What Is a Qualitative Calculus? A General Framework

Ligozat, Gérard; Renz, Jochen

doi:10.1007/978-3-540-28633-2_8

Cited by 86 publications

(106 citation statements)

References 12 publications

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“…We can, however, replace the composition operator in the path-consistency algorithm with the weak composition operator. The resulting algorithm is called the algebraic closure algorithm [12] which makes a network algebraically closed or a-closed.…”

Section: Algebraic Closurementioning

confidence: 99%

Weak Composition for Qualitative Spatial and Temporal Reasoning

Renz

Ligozat

2005

Lecture Notes in Computer Science

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Abstract. It has now been clear for some time that for many qualitative spatial or temporal calculi, for instance the well-known RCC8 calculus, the operation of composition of relations which is used is actually only weak composition, which is defined as the strongest relation in the calculus that contains the real composition. An immediate consequence for qualitative calculi where weak composition is not equivalent to composition is that the well-known concept of pathconsistency is not applicable anymore. In these cases we can only use algebraic closure which corresponds to applying the path-consistency algorithm with weak composition instead of composition. In this paper we analyse the effects of having weak compositions. Starting with atomic CSPs, we show under which conditions algebraic closure can be used to decide consistency in a qualitative calculus, how weak consistency affects different important techniques for analysing qualitative calculi and under which conditions these techniques can be applied. For our analysis we introduce a new concept for qualitative relations, the "closure under constraints". It turns out that the most important property of a qualitative calculus is not whether weak composition is equivalent to composition, but whether the relations are closed under constraints. All our results are general and can be applied to all existing and future qualitative spatial and temporal calculi. We close our paper with a road map of how qualitative calculi should be analysed. As a side effect it turns out that some results in the literature have to be reconsidered.

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Section: Algebraic Closurementioning

confidence: 99%

Weak Composition for Qualitative Spatial and Temporal Reasoning

Renz

Ligozat

2005

Lecture Notes in Computer Science

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“…reliable, way. Examples of generic formalisms of granular computing that are explicitly designed for handling imperfect information are, e.g., Dempster-Shafer theory of belief (Dempster 1967;Fine 1977), probability theory, possibility theory (Zadeh 1999;Dubois and Prade 2001), rough sets theory (Pawlak 1981), fuzzy logic (Zadeh 1965), shadowed sets (Pedrycz 1998), interval computation (Kreinovich 2008), or qualitative calculi (Ligozat and Renz 2004). The ability to utilize higher order information granules for reconciling seemingly contradictory information as, e.g., generated in collaborative work, by interpreting it as higher order data imperfection is considered an essential functionality of granular calculi in HDI.…”

Section: Gc Supports Intuitive Data Processing Logicsmentioning

confidence: 99%

Granular computing as a basis of human–data interaction: a cognitive cities use case

Wilke

Portmann

2016

Granul. Comput.

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The article proposes granular computing as a theoretical, formal and methodological basis for the newly emerging research field of human-data interaction (HDI). We argue that the ability to represent and reason with information granules is a prerequisite for data legibility. As such, it allows for extending the research agenda of HDI to encompass the topic of collective intelligence amplification, which is seen as an opportunity of today's increasingly pervasive computing environments. As an example of collective intelligence amplification in HDI, we introduce a collaborative urban planning use case in a cognitive city environment and show how an iterative process of user input and humanoriented automated data processing can support collective decision making. As a basis for automated human-oriented data processing, we use the spatial granular calculus of granular geometry.

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“…From these facts it follows that X and Z either stand in relation B, M, or O as can be verified graphically. This knowledge is captured in the so-called qualitative calculus [18,19], an algebraic construct that is induced by a set of qualitative relations. We note that qualitative spatial representations are always constructed in a way such that there are finitely many relations that are jointly exhaustive and pairwise disjoint [19] as this eases technicalities of the representation.…”

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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What Is a Qualitative Calculus? A General Framework

Cited by 86 publications

References 12 publications

Weak Composition for Qualitative Spatial and Temporal Reasoning

Weak Composition for Qualitative Spatial and Temporal Reasoning

Granular computing as a basis of human–data interaction: a cognitive cities use case

Leveraging Qualitative Reasoning to Learning Manipulation Tasks

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