14,516 research outputs found
The modal logic of Reverse Mathematics
The implication relationship between subsystems in Reverse Mathematics has an
underlying logic, which can be used to deduce certain new Reverse Mathematics
results from existing ones in a routine way. We use techniques of modal logic
to formalize the logic of Reverse Mathematics into a system that we name
s-logic. We argue that s-logic captures precisely the "logical" content of the
implication and nonimplication relations between subsystems in Reverse
Mathematics. We present a sound, complete, decidable, and compact tableau-style
deductive system for s-logic, and explore in detail two fragments that are
particularly relevant to Reverse Mathematics practice and automated theorem
proving of Reverse Mathematics results
On the Logic of Reverse Mathematics
The goal of reverse mathematics is to study the implication and non-implication relationships between theorems. These relationships have their own internal logic, allowing some implications and non-implications to be derived directly from others. The goal of this thesis is to characterize this logic in order to capture the relationships between specific mathematical works. The results of our study are a finite set of rules for this logic and the corresponding soundness and completeness theorems. We also compare our logic with modal logic and strict implication logic. In addition, we explain two applications of S-logic in topology and second order arithmetic
Complexity of the interpretability logic IL
We show that the decision problem for the basic system of interpretability
logic IL is PSPACE-complete. For this purpose we present an algorithm which
uses polynomial space with respect to the complexity of a given formula. The
existence of such algorithm, together with the previously known PSPACE hardness
of the closed fragment of IL, implies PSPACE-completeness.Comment: 7 page
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