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On the Use of the Constructive OmegaRule within Automated Deduction
, 1992
"... The cut elimination theorem for predicate calculus states that every proof may be replaced by one which does not involve use of the cut rule. This theorem no longer holds when the system is extended with Peano's axioms to give a formalisation for arithmetic. The problem of generalisation result ..."
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The cut elimination theorem for predicate calculus states that every proof may be replaced by one which does not involve use of the cut rule. This theorem no longer holds when the system is extended with Peano's axioms to give a formalisation for arithmetic. The problem of generalisation
On the Use of the Constructive OmegaRule within Automated Deduction
, 1992
"... The cut elimination theorem for predicate calculus states that every proof may be replaced by one which does not involve use of the cut rule. This theorem no longer holds when the system is extended with Peano's axioms to give a formalisation for arithmetic. The problem of generalisation re ..."
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The cut elimination theorem for predicate calculus states that every proof may be replaced by one which does not involve use of the cut rule. This theorem no longer holds when the system is extended with Peano's axioms to give a formalisation for arithmetic. The problem of generalisation
A Proof Environment for Arithmetic with the Omega Rule
 Proceedings of A ISMC2, Lecture Notes in Computer Science, SpringerVerlag
, 1994
"... An important technique for investigating derivability in formal systems of arithmetic has been to embed such systems into semiformal systems with the omegarule. This paper exploits this notion within the domain of automated theoremproving and discusses the implementation of such a proof environme ..."
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An important technique for investigating derivability in formal systems of arithmetic has been to embed such systems into semiformal systems with the omegarule. This paper exploits this notion within the domain of automated theoremproving and discusses the implementation of such a proof
THE OMEGA RULE IS Π1 1COMPLETE IN THE λβCALCULUS
, 2008
"... Vol. 5 (2:6) 2009, pp. 1–21 www.lmcsonline.org ..."
THE OMEGA RULE IS Π1 1COMPLETE IN THE λβCALCULUS
, 903
"... Abstract. In a functional calculus, the so called ωrule states that if two terms P and Q applied to any closed term N return the same value (i.e. PN = QN), then they are equal (i.e. P = Q holds). As it is well known, in the λβcalculus the ωrule does not hold, even when the ηrule (weak extensiona ..."
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Abstract. In a functional calculus, the so called ωrule states that if two terms P and Q applied to any closed term N return the same value (i.e. PN = QN), then they are equal (i.e. P = Q holds). As it is well known, in the λβcalculus the ωrule does not hold, even when the ηrule (weak
S.: NonCommutative Infinitary Peano Arithmetic
 In: Proceedings of CSL 2011
, 2011
"... Does there exist any sequent calculus such that it is a subclassical logic and it becomes classical logic when the exchange rules are added? The first contribution of this paper is answering this question for infinitary Peano arithmetic. This paper defines infinitary Peano arithmetic with noncommut ..."
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commutative sequents, called noncommutative infinitary Peano arithmetic, so that the system becomes equivalent to Peano arithmetic with the omegarule if the the exchange rule is added to this system. This system is unique among other noncommutative systems, since all the logical connectives have standard meaning
An Overview of the Linear Logic Programming Language Lygon
"... d premise is an axiom. D ::= A j D D j G oe A j 8x:D G ::= A j G G j G G j D oe G j 8x:G j 9x:G 5 Goaldirectedness in Linear Logic How do we find goaldirected proofs in linear logic? p; q; r ` p\Omega q; r \Phi s ffl multiple conclusions complicate matters ffl need to consider permutation p ..."
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properties ffl !rule and\Omega rule have awkward cases ffl make some (not necessarily arbitrary) choice of formula from \Delta ffl incorporate appropriate combination of left rules into a resolution rule 6 The Language Itself The cla
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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Cited by 9 (1 self)
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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 proof
On the proof theory of modal mucalculus
 Studia Logica
, 2008
"... We study the prooftheoretic relationship between two deductive systems for the modal mucalculus. First we recall an infinitary system which contains an omega rule allowing to derive the truth of a greatest fixed point from the truth of each of its (infinitely many) approximations. Then we recall a ..."
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Cited by 9 (2 self)
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We study the prooftheoretic relationship between two deductive systems for the modal mucalculus. First we recall an infinitary system which contains an omega rule allowing to derive the truth of a greatest fixed point from the truth of each of its (infinitely many) approximations. Then we recall
A Complete Axiomatization of Knowledge and Cryptography
"... The combination of firstorder epistemic logic and formal cryptography offers a potentially very powerful framework for security protocol verification. In this article, we address two main challenges towards such a combination; First, the expressive power, specifically the epistemic modality, needs ..."
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Cited by 19 (5 self)
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to the underlying theory of cryptographic terms, and to an omega rule for quantifiers. The axiomatization uses largely standard axioms and rules from firstorder modal logic. In addition, it includes some novel axioms for the interaction between knowledge and cryptography. To illustrate the usefulness of the logic
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