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      Using constrained intuitionistic linear logic for hybrid robotic planning problems

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      Author
      Saranlı, Uluç
      Pfenning F.
      Date
      2007
      Source Title
      Proceedings 2007 IEEE International Conference on Robotics and Automation
      Print ISSN
      1050-4729
      Publisher
      IEEE
      Pages
      3705 - 3710
      Language
      English
      Type
      Conference Paper
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      Abstract
      Synthesis of robot behaviors towards nontrivial goals often requires reasoning about both discrete and continuous aspects of the underlying domain. Existing approaches in building automated tools for such synthesis problems attempt to augment methods from either discrete planning or continuous control with hybrid elements, but largely fail to ensure a uniform treatment of both aspects of the domain. In this paper, we present a new formalism, Constrained Intuitionistic Linear Logic (CILL), merging continuous constraint solvers with linear logic to yield a single language in which hybrid properties of robotic behaviors can be expressed and reasoned with. Following a gentle introduction to linear logic, we describe the two new connectives of CILL, introduced to interface the constraint domain with the logical fragment of the language. We then illustrate the application of CILL for robotic planning problems within the Balanced Blocks World, a "physically realistic" extension of the Blocks World domain. Even though some of the formal proofs for the semantic foundations of the language as well as an efficient implementation of a theorem prover are yet to be completed, CILL promises to be a powerful formalism in reasoning within hybrid domains. © 2007 IEEE.
      Keywords
      Constraint theory
      Motion planning
      Problem solving
      Robotics
      Semantics
      Theorem proving
      Constrained Intuitionistic Linear Logic (CILL)
      Robot behaviors
      Semantic foundations
      Formal logic
      Permalink
      http://hdl.handle.net/11693/27079
      Published Version (Please cite this version)
      http://dx.doi.org/10.1109/ROBOT.2007.364046
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