Joinet J.-B., Schellinx H., Tortora de Falco L., SN and CR for free-style LK tq : linear decorations and simulation of normalization, to appear in the Journal of Symbolic Logic, 2000 Home/Search Document Not in Database Summary Related Articles Check |
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Strong Normalisation of Cut-Elimination in Classical Logic - Urban, Bierman (1999) (3 citations) (Correct)
....commuting cuts to pass over other cuts. A cut rule is said to be a logical cut when both cut formulae are introduced by axioms or logical inference rules; otherwise the cut is said to be a commuting cut. Our method is closely related to the cut elimination procedure developed for LK tq [6, 15]. However we do not need their colour annotations. The problem of non termination of cut elimination occurs in both intuitionistic logic and classical logic. One example of a non terminating reduction sequence in intuitionistic logic is given in [20] for classical logic [6] and [9] give the ....
J.-B. Joinet, H. Schellinx, and L. Tortora de Falco. SN and CR for Free-Style LK tq : Linear Decorations and Simulation of Normalisation. Preprint No. 1067, Utrecht University, Department of Mathematics, 1998.
Additives of linear logic and normalization-Part II: the.. - de Falco (2000) Self-citation (Tortora) (Correct)
....this occurrence of formula among its conclusions to be swallowed and duplicated. This is very natural: the embedding 2 in LL of the system for classical logic LK tq introduced in [DJS 97] requires, to be homoreductive (that is to be a morphism for cut elimination steps, see [DJS 97] and [JST 00] a variant of [Girard 87] s commutative e.r.s. for the additives which is a particular case of the one considered in this paper. Our generalization of the commutative e.r.s. for the additives requires a suitable (and general enough) notion of subproof net, and the presence of weakenings (which ....
Joinet J.-B., Schellinx H., Tortora de Falco L., SN and CR for free-style LK tq : linear decorations and simulation of normalization, to appear in the Journal of Symbolic Logic, 2000
Polarized and Focalized Linear and Classical Proofs - Olivier Laurent Iml-Cnrs (2000) (1 citation) Self-citation (De falco) (Correct)
....of linear logic proof nets. The starting point of the present work was to realize that these two papers are in fact tightly linked. We put together our knowledge on proof nets [Lau99b, Lau99a, TdF00a, TdF00b] on denotational semantics [Qua96] on the linear logic approach to classical logic [JSTdF98, TdF97, QTdF96], and focused on reversion and focalization. In this paper, we study these two properties both in a classical and in a linear framework. This leads us to consider two couples of classical linear systems (LK pol LLP and LK ; pol LL pol ) which can be considered as two twins , at least if ....
.... ax p p cut A A A A A A 1 p ax p p C C Figure 4: Commutative additive step on the ( translation in proof nets 26 Proof: An consequence of strong normalization for taLL [DJS97, JSTdF98] by proposition 5. Theorem 7 (Con uence) The normal form of a polarized proof net is unique. Proof: Let R 1 and R 2 be two normal forms of R, by proposition 5, R 1 and R 2 are two reducts of R which are obviously normal. Thus R 1 = R 2 by con uence of taLL [DJS97] and by lemma 4, we have R 1 ....
Jean-Baptiste Joinet, Harold Schellinx, and Lorenzo Tortora de Falco. SN and CR for free-style LK tq : linear decorations and simulation of normalization. Preprint 1067, Department of Mathematics (Universiteit Utrecht), May 1998.
Computational Isomorphisms in Classical Logic - Danos, Joinet, Schellinx (1996) (1 citation) Self-citation (Joinet Schellinx) (Correct)
....2 Review of basic notions In this sextion we quickly review some of the basic notions and a few results from [1] 2. 1 LK tq The speci c calculus LK we will consider and in which we formally distinguish between connectives with multiplicative and with additive introduction rules (cf. 1] [6]) can be found in the appendix. Recall that there are two major sources of indeterminism in Gentzen s original cut pushing elimination procedure for classical sequent calculus: a structural one (should one permute upwards to the left or to the right ) and a logical one (related to the order of ....
Joinet, J.-B., Schellinx, H. and Tortora de Falco, L. (1998) SN and CR for free-style LK tq : linear decorations and simulation of normalization. Preprint nr. 1067, Utrecht University, Department of Mathematics, 1998.
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