Abstract
Orthologic is defined by weakening the axioms and rules of inference of the classical propositional calculus. The resulting Lindenbaum-Tarski quotient algebra is an orthoimplication algebra which generalizes the author's implication algebra. The associated order structure is a semi-orthomodular lattice. The theory of orthomodular lattices is obtained by adjoining a falsity symbol to the underlying orthologic or a least element to the orthoimplication algebra.
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Allatum est die 1 Julii 1975
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Abbott, J.C. Orthoimplication algebras. Stud Logica 35, 173–177 (1976). https://doi.org/10.1007/BF02120879
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DOI: https://doi.org/10.1007/BF02120879