SYSTEMS OF NATURAL DEDUCTION WITHOUT ESSENTIAL RESTRICTIONS ON VARIABLES.
Final scientific rept.,
RENSSELAER POLYTECHNIC INST TROY N Y DEPT OF MATHEMATICS
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Research is summarized on the construction of a linear system in which the usually cumbersome quantifier rules are replaced by simpler ones. In it, the notion of a deduction is primitive, deducibility being the existence of a suitable deduction. A deduction is conceived as a finite sequence of formulas in which every formula appears with its number and with the set of assumption formulas on which it depends. No variables are flagged. The rules of the linear system are designed to make it correspond to the process of intuitive linear reasoning. The system is complete as to logical consequence and admits the positive, minimal, and intuitionistic subsystems. Author
- Theoretical Mathematics