Document Type : Research

Author

• Davood Hosseini

Al E Ahmad Highway, Tarbiat Modares University, Faculty Of Humanities, 3rd Floor, No. 323.

Abstract

Abstract: deRosset and Fine's impure logic of grounding is a modification of Fine's impure logic of grounding. deRosset and Fine show that this modified impure logic of grounding (despite the original one) is sound and complete with respect to a semantics they develop. After presenting Fine's original impure logic of grounding, I argue that it has some proof-theoretic shortcomings concerning the primitive notions and the definition of deduction. I further argue that a version of these shortcomings persists in deRosset and Fine's modified impure logic. I further improve deRosset and Fine's impure logic of ground and set up a higher-order sequent calculus for it. I show that this improved system is semantically equivalent to deRosset and Fine's logic while avoiding all of the aforementioned shortcomings. The result is that although the improved logic is semantically as good as deRosset and Fine's logic, it is superior to their logic from a proof-theoretic point of view.

Keywords

• impure logic of grounding
• higher-order sequent calculus
• deduction

Main Subjects

• Modern Logic