A Focusing Inverse Method Theorem Prover for First-Order Linear Logic

Chaudhuri, Kaustuv; Pfenning, Frank

doi:10.1007/11532231_6

Cited by 12 publications

(23 citation statements)

References 21 publications

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“…In prior work we have constructed a focusing system for intuitionistic linear logic which is consonant with Andreoli's classical version [8], and shown that restricting the inverse method to work only with big-step rules derived from focusing dramatically improves its efficiency [7]. The key feature of focusing is that each logical connective carries an intrinsic attribute called polarity that determines its behavior under focusing.…”

Section: Introductionmentioning

confidence: 97%

A Logical Characterization of Forward and Backward Chaining in the Inverse Method

2008

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The inverse method is a generalization of resolution that can be applied to non-classical logics. We have recently shown how Andreoli's focusing strategy can be adapted for the inverse method in linear logic. In this paper we introduce the notion of focusing bias for atoms and show that it gives rise to forward and backward chaining, generalizing both hyperresolution (forward) and SLD resolution (backward) on the Horn fragment. A key feature of our characterization is the structural, rather than purely operational, explanation for forward and backward chaining. A search procedure like the inverse method is thus able to perform both operations as appropriate, even simultaneously. We also present experimental results and an evaluation of the practical benefits of biased atoms for a number of examples from different problem domains.

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Section: Introductionmentioning

confidence: 97%

A Logical Characterization of Forward and Backward Chaining in the Inverse Method

2008

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“…Another important step towards the deployment of CILL for real robotic planning problems is an efficient implementation that is not only capable of overcoming various fundamental problems in writing effective theorem provers for linear logic [5], but also provides ways in which existing decision procedures for a variety of constraint domains can be modularly incorporated into the system. Even though the formalization of the proof theory goes a long way towards enforcing modularity, there are still architectural issues to be resolved before a fully practical implementation is achieved.…”

Section: Discussionmentioning

confidence: 99%

Using Constrained Intuitionistic Linear Logic for Hybrid Robotic Planning Problems

Saranlı

Pfenning

2007

Proceedings 2007 IEEE International Conference on Robotics and Automation

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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.

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“…We omit a detailed definition and proof here because it is a standard result; see e.g. [6] for the definition. With the strong subformula property, we can restrict the rules of fig.…”

Section: Forward Reasoning and The Inverse Methodsmentioning

confidence: 99%