In Raymond Jennings, Bryson Brown & Peter Schotch (eds.), On Preserving: Essays on Preservationism and Paraconsistent Logic. Toronto: University of Toronto Press. pp. 105-144 (2009)

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Gillman Payette
University of British Columbia
Abstract
In this paper Gillman Payette looks at various structural properties of the underlying logic X, and ascertains if these properties will hold of the forcing relation based on X. The structural properties are those that do not deal with particular connectives directly. These properties include the structural rules of inference, compactness, and compositionality among others. The presentation of the logic X is carried out in the style of algebraic logic; thus, a description of the resulting ‘forcing algebras’ is given. The paper concludes with a discussion of first-order classical forcing as a particular instance of these properties.
Keywords compositionality  algebraic logic  Paraconsistent Logic  classical logic  Forcing
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DOI 10.3138/9781442688742-008
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Getting the Most Out of Inconsistency.Gillman Payette - 2015 - Journal of Philosophical Logic 44 (5):573-592.

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