Graduate studies at Western
Studia Logica 81 (3):399 - 423 (2005)
|Abstract||The fixed point combinator (Y) is an important non-proper combinator, which is defhable from a combinatorially complete base. This combinator guarantees that recursive equations have a solution. Structurally free logics (LC) turn combinators into formulas and replace structural rules by combinatory ones. This paper introduces the fixed point and the dual fixed point combinator into structurally free logics. The admissibility of (multiple) cut in the resulting calculus is not provable by a simple adaptation of the similar proof for LC with proper combinators. The novelty of our proof—beyond proving the cut for a newly extended calculus–is that we add a fourth induction to the by-and-large Gentzen-style proof.|
|Keywords||combinatory logic structurally free logics substructural logics non-classical logics fked point combinator (multiple) cut rule elimination theorem|
|Categories||categorize this paper)|
|Through your library||Configure|
Similar books and articles
Max Kubierschky (2000). Yet Another Hierarchy Theorem. Journal of Symbolic Logic 65 (2):627-640.
Philip Kremer (2008). Supervaluation Fixed-Point Logics of Truth. Journal of Philosophical Logic 37 (5):407 - 440.
Roy Dyckhoff & Sara Negri (2000). Admissibility of Structural Rules for Contraction-Free Systems of Intuitionistic Logic. Journal of Symbolic Logic 65 (4):1499-1518.
Per Lindström (2006). Note on Some Fixed Point Constructions in Provability Logic. Journal of Philosophical Logic 35 (3):225 - 230.
Lou Goble (2004). Combinator Logics. Studia Logica 76 (1):17 - 66.
Katalin Bimbó (2003). The Church-Rosser Property in Dual Combinatory Logic. Journal of Symbolic Logic 68 (1):132-152.
Katalin Bombó (2005). The Church-Rosser Property in Symmetric Combinatory Logic. Journal of Symbolic Logic 70 (2):536 - 556.
Anuj Dawar & Yuri Gurevich (2002). Fixed Point Logics. Bulletin of Symbolic Logic 8 (1):65-88.
Sorry, there are not enough data points to plot this chart.
Added to index2009-01-28
Total downloads1 ( #292,750 of 741,433 )
Recent downloads (6 months)1 ( #61,802 of 741,433 )
How can I increase my downloads?