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ProofTheoretic Analysis of Termination Proofs
 APAL
, 1994
"... Introduction In [Cichon 1990] the question has been discussed (and investigated) whether the order type of a termination ordering places a bound on the lengths of reduction sequences in rewrite systems reducing under . It was claimed that at least in the cases of the recursive path ordering rpo a ..."
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Introduction In [Cichon 1990] the question has been discussed (and investigated) whether the order type of a termination ordering places a bound on the lengths of reduction sequences in rewrite systems reducing under . It was claimed that at least in the cases of the recursive path ordering rpo and the lexicographic path ordering lpo the following theorem holds. (0) If is the order type of a termination ordering for a nite rewrite system R then the function G from the SlowGrowing Hierarchy bounds the lengths of reduction sequences in R. From (0) together with Girard's Hierarchy Comparison Theorem one derives (I) If the rules of a nite rewrite system R are reducing under rpo then the lengths of reduction sequences in R are bounded by some primitive recursive function. (II) If the rules of a nite rewrite system R are reducing under lpo then the lengths of reduction sequences in R are bounded by some function F from the fastgrowing hierarchy below ! . Unfort
Prooftheoretic analysis by iterated reflection
 Arch. Math. Logic
"... Progressions of iterated reflection principles can be used as a tool for ordinal analysis of formal systems. Technically, in some sense, they replace the use of omegarule. We compare the information obtained by this kind of analysis with the results obtained by the more usual prooftheoretic techni ..."
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Progressions of iterated reflection principles can be used as a tool for ordinal analysis of formal systems. Technically, in some sense, they replace the use of omegarule. We compare the information obtained by this kind of analysis with the results obtained by the more usual prooftheoretic
The ProofTheoretic Analysis of ... Transfinite Dependent Choice
, 2000
"... This article provides an ordinal analysis of # 1 1 transfinite dependent choice. 1 Introduction # 1 1 TDC 0 (# 1 1 Transfinite Dependent Choice) is a natural strengthening of # 1 1 DC 0 . Both are subsystems of analysis and assure the existence of implicitly # 1 1 definable sequences (of set ..."
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is ##00. The prooftheoretic analysis given in this article shows that # 1 1 TDC 0 is in fact metapredicative. If we add complete induction for arbitrary formulas, then the corresponding prooftheoretic ordinals are ## 0 0 and ## 0 00. The theory # 1 1 TDC 0 and its prooftheoretic analysis typically
A ProofTheoretic Analysis of GoalDirected Provability
 Journal of Logic and Computation
, 1992
"... One of the distinguishing features of logic programming seems to be the notion of goaldirected provability, i.e. that the structure of the goal is used to determine the next step in the proof search process. It is known that by restricting the class of formulae it is possible to guarantee that a ..."
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One of the distinguishing features of logic programming seems to be the notion of goaldirected provability, i.e. that the structure of the goal is used to determine the next step in the proof search process. It is known that by restricting the class of formulae it is possible to guarantee
What Rests On What? The ProofTheoretic Analysis Of Mathematics
 Proc. 15 th International Wittgenstein Symposium
, 1992
"... analysis goes beyond concrete analysis by its use of arbitrary spaces of various kinds, e.g. metric spaces, Banach spaces, Hilbert spaces, etc. Moreover, for functional analysis, applications often involve spaces of functions such as the L p spaces, and, more abstractly, spaces of functions betwee ..."
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Cited by 12 (1 self)
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analysis goes beyond concrete analysis by its use of arbitrary spaces of various kinds, e.g. metric spaces, Banach spaces, Hilbert spaces, etc. Moreover, for functional analysis, applications often involve spaces of functions such as the L p spaces, and, more abstractly, spaces of functions
The prooftheoretic analysis of the Suslin operator in applicative theories
 Reflections on the Foundations of Mathematics: Essays in Honor of Solomon Feferman. A K Peters
, 2002
"... In this article we introduce the Suslin quantification functional E1 into the framework of Feferman’s explicit mathematics and analyze it from the point of view of proof theory. More precisely, we work in the first order part of explicit mathematics augmented by appropriate axioms for E1. Then we es ..."
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Cited by 2 (0 self)
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establish the exact prooftheoretic relationship between these applicative theories and (subsystems of) the second order theory (∆1 2CA), depending on the induction principles permitted. 1
A proof theoretic analysis of intruder theories
 CoRR
"... Abstract. We consider the problem of intruder deduction in security protocol analysis: that is, deciding whether a given message M can be deduced from a set of messages Γ under the theory of blind signatures and arbitrary convergent equational theories modulo associativity and commutativity (AC) of ..."
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Cited by 6 (3 self)
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and sequent calculus, we recast the intruder deduction problem as proof search in sequent calculus, in which locality is immediate. Using standard proof theoretic methods, such as permutability of rules and cut elimination, we show that the intruder deduction problem can be reduced, in polynomial time
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