Propositional Independence - Formula-Variable Independence and Forgetting

@article{Lang2003PropositionalI,
  title={Propositional Independence - Formula-Variable Independence and Forgetting},
  author={J{\'e}r{\^o}me Lang and Paolo Liberatore and Pierre Marquis},
  journal={J. Artif. Intell. Res.},
  year={2003},
  volume={18},
  pages={391-443}
}
Independence - the study of what is relevant to a given problem of reasoning - has received an increasing attention from the AI community. In this paper, we consider two basic forms of independence, namely, a syntactic one and a semantic one. We show features and drawbacks of them. In particular, while the syntactic form of independence is computationally easy to check, there are cases in which things that intuitively are not relevant are not recognized as such. We also consider the problem of… 
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References

SHOWING 1-10 OF 67 REFERENCES
Relevance from an Epistemic Perspective
A Logical Account of Relevance
TLDR
This paper focuses on one particular area, namely relevance in the context of logical theories, and shows close connections to two others that were recently proposed, point ing to some common ground at least as far as logical relevance is concerned.
Toward a Logic for Qualitative Decision Theory
Logics of Time and Computation
Sets out the basic theory of normal modal and temporal propositional logics; applies this theory to logics of discrete (integer), dense (rational), and continuous (real) time, to the temporal logic…
Updating Logical Databases (Cambridge Tracts in Theoretical Computer Science)
Updating logical databases
  • M. Winslett
  • Computer Science
    Cambridge tracts in theoretical computer science
  • 1990
TLDR
This paper presents a meta-modelling framework for model-based semantics of updates and some examples show how this framework can be applied to relational theories.
Updates, actions, and planning
TLDR
A new family of dependence-based update operators are given that are wellsuited to the representation of simple actions and the complexity of query entailment from an updated belief base is identified.
Update Operations: A Review
Possible Models Approach via Independency
Updating Epistemic States
TLDR
A class of update operators are extended to epistemic states, by defining an operation playing the same role as knowledge transmutations do for belief revision, which conveys much more information than belief sets since they express the relative plausibilities of the pieces of information believed by the agent.
...
...