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Labelled natural deduction for substructural logics

K Broda
1999 Logic Journal of the IGPL  
A natural deduction derivation is correct with respect to a given substructural logic, if, under the condition that the algorithmic procedures terminate, the associated set of constraints is satisfied  ...  In this paper a uniform methodology to perform Natural Deduction over the family of linear, relevance and intuitionistic logics is proposed.  ...  Acknowledgements The authors would like to thank Marcello D'Agostino and Hans-Jorgen Ohlbach for their helpful comments and also several anonymous referees for their suggestions for improvements.  ... 
doi:10.1093/jigpal/7.3.283 fatcat:w4ajop76fzbh5mztelb5dewlvm

Page 3852 of Mathematical Reviews Vol. , Issue 2000f [page]

2000 Mathematical Reviews  
A. da Costa (Sao Paulo) 2000f:03067 03B47 Broda, Krysia (4-LNDIC-C; London); Finger, Marcelo (BR-SPL-CS; Sao Paulo) ; Russo, Alessandra (4-LNDIC-C; London) Labelled natural deduction for substructural  ...  A natural deduction derivation is then defined to be correct with respect to a given substructural logic if, under the condition that the algorithmic procedures terminate, the associ- ated set of constraints  ... 

Page 3177 of Mathematical Reviews Vol. , Issue 2003e [page]

2003 Mathematical Reviews  
deductive system for modal, substructural and fuzzy logics.  ...  Here this method is applied on the one hand to logics given by labelled deduction systems and on the other hand to general semantics for such logics.  ... 

An Alternative Natural Deduction for the Intuitionistic Propositional Logic

Mirjana Ilić
2016 Bulletin of the Section of Logic  
A natural deduction system N I, for the full propositional intuitionistic logic, is proposed.  ...  The operational rules of N I are obtained by the translation from Gentzen's calculus LJ and the normalization is proved, via translations from sequent calculus derivations to natural deduction derivations  ...  In fact, the use of labels is quite standard in natural deduction systems of substructural logics (see e.g.  ... 
doi:10.18778/0138-0680.45.1.03 fatcat:xvkzaca5bvf5vjs2ew6iyckksq

Page 4934 of Mathematical Reviews Vol. , Issue 94i [page]

1994 Mathematical Reviews  
94i:03049 94i:03049 03B45 03B35 68T15 Chau, Hiu Fai (4-LNDIC-C; London) A proof search system for a modal substructural logic based on labelled deductive systems.  ...  Summary: “This paper describes a proof search system for a modal substructural (concatenation) logic based on Gabbay’s labelled de- ductive systems (LDSs) as a case study.  ... 

Labelled Deduction in the Composition of Form and Meaning [chapter]

Michael Moortgat
1999 Trends in Logic  
Following up on this suggestion, we have compared a number of proof formats for grammatical reasoning from a 'Labelled Deduction' point of view.  ...  Labelled presentations of the categorial proof theory turn out to be attractive: they naturally accommodate the required modular treatment of logical and structural aspects of grammatical resource management  ...  structuring in the (labelled) Natural Deduction presentation of Def 2.3.  ... 
doi:10.1007/978-94-011-4574-9_15 fatcat:quxwaccmbbevri56fmtrpkq7eu

Algebraization, Parametrized Local Deduction Theorem and Interpolation for Substructural Logics over FL

Nikolaos Galatos, Hiroakira Ono
2006 Studia Logica: An International Journal for Symbolic Logic  
Substructural logics have received a lot of attention in recent years from the communities of both logic and algebra.  ...  We discuss the algebraization of substructural logics over the full Lambek calculus and their connections to residuated lattices, and establish a weak form of the deduction theorem that is known as parametrized  ...  We would like to thank Josep Maria Font and James Raftery for reading through our draft and for their helpful suggestions.  ... 
doi:10.1007/s11225-006-8305-5 fatcat:jfwnjin2kra3dixd5zqf2uwtfm

Page 1299 of Mathematical Reviews Vol. , Issue 96c [page]

1996 Mathematical Reviews  
1299 03B General logic 96c:03062 03B65 03F07 Oehrle, Dick (1-AZ-LN; Tucson, AZ) Some 3-dimensional systems of labelled deduction. Deduction and language. Bull. IGPL 3 (1995), no. 2-3, 429-448.  ...  This simplification opens up the way for an account of quantifier-scope ambiguities as a form of proof in- determinacy and for a preliminary inspection of a new family of labelled deductive systems.”  ... 

Forthcoming Papers

2002 Journal of Logic and Computation  
The relevance principle does not hold for substructural logics with mingle and usual negation, but holds for those with mingle and strong negation.  ...  We introduce intuitionistic and classical substructural logics with structural rules mingle and connective strong negation, and investigate the cut-elimination property and the relevance principle for  ...  The label formalism à Å, introduced to account for the semantics of normal modal logics, is easily adapted to the semantics of conditional logic by simply indexing labels with formulas.  ... 
doi:10.1093/logcom/12.5.911 fatcat:uba4ocmuhrfvrdxxxdgytudoee

Constructive Logic with Strong Negation is a Substructural Logic. II

M. Spinks, R. Veroff
2008 Studia Logica: An International Journal for Symbolic Logic  
It follows from the definitional equivalence of these systems that constructive logic with strong negation is a substructural logic.  ...  The goal of this two-part series of papers is to show that constructive logic with strong negation N is definitionally equivalent to a certain axiomatic extension NFLew of the substructural logic FLew.  ...  The first author would like to thank Nick Galatos for numerous helpful conversations about residuated lattices and Lloyd Humberstone for extensive discussions concerning logic, in particular substructural  ... 
doi:10.1007/s11225-008-9138-1 fatcat:7xpk52gymveo7f75hhynza2t2q

Applications of scott's notion of consequence to the study of general binary intensional connectives and entailment

Dov M. Gabbay
1973 Journal of Philosophical Logic  
This paper outlines a general method for proving decidability and undecidability for non-classical logical systems.  ...  Fibred Semantics for Feature Based Grammar Logic (with J. Dörre and E. König)  ...  Woods) In Dealing with label dependent deontic modalities (with G. Governatori) In A unified compilation style labelled deductive system for modal, substructural and fuzzy logic (with K.  ... 
doi:10.1007/bf00129607 fatcat:e6lokulrwrfcvl525fgj6dcr3m

Substructural logics on display

R Gore
1998 Logic Journal of the IGPL  
Although all these logics can be seen as substructural logics, these display calculi are not suitable for capturing bi-intuitionistic and bi-classical substructural (modal) logics in a uniform way.  ...  in non-commutative substructural logics [74] , the intricacies of cutelimination for full intuitionistic linear logic [41, 12] , and the (unsettled?)  ...  Labelled Deductive Systems Gabbay's Labelled Deductive Systems [29] have been applied to obtain labelled tableaux systems for intuitionistic and classical substructural logics [13] and also to the  ... 
doi:10.1093/jigpal/6.3.451 fatcat:erqlhxit7fe25a4gmybgimeuzy

Labelled Proof Systems for Intuitionistic Provability [chapter]

Vincent Balat, Didier Galmiche
2000 Applied Logic Series  
Therefore, suitable characterizations of intuitionistic provability and related labelled sequent calculi are defined for linear logic.  ...  proof-nets for sequents of classical linear logic.  ...  We know that natural deduction is a suitable deduction system for IL but not for CL for which sequent calculus seems better suited.  ... 
doi:10.1007/978-94-011-4040-9_1 fatcat:zsmdap7xrnc7jlpwc5cpduc36u

TOWER-Complete Problems in Contraction-Free Substructural Logics [article]

Hiromi Tanaka
2022 arXiv   pre-print
We investigate the computational complexity of a family of substructural logics with exchange and weakening but without contraction.  ...  The same complexity result holds even for deducibility in BCK-logic, i.e., the implicational fragment of 𝐅𝐋_𝐞𝐰.  ...  Acknowledgments The author would like to thank Koji Mineshima for useful suggestions.  ... 
arXiv:2201.02496v2 fatcat:ybhpmtuq3fcalegong47rfvilu

Page 778 of Mathematical Reviews Vol. , Issue 2002B [page]

2002 Mathematical Reviews  
The authors describe a uniform Kripke-style semantic framework for this family of substructural logics and then apply it in a labelled tableau refutation system.  ...  “Tableau methods for modal and temporal logics”, by Gore, is an introduction to tableau methods for automated deduction in modal and temporal logics.  ... 
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