A Structuralist Theory of Logic

Cambridge University Press (1992)
Professor Koslow advances a new account of the basic concepts of logic. A central feature of the theory is that it does not require the elements of logic to be based on a formal language. Rather, it uses a general notion of implication as a way of organizing the formal results of various systems of logic in a simple, but insightful way. The study has four parts. In the first two parts the various sources of the general concept of an implication structure and its forms are illustrated and explained. Part 3 defines the various logical operations and systematically explores their properties. A generalized account of extensionality and dual implication is given, and the extensionality of each of the operators, as well as the relation of negation and its dual are given substantial treatment because of the novel results they yield. Part 4 considers modal operators and studies their interaction with logical operators. By obtaining the usual results without the usual assumptions this new approach allows one to give a very simple account of modal logic minus the excess baggage of possible world semantics.
Keywords Logic, Symbolic and mathematical  Implication (Logic  Structuralism
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Call number BC135.K67 1992
ISBN(s) 9780521412674   0521023726   0521412676   9780521023726  
DOI 10.2307/2956395
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Alessio Moretti (2012). Why the Logical Hexagon? Logica Universalis 6 (1-2):69-107.
Lloyd Humberstone (2000). The Revival of Rejective Negation. Journal of Philosophical Logic 29 (4):331-381.

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