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Abstract: A classical quantified modal logic is used to define a "feasible" arithmetic A 1 2 whose provable functions are exactly the polynomial-time computable functions. Informally, one understands # as "# is feasibly demonstrable". A 1 2 di#ers from a system A2 that is as powerful as Peano Arithmetic only by the restriction of induction to ontic (i.e. -free) formulas. Thus, A 1 2 is defined without any reference to bounding terms, and admitting induction over formulas having arbitrarily... (Update)
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BibTeX entry: (Update)
@misc{ bellantoni-new,
author = "S. Bellantoni and Martin Hofmann",
title = "A New "Feasible" Arithmetic",
url = "citeseer.ist.psu.edu/bellantoni00new.html" }
Citations (may not include all citations):233 Computational interpretations of linear logic - Abramsky - 1993
211 Languages that capture complexity classes - Immerman - 1987
112 Constructivism in Mathematics (context) - Troelstra, van Dalen - 1988
103 Bounded Arithmetic (context) - Buss - 1986
96 A New Recursion-Theoretic Characterization of the Polytime F.. (context) - Bellantoni, Cook - 1992
45 Quantification in Modal Logic (context) - Garson - 1984
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38 Ramified Recurrence and Computational Complexity IV: Predica.. (context) - Leivant, Marion
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32 Princeton University Press (context) - Nelson, Arithmetic - 1986
30 and Complexity Theory (context) - Krajicek, Arithmetic et al. - 1995
22 Type systems for polynomial-time computation - Hofmann - 1999
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11 Safe recursion with higher types and BCK-algebras - Hofmann
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9 An Interpretation of the Intuitionistic Sentential Logic (context) - Godel - 1969
8 Epistemic and Intuitionistic Arithmetic (context) - Shapiro - 1985
5 A new method for establishing conservativity of classical sy.. - Coquand, Hofmann
4 Epistemic Arithmetic is a Conservative Extension of Intuitio.. (context) - Goodman - 1984
4 Intrinsic theories and computational complexity (context) - Leivant - 1995
2 Provability: the emergence of a mathematical modality (context) - Boolos, Sambin - 1991
1 A mixed modal/linear lambda calculus with applications to Be.. - Hofmann - 1998
1 Ramified Recursion and Intuitionism - Nelson - 1997
1 Ranking Arithmetic Proofs by Implicit Ramification - Bellantoni - 1998
1 Ramification, Modality, and Linearity in Higher Type Recursi.. (context) - Bellantoni, Niggl et al.
1 Computational Content of Classical Proofs (context) - Coquand - 1997
1 The Realm of Primitive Recursion (context) - Simmons - 1988
1 Understanding Intuitionism - Nelson - 1997
1 Ranking Recursions: the Low Grzegorczyk Hierarchy Reconsider.. (context) - Bellantoni, Niggl
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