David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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Studia Logica 38 (2):211 - 231 (1979)
A system FDQ of first degree entailment with quantification, extending classical quantification logic Q by an entailment connective, is axiomatised, and the choice of axioms defended and also, from another viewpoint, criticised. The system proves to be the equivalent to the first degree part of the quantified entailmental system EQ studied by Anderson and Belnap; accordingly the semantics furnished are alternative to those provided for the first degree of EQ by Belnap. A worlds semantics for FDQ is presented, and the soundness and completeness of FDQ proved, the main work of the paper going into the proof of completeness. The adequacy result is applied to yield, as well as the usual corollaries, weak relevance of FDQ and the fact that FDQ is the common first degree of a wide variety of (constant domain) quantified relevant logics. Finally much unfinished business at the first degree is discussed.
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References found in this work BETA
Rudolf Carnap (1962). Logical Foundations of Probability. Chicago]University of Chicago Press.
Elliott Mendelson (1964). Introduction to Mathematical Logic. Princeton, N.J.,Van Nostrand.
Rudolf Carnap (1959). Introduction to Semantics. Cambridge, Harvard University Press.
Arthur N. Prior (1962). Formal Logic. Oxford, Clarendon Press.
Robert K. Meyer, J. Michael Dunn & Hugues Leblanc (1974). Completeness of Relevant Quantification Theories. Notre Dame Journal of Formal Logic 15 (1):97-121.
Citations of this work BETA
Dominic Hyde (2001). Richard (Routley) Sylvan: Writings on Logic and Metaphysics. History and Philosophy of Logic 22 (4):181-205.
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