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Abstract
This article uses possible-world semantics to model the changes that may occur in an agent's knowledge as she loses information. This builds on previous work in which the agent may forget the truth-value of an atomic proposition, to a more general case where she may forget the truth-value of a propositional formula. The generalization poses some challenges, since in order to forget whether a complex proposition pi is the case, the agent must also lose information about the propositional atoms that appear in it, and there is no unambiguous way to go about this. We resolve this situation by considering expressions of the form [double dagger pi]phi, which quantify over all possible (but 'minimal') ways of forgetting whether pi. Propositional atoms are modified non-deterministically, although uniformly, in all possible worlds. We then represent this within action model logic in order to give a sound and complete axiomatization for a logic with knowledge and forgetting. Finally, some variants are discussed, such as when an agent forgets pi (rather than forgets whether pi) and when the modification of atomic facts is done non-uniformly throughout the model.
Keywords
Forgetting, dynamic epistemic logic, action models, theory contraction, knowledge representation, BELIEF CHANGE, KNOWLEDGE, LOGIC, CONTRACTION, SEMANTICS, REVISION, UPDATE

Citation

Please use this url to cite or link to this publication:

MLA
Fernández-Duque, David et al. “Forgetting Complex Propositions.” LOGIC JOURNAL OF THE IGPL 23.6 (2015): 942–965. Print.
APA
Fernández-Duque, D., Nepomuceno-Fernández, Á., Sarrión-Morrillo, E., Soler-Toscano, F., & Velázquez-Quesada, F. R. (2015). Forgetting complex propositions. LOGIC JOURNAL OF THE IGPL, 23(6), 942–965.
Chicago author-date
Fernández-Duque, David, Ángel Nepomuceno-Fernández, Enrique Sarrión-Morrillo, Fernando Soler-Toscano, and Fernando R Velázquez-Quesada. 2015. “Forgetting Complex Propositions.” Logic Journal of the Igpl 23 (6): 942–965.
Chicago author-date (all authors)
Fernández-Duque, David, Ángel Nepomuceno-Fernández, Enrique Sarrión-Morrillo, Fernando Soler-Toscano, and Fernando R Velázquez-Quesada. 2015. “Forgetting Complex Propositions.” Logic Journal of the Igpl 23 (6): 942–965.
Vancouver
1.
Fernández-Duque D, Nepomuceno-Fernández Á, Sarrión-Morrillo E, Soler-Toscano F, Velázquez-Quesada FR. Forgetting complex propositions. LOGIC JOURNAL OF THE IGPL. 2015;23(6):942–65.
IEEE
[1]
D. Fernández-Duque, Á. Nepomuceno-Fernández, E. Sarrión-Morrillo, F. Soler-Toscano, and F. R. Velázquez-Quesada, “Forgetting complex propositions,” LOGIC JOURNAL OF THE IGPL, vol. 23, no. 6, pp. 942–965, 2015.
@article{8566412,
  abstract     = {This article uses possible-world semantics to model the changes that may occur in an agent's knowledge as she loses information. This builds on previous work in which the agent may forget the truth-value of an atomic proposition, to a more general case where she may forget the truth-value of a propositional formula. The generalization poses some challenges, since in order to forget whether a complex proposition pi is the case, the agent must also lose information about the propositional atoms that appear in it, and there is no unambiguous way to go about this. We resolve this situation by considering expressions of the form [double dagger pi]phi, which quantify over all possible (but 'minimal') ways of forgetting whether pi. Propositional atoms are modified non-deterministically, although uniformly, in all possible worlds. We then represent this within action model logic in order to give a sound and complete axiomatization for a logic with knowledge and forgetting. Finally, some variants are discussed, such as when an agent forgets pi (rather than forgets whether pi) and when the modification of atomic facts is done non-uniformly throughout the model.},
  author       = {Fernández-Duque, David and Nepomuceno-Fernández, Ángel and Sarrión-Morrillo, Enrique and Soler-Toscano, Fernando and Velázquez-Quesada, Fernando R},
  issn         = {1367-0751},
  journal      = {LOGIC JOURNAL OF THE IGPL},
  keywords     = {Forgetting,dynamic epistemic logic,action models,theory contraction,knowledge representation,BELIEF CHANGE,KNOWLEDGE,LOGIC,CONTRACTION,SEMANTICS,REVISION,UPDATE},
  language     = {eng},
  number       = {6},
  pages        = {942--965},
  title        = {Forgetting complex propositions},
  url          = {http://dx.doi.org/10.1093/jigpal/jzv049},
  volume       = {23},
  year         = {2015},
}

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