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Towards a Semantic Characterization of Cut-Elimination

Agata Ciabattoni, Kazushige Terui
2006 Studia Logica: An International Journal for Symbolic Logic  
We introduce necessary and sufficient conditions for 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  ... 
doi:10.1007/s11225-006-6607-2 fatcat:soygnhdryba7jikhisajkq6iwy

Proofnets and Context Semantics for the Additives [chapter]

Harry G. Mairson, Xavier Rival
2002 Lecture Notes in Computer Science  
We provide 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.  ... 
doi:10.1007/3-540-45793-3_11 fatcat:dt2wq43skbedljulj6wa3ttpei

Two Many Values: An Algorithmic Outlook on Suszko's Thesis

Carlos Caleiro, João Marcos
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.  ... 
doi:10.1109/ismvl.2010.25 dblp:conf/ismvl/CaleiroM10 fatcat:v4rracrrara7poqvc5bam6fijy

CONSTRUCTIVE CLASSICAL LOGIC AS CPS-CALCULUS

ICHIRO OGATA
2000 International Journal of Foundations of Computer Science  
CPS-calculus exactly means the target language 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.  ... 
doi:10.1142/s0129054100000065 fatcat:qt4xrvsvsrc5xf62vheeqvavkq

Conjunction and Disjunction in Infectious Logics [chapter]

Hitoshi Omori, Damian Szmuc
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 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.  ... 
doi:10.1007/978-3-662-55665-8_19 fatcat:kr4i6epsnvb5layl7wtvelpad4

Event recognition in sport programs using low-level motion indices

A. Bonzanini, R. Leonardi, P. Migliorati
2001 IEEE International Conference on Multimedia and Expo, 2001. ICME 2001.  
The proposed algorithm is an example 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.  ... 
doi:10.1109/icme.2001.1237894 dblp:conf/icmcs/BonzaniniLM01 fatcat:32mk5i7t45de3gwwxibsgijtvy

A CPS-Transform of Constructive Classical Logic [chapter]

Ichiro Ogata
1999 Lecture Notes in Computer Science  
The constructive classical logic LK is 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!  ... 
doi:10.1007/3-540-46674-6_23 fatcat:e4g7ibzw4jdtxmfowqh655ozby

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.  ... 

A proof-theoretic view on scheduling in concurrency [article]

Emmanuel Beffara
2014 arXiv   pre-print
In our logical system, processes and schedulers appear explicitly as proofs in different fragments 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  ... 
arXiv:1402.6459v4 fatcat:5ixcjtbwxbdmtcnzrxpia6axui

A proof-theoretic view on scheduling in concurrency

Emmanuel Beffara
2014 Electronic Proceedings in Theoretical Computer Science  
In our logical system, processes and schedulers appear explicitly as proofs in different fragments 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  ... 
doi:10.4204/eptcs.164.6 fatcat:5oj2vofdlbeuffzeoe7z3p5uom

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  ... 

Cut as Consequence

Curtis Franks
2010 History and Philosophy of Logic  
between 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.  ... 
doi:10.1080/01445340.2010.522365 fatcat:dnibzkfrlfapjkdfxfpaj4d2bm

The logic of Quantifier Raising

Chris Barker
2020 Semantics and Pragmatics  
to 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.  ... 
doi:10.3765/sp.13.20 fatcat:grcv64xp6beppb76mdyyntw6mq
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