LF and natural logic
In Georg Peter & Gerhard Preyer (eds.), Logical Form and Language. Oxford University Press (2002)
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Peter Schroeder-Heister (1984). A Natural Extension of Natural Deduction. Journal of Symbolic Logic 49 (4):1284-1300.
Greg Restall & Francesco Paoli (2005). The Geometry of Non-Distributive Logics. Journal of Symbolic Logic 70 (4):1108 - 1126.
Wilfrid Hodges (2009). Traditional Logic, Modern Logic and Natural Language. Journal of Philosophical Logic 38 (6).
Daniel Gallin (1975). Intensional and Higher-Order Modal Logic: With Applications to Montague Semantics. American Elsevier Pub. Co..
Francis Jeffry Pelletier (1999). A Brief History of Natural Deduction. History and Philosophy of Logic 20 (1):1-31.
George Lakoff (1970). Linguistics and Natural Logic. Synthese 22 (1-2):151 - 271.
Charles Gray Shaw (1935). Logic in Theory and Practice. New York, Prentice-Hall, Inc..
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