-defined semantics. This article proposes the qualitative spatial logic QSL, a representation that combines qualitative abstraction with linear temporal logic, allowing us to represent relevant information about the learning task, possible actions, and their consequences. Doing so, we empower reasoning processes to enhance learning performance beyond the positive effects of learning in abstract state spaces. Proof-of-concept experiments in two simulation environments show that this approach can help to improve learning-based robotics by quicker convergence and leads to more reliable action planning.Keywords: qualitative spatial reasoning; robot learning; AI robotics MotivationRobotic applications have evolved considerably, yet they still lack the efficiency, flexibility and adaptability that is needed to improve our everyday life as versatile service robots. Planning and learning Robotics 2015, 4 254 are the two major paradigms employed to make a robot act intelligently. Planning is a form of symbolic reasoning applied on various levels of abstraction. Planning is effective whenever reliable forward models of the robot and its environment are available. Learning is a powerful method to generate such models from data. However, it requires carefully handcrafted state space representations to converge to high-quality models in reasonable time. Neither planning nor learning on their own suffice to meet the demands of versatile service robots. By integrating both paradigms one can benefit from their respective strengths. So far, a true integration of learning and planning has not been achieved that allows a robot to acquire new skills efficiently in a truly autonomous way.Our work is motivated by this basic question of how to integrate learning and planning, leveraging their individual strengths to produce reliable and versatile robot behavior. We propose a qualitative reasoning framework as the glue between those two paradigms. Qualitative reasoning lifts information, e.g., obtained by perception, to a knowledge level, enabling us to integrate it with common sense knowledge and to use available reasoning techniques [1][2][3]. The qualitative representation serves two purposes: (1) to make a planning or action selection process with learned models more efficient; and (2) to control selection of learning samples in order to make a learning process more reliable and to obtain high-quality models with little manual design effort. We present two experimental studies in simulation for a specific robot task: to throw an object to a specific destination. The results ind...

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Tractability Results in the Block Algebra

Cited by 31 publications

References 17 publications

Reasoning with Cardinal Directions in 3D Space Based on Block Algebra

Reasoning with Cardinal Directions in 3D Space Based on Block Algebra

Converting heterogeneous statistical tables on the web to searchable databases

Leveraging Qualitative Reasoning to Learning Manipulation Tasks

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