Abstract
In part I, we presented an algebraic-style of semantics, which we called “content semantics,” for quantified relevant logics based on the weak systemBBQ. We showed soundness and completeness with respect to theunreduced semantics ofBBQ. In part II, we proceed to show soundness and completeness for extensions ofBBQ with respect to this type of semantics. We introducereduced semantics which requires additional postulates for primeness and saturation. We then conclude by showing soundness and completeness forBB d Q and its extentions with respect to this reduced semantics.
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References
R. T. Brady,Natural deduction systems for some quantified relevant logics,Logique et Analyse, 27 Année, 1984, pp. 355–377.
R. T. Brady,Universal Logic, in preparation.
D. Gabray,On 2nd order intuitionistic propositional calculus with full comprehension,Archiv für Mathematische Logik, Vol. 16 (1974), pp. 177–186.
P. S. Lavers,Generating Intensional Logics, M. A. Thesis, University of Adelaide, 1985.
R. Routley, R. K. Meyer, V. Plumwood, R. T. Brady Relevant Logics and their Rivals, Vol. 1, Ridgeview, Calif., 1982.
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Brady, R.T. A content semantics for quantified relevant logics. II. Stud Logica 48, 243–257 (1989). https://doi.org/10.1007/BF02770515
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DOI: https://doi.org/10.1007/BF02770515