Naming Proofs in Classical Propositional Logic

Lamarche, F.; Straßburger, Lutz

doi:10.1007/11417170_19

Cited by 30 publications

(66 citation statements)

References 17 publications

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“…We now think that these standard postulates deserve more scrutiny [LS05b,LS05a], but we make no predictions about the conclusions we will eventually reach.…”

Section: Resultsmentioning

confidence: 93%

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From Proof Nets to the Free *-Autonomous Category

Lamarche¹,

Straßburger²

2006

Logical Methods in Computer Science

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Abstract. In the first part of this paper we present a theory of proof nets for full multiplicative linear logic, including the two units. It naturally extends the well-known theory of unit-free multiplicative proof nets. A linking is no longer a set of axiom links but a tree in which the axiom links are subtrees. These trees will be identified according to an equivalence relation based on a simple form of graph rewriting. We show the standard results of sequentialization and strong normalization of cut elimination. In the second part of the paper we show that the identifications enforced on proofs are such that the class of two-conclusion proof nets defines the free * -autonomous category.

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“…We now think that these standard postulates deserve more scrutiny [LS05b,LS05a], but we make no predictions about the conclusions we will eventually reach.…”

Section: Resultsmentioning

confidence: 93%

“…While we were writing this, we became aware of [FP04b,FP04c,FP04a], which tackle this very problem. Some additional research [LS05b,LS05a,Lam06,Str05] allows us to say that the last word on the relationship between classical logic and categories will not be said in the near future.…”

Section: 2mentioning

confidence: 99%

From Proof Nets to the Free *-Autonomous Category

Lamarche¹,

Straßburger²

2006

Logical Methods in Computer Science

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“…The answer given in [LS05] naturally is closely related to that given by the CM, namely that this essence is basically given by the connection structure underlying a proof. The paper in addition clari es the e ect of the cut rule in terms of a composition operation on such structures (without addressing the questions underlying our conjecture).…”

Section: 1mentioning

confidence: 95%

Research Perspectives for Logic and Deduction

Bibel

2006

Reasoning, Action and Interaction in AI Theories and Systems

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The article is meant to be kind of the author's manifesto for the role of logic and deduction within Intellectics. Based on a brief analysis of this role the paper presents a number of proposals for future scienti c research along the various dimensions in the space of logical explorations. These dimensions include the range of possible applications including modelling intelligent behavior, the grounding of logic in some semantic context, the choice of an appropriate logic from the great variety of alternatives, then the choice of an appropriate formal system for representing the chosen logic, and nally the issue of developing the most e cient search strategies. Among the proposals is a conjecture concerning the treatment of cuts in proof search.

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“…Other researchers have given abstract notions of proof-net for classical logic; these make the identifications we wish to make but lack a strong connection to the sequent calculus. Lamarche and Strassburger [12] give two notions of proof-net, both of which validate more identities than Robinson. The B-nets are nothing more than binary linkings on a sequent forest: they possess sequentialization into an additive sequent calculus, but checking correctness of such a net is no more efficient than checking the truth-table of the conclusion.…”

Section: Conclusion and Further Workmentioning

confidence: 98%

“…Investigations by several researchers over the last ten years [16,7,12,13,2,11] have only served to underline the difficulty of the problem. Many of these problems concern proofs with cuts, since the problem of proof-identity must account for the nonconfluence of cut-elimination.…”

Section: Introductionmentioning

confidence: 99%

Expansion Nets: Proof-Nets for Propositional Classical Logic

McKinley

2010

Logic for Programming, Artificial Intelligence, and Reasoning

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Abstract. We give a calculus of proof-nets for classical propositional logic. These nets improve on a proposal due to Robinson by validating the associativity and commutativity of contraction, and provide canonical representants for classical sequent proofs modulo natural equivalences. We present the relationship between sequent proofs and proof-nets as an annotated sequent calculus, deriving formulae decorated with expansion/deletion trees. We then see a subcalculus, expansion nets, which in addition to these good properties has a polynomial-time correctness criterion.

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Naming Proofs in Classical Propositional Logic

Cited by 30 publications

References 17 publications

From Proof Nets to the Free *-Autonomous Category

From Proof Nets to the Free *-Autonomous Category

Research Perspectives for Logic and Deduction

Expansion Nets: Proof-Nets for Propositional Classical Logic

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