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Towards a Semantic Characterization of Cut-Elimination

2006
*
Studia Logica: An International Journal for Symbolic Logic
*

We introduce necessary and sufficient conditions for

doi:10.1007/s11225-006-6607-2
fatcat:soygnhdryba7jikhisajkq6iwy
*a*(single-conclusion) sequent calculus to admit (reductive)*cut*-*elimination*. Our conditions are formulated both syntactically and*semantically*. ...*A*. Ciabattoni was supported by C. Bühler-Habilitations-Stipendium H191-N04, from the Austrian Science Fund (FWF). K. Terui was supported by Grant-in-Aid for Scientific Research, MEXT, Japan. ...*A**characterization**of**cut*-*elimination*, i.e. the definition*of*formal criteria that, when satisfied by*a*sequent calculus guarantee*cut*-*elimination*and, when not satisfied they provide*a*counterexample ...##
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Proofnets and Context Semantics for the Additives
[chapter]

2002
*
Lecture Notes in Computer Science
*

We provide

doi:10.1007/3-540-45793-3_11
fatcat:dt2wq43skbedljulj6wa3ttpei
*a*context*semantics*for Multiplicative-Additive Linear Logic (MALL), together with proofnets whose reduction preserves*semantics*, where proofnet reduction is equated with*cut*-*elimination*on ... Linear Logic was initially*a*sequent calculus, but this sequentialized structure was too strong and the design*of**a*nice*cut*-*elimination*procedure was complicated. ... Our proofnet syntax gives*a*sort*of*low-level implementation*of*this*semantics*. ...##
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Two Many Values: An Algorithmic Outlook on Suszko's Thesis

2010
*
2010 40th IEEE International Symposium on Multiple-Valued Logic
*

*of*its most favorable crops on the domains

*of*

*semantics*and proof-theory. ... In spite

*of*the multiplication

*of*truth-values,

*a*noticeable shade

*of*bivalence lurks behind the canonical notion

*of*entailment that many-valued logics inherit from the 2-valued case. ... ACKNOWLEDGMENT The first author was partly supported by FCT and EU FEDER, namely via the KLog project PTDC/MAT/ 68723/2006

*of*SQIG-IT. The second author acknowledges partial support by CAPES. ...

##
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CONSTRUCTIVE CLASSICAL LOGIC AS CPS-CALCULUS

2000
*
International Journal of Foundations of Computer Science
*

CPS-calculus exactly means the target language

doi:10.1142/s0129054100000065
fatcat:qt4xrvsvsrc5xf62vheeqvavkq
*of*Continuation Passing Style(CPS) transforms. Constructive classical logic we refer to are LKT and LKQ introduced by Danos et al.(1993). ... The unied*semantics*should be*a**semantics*for the CBN/CBV function. Because*Cut*-*elimination*procedure for the MELL is proven to be SN and CR [2] . Proof. ... Denotational*semantics*for the CBN/CBV functions also deserve further study. Our*characterization**of*CBN/CBV is purely syntactical. ...##
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Conjunction and Disjunction in Infectious Logics
[chapter]

2017
*
Lecture Notes in Computer Science
*

Infectious logics are peculiar manyvalued logics whose underlying algebra has an absorbing or infectious element, which is assigned to

doi:10.1007/978-3-662-55665-8_19
fatcat:kr4i6epsnvb5layl7wtvelpad4
*a*compound formula whenever it is assigned to one*of*its components ... This is why we finally turn to the analysis*of*the truth-conditions for conjunction and disjunction in infectious logics, employing the framework*of*plurivalent logics, as discussed by Priest. ... In such cases, the failure*of*∧-*Elimination*is properly understood in epistemic terms by taking conjunction as*cut*-down conjunction. ...##
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Event recognition in sport programs using low-level motion indices

2001
*
IEEE International Conference on Multimedia and Expo, 2001. ICME 2001.
*

The proposed algorithm is an example

doi:10.1109/icme.2001.1237894
dblp:conf/icmcs/BonzaniniLM01
fatcat:32mk5i7t45de3gwwxibsgijtvy
*of*solution to the problem*of*finding*a**semantic*relevant event (e.g., scoring*of**a*goal in*a*soccer game) in case*of*specific categories*of*audio-visual programmes ... In literature we can find many video indexing algorithms, based on various types*of*low-level features, but the problem*of**semantic*indexing is less studied and surely it is*a*great challenging one. ...*A*good*semantic*index*of**a*soccer video sequence could be therefore*a*summary made up*of**a*list*of*all game actions, each*characterized*by its beginning and ending event. ...##
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A CPS-Transform of Constructive Classical Logic
[chapter]

1999
*
Lecture Notes in Computer Science
*

The constructive classical logic LK is

doi:10.1007/3-540-46674-6_23
fatcat:e4g7ibzw4jdtxmfowqh655ozby
*a*variant*of*LK. The CR property*of**cut*-*elimination*scheme (called tq-protocol) is recovered by adding some restrictions on logical rules to LK. ... The t presents*a*new Curry-Howard \classical proofs as programs",\*cut**elimination*as computation" paradigm. In the second part, we show how n can be simulated by t . ... The reader who is interested should access the original paper [3] .*cut**elimination*? skeleton -*cut**elimination*? skeleton*cut**elimination*t (x*A*:t) (*A*:s) 0! t [x :=*A*:s] s 0! ...##
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Page 622 of Mathematical Reviews Vol. , Issue 91B
[page]

1991
*
Mathematical Reviews
*

Lyubetskii,

*A*transfer theorem in the theory*of*rings (pp. 101-111); V. I. Shalak,*Toward**a*categorical*characterization**of*relevant logic (pp. 112-119); V. L. ... Ishmura- tov, The logic*of*intensional acts and game theory (pp. 204-213); O. F. Serebryannikov, An elementary proof*of**a**cut*-*elimination*theorem in second-order logic (pp. 214-218); P. I. ...##
###
Page 4398 of Mathematical Reviews Vol. , Issue 2001G
[page]

2001
*
Mathematical Reviews
*

But it is more desirable to achieve

*a*more fundamental goal, namely using appropriate extensions*of*syntactical tools in*a*con- structive proof*of*the transition from the*cut*-*elimination*theorem to the ... “More specifically, modified Gentzen-type sequent calculi for modal and relevant propositional logics are constructed for each*of*which the*cut*-*elimination*theorem holds. ...##
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A proof-theoretic view on scheduling in concurrency
[article]

2014
*
arXiv
*
pre-print

In our logical system, processes and schedulers appear explicitly as proofs in different fragments

arXiv:1402.6459v4
fatcat:5ixcjtbwxbdmtcnzrxpia6axui
*of*the proof language and*cut**elimination*between them does correspond to execution*of**a*concurrent system ... This separation*of*roles suggests new insights for the denotational*semantics**of*processes and new methods for the translation*of*pi-calculi into prefix-less formalisms (like solos) as the operational ... actions in*a*given process without introducing new actions. • An execution*of*P corresponds to*a**cut**elimination*sequence*of*P*cut*against*a*schedule for reducing P to some Q; various*cut**elimination*...##
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A proof-theoretic view on scheduling in concurrency

2014
*
Electronic Proceedings in Theoretical Computer Science
*

In our logical system, processes and schedulers appear explicitly as proofs in different fragments

doi:10.4204/eptcs.164.6
fatcat:5oj2vofdlbeuffzeoe7z3p5uom
*of*the proof language and*cut**elimination*between them does correspond to execution*of**a*concurrent system ... This separation*of*roles suggests new insights for the denotational*semantics**of*processes and new methods for the translation*of*π-calculi into prefix-less formalisms (like solos) as the operational counterpart ... actions in*a*given process without introducing new actions. • An execution*of*P corresponds to*a**cut**elimination*sequence*of*P*cut*against*a*schedule for reducing P to some Q; various*cut**elimination*...##
###
Page 1997 of Mathematical Reviews Vol. , Issue 96d
[page]

1996
*
Mathematical Reviews
*

We develop

*a*method*of*complete- ness proof for the associative labelled Lambek calculus, prove*cut*03B General logic 964:03047*elimination*and indicate*a*possible linguistic application. ... The generalized quan- tifier (GQ) approach*characterizes*quantified NPs and names as elements*of**a*unified syntactic category and*semantic*type. Ac- cording to the logicality thesis [R. ...##
###
Page 8148 of Mathematical Reviews Vol. , Issue 2004j
[page]

2004
*
Mathematical Reviews
*

Bradfield, Par-
ity

*of*imperfection or fixing independence (72-85); Kai Briinnler, 68 COMPUTER SCIENCE 8148 Atomic*cut**elimination*for classical logic (86-97); Bruno Buch- berger, Computational mathematics ... explanations for queries on propositional Horn theories (197-211); Philipp Gerhardy, Refined complexity analysis*of**cut**elimination*(212-225); Martin Grohe and Nicole Schweikardt, Comparing the succinctness ...##
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Cut as Consequence

2010
*
History and Philosophy of Logic
*

between

doi:10.1080/01445340.2010.522365
fatcat:dnibzkfrlfapjkdfxfpaj4d2bm
*a*system as*a*whole and its '*semantics*'). ... Gentzen's conception*of*logic is compelling in its own right. It is also*of*historical interest because it allows for*a*better understanding*of*the invention*of*natural deduction and sequent calculi. ... Graham Leach-Krouse, Neil Tennant, and two anonymous referees for History and Philosophy*of*Logic offered helpful suggestions on an earlier draft*of*the paper. ...##
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The logic of Quantifier Raising

2020
*
Semantics and Pragmatics
*

to

doi:10.3765/sp.13.20
fatcat:grcv64xp6beppb76mdyyntw6mq
*a**semantically*equivalent proof in QRT, and vice-versa. ... I settle these issues by defining QRT (Quantifier Raising with Types),*a*substructural logic that is*a*faithful model*of*QR in the following respect: every*semantically*coherent QR derivation corresponds ...*A*.5 Hint for the problem posed in (13) One*of*the two*semantically*distinct analyses requires at least one instance*of*quantifier raising; the other requires at least two. ...
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