The many faces of interpolation

Benthem, Johan van

doi:10.1007/s11229-008-9351-5

Cited by 19 publications

(10 citation statements)

References 20 publications

(4 reference statements)

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“…An open question was posted in [19]: How far can the results be established for sub-classical (e.g., intuitionistic) consequence relations or supra-classical ones? This is by no means a trivial question, because Kourousias and Makinson's proof of the Finest Splitting Theorem is based on Craig's Interpolation Theorem, which fails in many non-classical logics [12]. In addition, Parikh's relevance criterion is a syntactical requirement, which is sensitive to variations of languages.…”

Section: Related and Future Workmentioning

confidence: 99%

“…In mathematical logic, Beth definability connects the implicit definability of a property and its explicit definability [12]. Specifically, the theorem proposed by Evert Willem Beth states that the two senses of definability are equivalent [24].…”

Section: Related and Future Workmentioning

confidence: 99%

“…It is a well-known technology in logic that definability can reduce irrelevant factors in knowledge base presented by logic. There has been a lot of literature on Beth definability in logic and related fields [12, 25, 11, 13, 26]. In this paper, we first split robotic knowledge base into the finest robotic sub-knowledge base without common propositional atoms each other.…”

Section: Related and Future Workmentioning

confidence: 99%

“…Definability in logic has shown that some propositional atoms are defined by other propositional atoms. Therefore, definability technology is important in the robotic knowledge field since it can eliminate inessential propositional atoms [12, 13]. At the same time, the splitting technique splits entire robotic knowledge equivalently into the same simple sub-knowledge without sharing propositional atoms with others [14].…”

Section: Introductionmentioning

confidence: 99%

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The Local Definability of Robotic Large-Scale Knowledge Based on Splitting

Jiang

Zhu

2016

International Journal of Advanced Robotic Systems

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In order to reduce the computational tasks in robots with large-scale and complex knowledge, several methods of robotic knowledge localization have been proposed over the past decades. Logic is an important and useful tool for complex robotic reasoning, action planning, learning and verification. This paper uses propositional atoms in logic to describe the affecting factors of robotic large-scale knowledge. Definability in logic reasoning shows that truths of some propositional atoms are decided by other propositional atoms. Definability technology is an important method to eliminate inessential propositional atoms in robotic large-scale and complex knowledge, so the computational tasks in robotic knowledge can be completed faster. On the other hand, by applying the splitting technique, the knowledge base can be equivalently divided into a number of sub-knowledge bases, without sharing any propositional atoms with others. In this paper, we show that the inessential propositional atoms can be decided faster by the local definability technology based on the splitting method, first formed in local belief revision by Parikh in 1999. Hence, the decision-making in robotic large-scale and complex knowledge is more effective.

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Section: Related and Future Workmentioning

confidence: 99%

Section: Related and Future Workmentioning

confidence: 99%

Section: Related and Future Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The Local Definability of Robotic Large-Scale Knowledge Based on Splitting

Jiang

Zhu

2016

International Journal of Advanced Robotic Systems

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“…In my view, the Restaurant is about the simplest realistic logical scenario , van Benthem 2008. Several basic informational actions take place intertwined: questions, answers, and inferences, and the setting crucially involves more than one agent.…”

Section: Inference Structural Rules and Information-producing Actionsmentioning

confidence: 99%

Inference in action

Benthem

2007

Publ Inst Math (Belgr)

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Substructural logics arise whenever classical logic is put to new uses, and logicians from Serbia have been in the forefront here. In this paper, we join the substructural tradition with another recent trend, viz. dynamic logic of information update. We show how these two approaches fit together, in particular, through a number of representation theorems concerning structural rules. The proper background for these results turn out to be modal and dynamic logics of cross-model relations. We connect this finding with recent accounts of generalized inference, interpolation, and preservation results.

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Through an Inference Rule, Darkly

Kuznets

2019

Mathesis Universalis, Computability and Proof

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The many faces of interpolation

Abstract: We present a number of, somewhat unusual, ways of describing what Craig's interpolation theorem achieves, and use them to identify some open problems and further directions.

Cited by 19 publications

References 20 publications

The Local Definability of Robotic Large-Scale Knowledge Based on Splitting

The Local Definability of Robotic Large-Scale Knowledge Based on Splitting

Inference in action

Through an Inference Rule, Darkly

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