Density Elimination and Rational Completeness for First-Order Logics 1st Edition by Agata Ciabattoni, George Metcalfe ISBN 9783540727347
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Authors:Agata Ciabattoni; George Metcalfe , Tags:Logical Foundations of Computer Science , Author sort:Ciabattoni, Agata & Metcalfe, George , Languages:Languages:eng , Comments:Comments:Logical Foundations of Computer Science
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ISBN 13: 9783540727347
Author: Agata Ciabattoni, George Metcalfe
Density elimination by substitutions is introduced as a uniform method for removing applications of the Takeuti-Titani density rule from proofs in first-order hypersequent calculi. For a large class of calculi, density elimination by this method is guaranteed by known sufficient conditions for cut-elimination. Moreover, adding the density rule to any axiomatic extension of a simple first-order logic gives a logic that is rational complete; i.e., complete with respect to linearly and densely ordered algebras: a precursor to showing that it is a fuzzy logic (complete for algebras with a real unit interval lattice reduct). Hence the sufficient conditions for cut-elimination guarantee rational completeness for a large class of first-order substructural logics.
Density Elimination and Rational Completeness for First-Order Logics 1st Table of contents:
- Background and Motivation
- Density Elimination in First-Order Logic
- Rational Completeness in First-Order Logics
- Theoretical Foundations
- Algorithmic Approaches to Density Elimination
- Case Studies and Applications
- Challenges and Open Problems
- Future Research Directions
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