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Spatial reasoning in a fuzzy region connection calculus
 Artificial Intelligence
, 2009
"... Although the region connection calculus (RCC) offers an appealing framework for modelling topological relations, its application in real–world scenarios is hampered when spatial phenomena are affected by vagueness. To cope with this, we present a generalization of the RCC based on fuzzy set theory, ..."
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Cited by 13 (2 self)
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Although the region connection calculus (RCC) offers an appealing framework for modelling topological relations, its application in real–world scenarios is hampered when spatial phenomena are affected by vagueness. To cope with this, we present a generalization of the RCC based on fuzzy set theory, and discuss how reasoning tasks such as satisfiability and entailment checking can be cast into linear programming problems. We furthermore reveal that reasoning in our fuzzy RCC is NP–complete, thus preserving the computational complexity of reasoning in the RCC, and we identify an important tractable subfragment. Moreover, we show how reasoning tasks in our fuzzy RCC can also be reduced to reasoning tasks in the original RCC. While this link with the RCC could be exploited in practical reasoning algorithms, we mainly focus on the theoretical consequences. In particular, using this link we establish a close relationship with the Egg–Yolk calculus, and we demonstrate that satisfiable knowledge bases can be realized by fuzzy regions in any dimension.
Fuzzy region connection calculus: representing vague topological information
 In: Int. J. Approx. Reasoning
"... Abstract Qualitative spatial information plays a key role in many applications. While it is wellrecognized that all but a few of these applications deal with spatial information that is affected by vagueness, relatively little work has been done on modelling this vagueness in such a way that spati ..."
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Cited by 7 (3 self)
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Abstract Qualitative spatial information plays a key role in many applications. While it is wellrecognized that all but a few of these applications deal with spatial information that is affected by vagueness, relatively little work has been done on modelling this vagueness in such a way that spatial reasoning can still be performed. This paper presents a general approach to represent vague topological information (e.g., A is a part of B, A is bordering on B), using the wellknown region connection calculus as a starting point. The resulting framework is applicable in a wide variety of contexts, including those where space is used in a metaphorical way. Most notably, it can be used for representing, and reasoning about, qualitative relations between regions with vague boundaries.
Uncertain Spatiotemporal Logic for General Intelligence
"... Spatiotemporal reasoning is an important skill that an AGI is expected to have, innately or not. Much work has already been done in defining reasoning systems for space, time and spacetime, such as the Region Connection Calculus for space, Allen’s Interval Algebra for time, or the Qualitative Trajec ..."
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Spatiotemporal reasoning is an important skill that an AGI is expected to have, innately or not. Much work has already been done in defining reasoning systems for space, time and spacetime, such as the Region Connection Calculus for space, Allen’s Interval Algebra for time, or the Qualitative Trajectory Calculus for motion. However, these reasoning systems rarely take adequate account of uncertainty, which poses an obstacle to using them in an AGI system confronted with an uncertain reality. In this paper we show how to use PLN (Probabilistic Logic Networks) to represent spatiotemporal knowledge and reasoning, via incorporating existing spatiotemporal calculi, and considering a novel extension of standard PLN truth values inspired by P(Z)logic. This ”PLNization ” of existing spatiotemporal calculi, we suggest, constitutes an approach to spatiotemporal inference suitable for use in AGI systems that incorporate logicbased components.
A logic framework for reasoning with movement based on fuzzy
"... qualitative representationI ..."
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