Graduate studies at Western
Notre Dame Journal of Formal Logic 30 (3):459-484 (1989)
|Abstract||Kalrnaric. We set out a system T, consisting of normal proofs constructed by means of elegantly symmetrical introduction and elimination rules. In the system T there are two requirements, called ( ) and ()), on applications of discharge rules. T is sound and complete for Kalmaric arguments. ( ) requires nonvacuous discharge of assumptions; ()) requires that the assumption discharged be the sole one available of highest degree. We then consider a 'Duhemian' extension T*, obtained simply by dropping the requirement ()). T* is a proper subsystem of intuitionistic relevant logic. Our main result is that T* is a double negation consistency companion to classical logic. Thus all one needs to add to T* to obtain classical logic is the (intuitionistic) absurdity rule, and the (classical) rule of double nega-|
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
|Through your library||Configure|
Similar books and articles
Jonathan P. Seldin (2000). On the Role of Implication in Formal Logic. Journal of Symbolic Logic 65 (3):1076-1114.
Frank Stephan (2001). On the Structures Inside Truth-Table Degrees. Journal of Symbolic Logic 66 (2):731-770.
L. Humberstone & D. Makinson (2012). Intuitionistic Logic and Elementary Rules. Mind 120 (480):1035-1051.
Henry Africk (1992). Classical Logic, Intuitionistic Logic, and the Peirce Rule. Notre Dame Journal of Formal Logic 33 (2):229-235.
Kosta Došen (1992). Modal Translations in Substructural Logics. Journal of Philosophical Logic 21 (3):283 - 336.
Neil Tennant (1994). Intuitionistic Mathematics Does Not Needex Falso Quodlibet. Topoi 13 (2):127-133.
Takahito Aoto (1999). Uniqueness of Normal Proofs in Implicational Intuitionistic Logic. Journal of Logic, Language and Information 8 (2):217-242.
Lloyd Humberstone (2001). The Pleasures of Anticipation: Enriching Intuitionistic Logic. [REVIEW] Journal of Philosophical Logic 30 (5):395-438.
Ryo Kashima & Norihiro Kamide (1999). Substructural Implicational Logics Including the Relevant Logic E. Studia Logica 63 (2):181-212.
Stefano Berardi (1999). Intuitionistic Completeness for First Order Classical Logic. Journal of Symbolic Logic 64 (1):304-312.
L. A. Zadeh (1975). Fuzzy Logic and Approximate Reasoning. Synthese 30 (3-4):407-428.
Jerome Frazee (1988). A New Symbolic Representation of the Basic Truth-Functions of the Propositional Calculus. History and Philosophy of Logic 9 (1):87-91.
Ross Thomas Brady (2010). Free Semantics. Journal of Philosophical Logic 39 (5):511 - 529.
Sorry, there are not enough data points to plot this chart.
Added to index2010-08-24
Total downloads1 ( #291,948 of 722,946 )
Recent downloads (6 months)0
How can I increase my downloads?