Unfolding Feasible Arithmetic and Weak Truth

Eberhard, Sebastian; Strahm, Thomas Adrian (2015). Unfolding Feasible Arithmetic and Weak Truth. In: Achourioti, Theodora; Galinon, Henri; Martínez Fernández, José; Fujimoto, Kentaro (eds.) Unifying the Philosophy of Truth. Logic, Epistemology, and the Unity of Science: Vol. 36 (pp. 153-167). Dordrecht: Springer Netherlands 10.1007/978-94-017-9673-6_7

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In this paper we continue Feferman’s unfolding program initiated in (Feferman, vol. 6 of Lecture Notes in Logic, 1996) which uses the concept of the unfolding U(S) of a schematic system S in order to describe those operations, predicates and principles concerning them, which are implicit in the acceptance of S. The program has been carried through for a schematic system of non-finitist arithmetic NFA in Feferman and Strahm (Ann Pure Appl Log, 104(1–3):75–96, 2000) and for a system FA (with and without Bar rule) in Feferman and Strahm (Rev Symb Log, 3(4):665–689, 2010). The present contribution elucidates the concept of unfolding for a basic schematic system FEA of feasible arithmetic. Apart from the operational unfolding U0(FEA) of FEA, we study two full unfolding notions, namely the predicate unfolding U(FEA) and a more general truth unfolding UT(FEA) of FEA, the latter making use of a truth predicate added to the language of the operational unfolding. The main results obtained are that the provably convergent functions on binary words for all three unfolding systems are precisely those being computable in polynomial time. The upper bound computations make essential use of a specific theory of truth TPT over combinatory logic, which has recently been introduced in Eberhard and Strahm (Bull Symb Log, 18(3):474–475, 2012) and Eberhard (A feasible theory of truth over combinatory logic, 2014) and whose involved proof-theoretic analysis is due to Eberhard (A feasible theory of truth over combinatory logic, 2014). The results of this paper were first announced in (Eberhard and Strahm, Bull Symb Log 18(3):474–475, 2012).

Item Type: Book Section (Book Chapter)
Division/Institute: 08 Faculty of Science > Institute of Computer Science (INF) > Logic and Theory Group (LTG)
08 Faculty of Science > Institute of Computer Science (INF)
UniBE Contributor: Eberhard, Sebastian and Strahm, Thomas Adrian
Subjects: 000 Computer science, knowledge & systems
500 Science > 510 Mathematics
ISBN: 978-94-017-9672-9
Series: Logic, Epistemology, and the Unity of Science
Publisher: Springer Netherlands
Language: English
Submitter: Florian Ranzi
Date Deposited: 10 Aug 2015 12:04
Last Modified: 18 Jun 2016 02:30
Publisher DOI: 10.1007/978-94-017-9673-6_7
BORIS DOI: 10.7892/boris.70703
URI: http://boris.unibe.ch/id/eprint/70703

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