Logic and Truth: Some Logics without Theorems

  • Jayanta Sen Presidency College, 86/1, College Street, Kolkata - 73, INDIA.
  • Mihir Kumar Chakraborty University of Calcutta
Keywords: logical truth, logical consequence, lattice

Abstract

Two types of logical consequence are compared: one, with respect to matrix and designated elements and the other with respect to ordering in a suitable algebraic structure. Particular emphasis is laid on algebraic structures in which there is no top-element relative to the ordering. The significance of this special condition is discussed. Sequent calculi for a number of such structures are developed. As a consequence it is re-established that the notion of truth as such, not to speak of tautologies, is inessential in order to define validity of an argument.

Downloads

Download data is not yet available.

Author Biographies

Jayanta Sen, Presidency College, 86/1, College Street, Kolkata - 73, INDIA.
Lecturer, Department of Mathematics
Mihir Kumar Chakraborty, University of Calcutta
Professor, Deapartment of Pure Mathematics

References

Belnap, N. (1977). A useful four-valued logic, in J. Dunnand, G. Epstein (eds), Modern uses of multiple-valued logic, Reidel, Dordrecht, Boston, pp.8-37.

Copi ,I. (1998). Symbolic logic, Prentice Hall of India.

Font, J.M. (1997). Belnap’s four-valued logic and de Morgan lattices, L.J. of the IGPL 5:1-29.

Gentzen, G. (1969). Investigations in to logical deduction, in M. Szabo (ed.), The collected papers of Gerhard Gentzen, North-Holland, Amsterdam, pp.68-131.

Girard, J.-Y. (1987). Linear logic, Theoretical Computer Science 50:1-102.

Sen, J. and Chakraborty, M.K. (2002). A study of interconnections between rough and Lukasiewicz 3-valued logic, Fundamenta Informaticae 51:311-324.

Simons, L. (1974). Logic without tautologies, Notre Dame Journal of Formal Logic 15: 411-431.

Simons, L.(1978). More logics without tautologies, Notre Dame Journal of Formal Logic 19: 543-557.

Troelstra, A.S. (1992). Lectures on linear logic, Vol.2 CSLI, Stanford.

Published
2008-09-01
How to Cite
Sen, J., & Chakraborty, M. K. (2008). Logic and Truth: Some Logics without Theorems. Studia Philosophica Estonica, 104-117. https://doi.org/10.12697/spe.2008.1.1.06