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1. Substructural Logics (Stanford Encyclopedia Of Philosophy)
Substructural logics are nonclassical logics weaker than classical logic, notable for the absence of structural rules present in classical logic.
http://plato.stanford.edu/entries/logic-substructural/
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##### Substructural Logics
First published Tue Jul 4, 2000; substantive revision Fri May 17, 2002 Substructural logics are non-classical logics weaker than classical logic, notable for the absence of structural rules present in classical logic. These logics are motivated by considerations from philosophy (relevant logics), linguistics (the Lambek calculus) and computing (linear logic). In addition, techniques from substructural logics are useful in the study of traditional logics such as classical and intuitionistic logic. This article provides a brief overview of the field of substructural logic. For a more detailed introduction, complete with theorems, proofs and examples, the reader can consult the books and articles in the Bibliography.
##### Residuation
Logic is about logical consequence . As a result, the conditional is a central notion in logic because of its intimate connection with logical consequence. This connection is neatly expressed in residuation condition p q r if and only if p q r It says that r follows from p together with q just when q r follows from p alone. The validity of the transition from

2. Substructural Logic - Wikipedia, The Free Encyclopedia
In mathematical logic, in particular in connection with proof theory, a number of Substructural logics have been introduced, as systems of propositional
http://en.wikipedia.org/wiki/Substructural_logic
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##### Substructural logic
Jump to: navigation search In mathematical logic , in particular in connection with proof theory , a number of substructural logics have been introduced, as systems of propositional calculus that are weaker than the conventional one. They differ in having fewer structural rules available: the concept of structural rule is based on the sequent presentation, rather than the natural deduction formulation. Two of the more significant substructural logics are relevant logic and linear logic In a sequent calculus , one writes each line of a proof as Here the structural rules are rules for rewriting the LHS ÃÂ of the sequent, initially conceived of as a string of propositions. The standard interpretation of this string is as conjunction : we expect to read as the sequent notation for
A and B implies C
Here we are taking the RHS ÃÂ£ to be a single proposition C (which is the intuitionistic style of sequent); but everything applies equally to the general case, since all the manipulations are taking place to the left of the turnstile symbol.

3. Algebra & Substructural Logics
Algebra Substructural logics is a workshop on algebraic structures related to Substructural logic, organised by Hiroakira Ono and Tomasz Kowalski at Japan
http://www.jaist.ac.jp/~kowalski/workshop.html
take two
##### 12 - 14 November 2002
is a workshop on algebraic structures related to substructural logic, organised by Hiroakira Ono and Tomasz Kowalski at Japan Advanced Institute of Science and Technology ( JAIST Substructural logics, named thus because when formulated as Gentzen systems they lack one or more structural rules, have recently been enjoying considerable popularity among logicians and computer scientists. It seems promising to believe that universal algebra can provide a unifying framework for studying these. By a fortunate coincidence, the interest in algebraic structures related to substructural logics is also undergoing a revival among algebraists. The main objective of AsubL is to encourage further interaction in the area by providing a meeting point, which the organisers hope will become also a melting pot. AsubL take one was held at JAIST from 10 to 17 November 1999. Its proceedings have been published as a special issue of Reports on Mathematical Logic (vol. 34, 2000). AsubL take two was held at JAIST from 12 to 14 November 2002. The proceedings will appear in two special issues of

4. Substructural Logic --Â Britannica Online Encyclopedia
Perhaps more important have been various socalled Substructural logics in which the usual properties of the deduction symbol are weakened relevance logic
http://www.britannica.com/eb/topic-571118/substructural-logic
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##### substructural logic
A selection of articles discussing this topic.
##### foundations of mathematics
...a precise equality relation); and quantum logic, where conjunction may be only partially defined and implication may not be defined at all. Perhaps more important have been various so-called substructural logics in which the usual properties of the deduction symbol are weakened: relevance logic is studied by philosophers, linear logic by computer scientists, and a noncommutative version... No results were returned. Please consider rephrasing your query. For additional help, please review Search Tips Search Britannica for substructural logic About Us Legal Notices ... Test Prep Other Britannica sites: Australia France India Korea ... Encyclopedia

5. Substructural Logic Page
We give an implicational formula X such the results of strengthening each of the Substructural logics BCI, BCIW and BCK by the addition of X is a distict
http://users.rsise.anu.edu.au/~jks/substructural.html
##### John Slaney
More Proofs of an Axiom of Lukasiewicz This is the abstract of the paper: John Slaney.
More Proofs of an Axiom of Lukasiewicz.
Journal of Automated Reasoning This paper reports results and some new problems in one of the domains to which automatic first-order theorem provers have been most successfully applied: axiomatics of non-classical propositional logics. It is well known that one of the standard axioms of the denumerable-valued pure implication logic of Lukasiewicz becomes derivable from the remainder in the presence of negation. Here it is shown that the same axiom is similarly derivable using conjunction and disjunction instead of negation. This closes a problem left open by Harris and Fitelson Journal of Automated Reasoning 27, 2001). Related problems are discussed, and five such open problems are hereby proposed as challenges to the automated reasoning community.
Logic for Two
This is the abstract of the paper: John Slaney and Robert Meyer.

6. Substructural Logics In Natural Deduction -- Zimmermann 15 (3): 211 -- Logic Jou
Extensions of Natural Deduction to Substructural logics of Intuitionistic Logic are shown Fragments of Intuitionistic Linear, Relevant and BCK Logic.
http://jigpal.oxfordjournals.org/cgi/content/abstract/15/3/211
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Logic Journal of IGPL Advance Access originally published online on June 5, 2007
Logic Journal of IGPL 2007 15(3):211-232; doi:10.1093/jigpal/jzm008
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##### Substructural Logics in Natural Deduction
Ernst Zimmermann Elzacher Strasse 3, D-71034 Boeblingen.
Abstract Extensions of Natural Deduction to Substructural Logics of Intuitionistic Logic are shown: Fragments of Intuitionistic Linear, Relevant and BCK Logic. Rules for implication, conjunction, disjunction and falsum are defined, where conjunction and disjunction respect

7. Residuated Lattices An Algebraic Glimpse At Substructural Logics
The first and more obvious one is to present state of the art results in algebraic research into residuated structures related to Substructural logics.
http://www.elsevier.com/wps/product/cws_home/711437

8. An Introduction To Substructural Logics
Website for the book ``Consequences An Introduction to Substructural logics . Information on Philosophical Logic, Relevant/Relevance Logic, Linear Logic,
http://consequently.org/isl/
An Introduction to Substructural Logics Places: Main Solutions Links Errata ... Author Welcome to the web site for the book An Introduction to Substructural Logics. The book is an introduction to the field of relevant, linear, and other substructural logics, aimed at introducing this new and exciting field of logic to anyone and everyone. In practice, this means that the book will suit the advanced undergraduate, postgraduate, or researcher in logic (in philosophy, mathematics, computer science or theoretical linguistics). The book contains an overview of the major results and techniques in the field, in proof theory and semantics of these logics.
##### News
The book has been published, as of January 2000. Routledge have done a fine job with it, and it is available direct from them in their catalogue . Residents of the US or Canada should go instead to the Routledge NY site, to find details of the book here You can order it now at Amazon.com and Amazon.co.uk The bibliography used in the book is available on-line. The file is a BibTeX file, which is a simple encoded text-file with bibliography data of every article cited in the book, together with whatever else I have referred to in the last few years. While you wait to get your hands on the book, you can at least read what other people have

9. Atlas: Relational Semantics For Distributive Substructural Logics By Tomoyuki Su
In the present talk, we discuss relational semantics for distributive Substructural logics, i.e. Substructural logics over FL satisfying the distributive
http://atlas-conferences.com/cgi-bin/abstract/caug-26
 Atlas home Conferences Abstracts about Atlas ALGEBRAIC AND TOPOLOGICAL METHODS IN NON-CLASSICAL LOGICS III (TANCL'07) August 5-9, 2007 St Anne's College, University of Oxford Oxford, England Organizers Mai Gehrke and Hilary Priestley View Abstracts Conference Homepage Relational semantics for distributive substructural logics by Tomoyuki Suzuki Japan Advanced Institute of Science and Technology In the present talk, we discuss relational semantics for distributive substructural logics , i.e. substructural logics over FL satisfying the distributive law. Many attempts have been done of introducing relational semantics for substructural logics, but in most cases these semantics are unsatisfactory in their tractability and generality if we compare them with relational semantics for modal logics. Starting from the definition of DFL frames and general DFL frames, we will show how far we can develop a theory of relational semantics for distributive substructural logics in parallel with that for modal logics. This will include correspondence theory and completeness with respect to descriptive frames. Also, comparisons of our relational semantics with existing relational semantics for subclasses of distributive substructural logics, including intuitionistic and relevance logics, will be discussed. PDF Date received: April 30, 2007

10. CTO : Substructural Logics 101
The book An introduction to Substructural logics seems to be the only good introductory resource to the whole field together. There are, though, lots of
http://tunes.org/wiki/substructural_20logics_20101.html
CTO CLiki for the TUNES project Home Recent Changes About CLiki Text Formatting ... Create New Page
##### Substructural Logics 101
A Learning Lounge course.

11. (H. Ishihara) A Canonical Model Construction For Substructural Logics
Abstract In this paper, we introduce a class of Substructural logics, called normal Substructural logics, which includes not only relevant logic, BCK logic
http://www.jucs.org/jucs_6_1/a_canonical_model_construction
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##### A Canonical Model Construction for Substructural Logics
Hajime Ishihara (School of Information Science, Japan Advanced Institute of Science and Technology, Japan)
Abstract: In this paper, we introduce a class of substructural logics, called normal substructural logics , which includes not only relevant logic, BCK logic, linear logic and the Lambek calculus but also weak logics with strict implication, and de ne Kripke- style semantics (Kripke frames and models) for normal substructural logics. Then we show a correspondence between axioms and properties on frames, and give a canonical construction of Kripke models for normal substructural logics. 1 C.S.Calude and G.Stefanescu (eds.). Automata, Logic, and Computability. Special issue dedicated to Professor Sergiu Rudeanu Festschrift. Keywords: Kripke-type semantics, canonical model, linear logic, relevant logics, strict implication, substructural logics

 12. Substructural Logic And Partial Correctness An Introduction to Substructural logics. Routledge. 23. Troelstra, A. S. 1992. Lectures on Linear Logic. CSLI Lecture Notes, vol. 29.http://portal.acm.org/citation.cfm?id=772066

13. An Algebraic Approach To The Disjunction Property Of Substructural
Some of the basic Substructural logics are shown by Ono to have the disjunction property (DP) by using cut elimination of sequent calculi for these logics.
http://projecteuclid.org/handle/euclid.ndjfl/1193667706
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##### An Algebraic Approach to the Disjunction Property of Substructural Logics
Daisuke Souma Source: Notre Dame J. Formal Logic Volume 48, Number 4 (2007), 489-495.
##### Abstract
Some of the basic substructural logics are shown by Ono to have the disjunction property (DP) by using cut elimination of sequent calculi for these logics. On the other hand, this syntactic method works only for a limited number of substructural logics. Here we show that Maksimova's criterion on the DP of superintuitionistic logics can be naturally extended to one on the DP of substructural logics over FL . By using this, we show the DP for some of the substructural logics for which syntactic methods don't work well. Primary Subjects: Keywords: substructural logic; residuated lattice; disjunction property; well-connectedness Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription.

14. Relevance Principle For Substructural Logics With Mingle And Strong Negation --
We introduce intuitionistic and classical Substructural logics with structural rules mingle and connective strong negation, and investigate the
http://logcom.oxfordjournals.org/cgi/content/abstract/12/6/913
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##### Relevance Principle for Substructural Logics with Mingle and Strong Negation
Norihiro Kamide Wakayama National College of Technology, Noshima 77, Nada, Gobo, Wakayama 644-0023 Japan. E-mail: 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 these logics. The relevance principle does not

15. IngentaConnect Kripke Semantics For Modal Substructural Logics
We introduce Kripke semantics for modal Substructural logics, and prove the completeness theorems with respect to the semantics.
http://www.ingentaconnect.com/content/klu/jlli/2002/00000011/00000004/05092296
var tcdacmd="dt";

 16. JSTOR An Introduction To Substructural Logics An introduction to Substructural logics. Routledge, London and New York 2000, xiv + 381 pp. Substructural logics, the designation for logics withhttp://links.jstor.org/sici?sici=1079-8986(200112)7:4<527:AITSL>2.0.CO;2-N

17. 6th Panhellenic Logic Symposium :: Invited Lectures
The focus of this talk is Substructural logics and their algebraic counterparts. Substructural logics are nonclassical logics that are weaker than
http://pls6.pre.uth.gr/invitedl.php
##### Invited Lectures
Ayse Berkman (Middle East Technical University):
Groups of Finite Morley Rank I shall make a quick introduction to the subject, give examples and present the Borovik program that shaped around the main conjecture of the area:
Algebraicity Conjecture An infinite simple group of finite Morley rank is isomorphic to an algebraic group over an algebraically closed field.
In the second half of my talk, I shall present some recent results from the study of groups of finite Morley rank with pseudoreflection subgroups:
If G acts on an abelian group V , with an infinite definable connected abelian subgroup R such that V V R C V R ) and R acts transitively on the non-zero elements of [ V R ], then R is called a pseudoreflection subgroup of G
Stuart Barry Cooper (University of Leeds):
The Interactive Structure of Information: Post's Program Revisited Computability theory concerns information with a causal structure. As such, it provides a schematic analysis of many naturally occurring situations.
Emil Post was the first to focus on the close relationship between information, coded as real numbers, and its algorithmic infrastructure. Having characterized the close connection between the quantifier type of a real and the Turing jump operation, he looked for more subtle ways in which information entails a particular causal context. Specifically, he wanted to find simple relations on reals which produced richness of local computability-theoretic structure. To this extent, he was not just interested in causal structure as an abstraction, but in the way in which this structure emerges in natural contexts. "Post's program" was the genesis of a more far reaching research project.

18. Residuated Lattices An Algebraic Glimpse At Substructural Logics
Residuated Lattices An Algebraic Glimpse at Substructural logics, 151 Residuated Lattices An Algebraic Glimpse at Substructural logics, 151
http://www.biolc.com/wps/find/booksorderform.cws_home/711437/bookorderform1_1

19. CiNii - Glueing Of Algebras For Substructural Logics(Non-Classical Logics And Th
127139. Kyoto University. Bibliography. Glueing of Algebras for Substructural logics(Non-Classical logics and Their Kripke Semantics)
http://ci.nii.ac.jp/naid/110004707196/en/
Top Page Browse Publications Citation Index CiNii+Citation Index ... Japanese Journal Title
##### RIMS Kokyuroku
Vol.0927(19951100) pp. 127-139 Kyoto University Bibliography
##### SHIRASU Hiroyuki
School of Information Science, JAIST Read/Search Full Text Holdings NII Article ID (NAID) NII NACSIS-CAT ID (NCID) Text Lang ENG Databases NII-ELS Export Refer/BibIX Format BibTex Format Tab Separated Text (TSV) NII HOME ... NII-REO National Institute of Informatics

20. Research
Residuated Lattices an algebraic glimpse at Substructural logics, with P. Jipsen, Glivenko theorems for Substructural logics over FL, with H. Ono,
http://www.math.du.edu/~ngalatos/research/research.html
 Research Research Interests Publications Presentations Other Activities ... CV Research Interests Universal Algebra, Ordered Algebraic Structres and Algebraic Logic. Publications Book. Residuated Lattices: an algebraic glimpse at substructural logics, with P. Jipsen, T. Kowalski and H. Ono, Studies in Logics and the Foundations of Mathematics, Elsevier, pp. 509+ (2007). Refereed papers. The undecidability of the word problem for distributive residuated lattices Ordered Algebraic Structures (J. Martinez, ed.), Kluwer Academic Publishers, Dordrecht, 2002, 231-243 (pdf) Cancellative residuated lattices , with P. Bahls, J. Cole, P. Jipsen and C. Tsinakis, Algebra Universalis (2003), no. 1, 83-106. (pdf) Equational bases for joins of residuated-lattice varieties , Studia Logica (pdf) Adding involution to residuated structures , with J. Raftery, Studia Logica (pdf) Generalized MV-algebras , with C. Tsinakis, Journal of Algebra (pdf) Minimal varieties of residuated lattices , Algebra Universalis (pdf) Algebraization, paremetrized local deduction theorem and interpolation for substructural logics over FL

21. Math: Logic And Foundations: Nonstandard Logics And Extensions: Substructural Lo
A section of the SWIF map of logic on the WWW. Resources are in English and Italian. http//lgxserver.uniba.it/lei/logica/lglin_lo.htm. Substructural logics
http://www.spacetransportation.org/Math/Logic_and_Foundations/Nonstandard_Logics
##### Categories
Substructural and Paraconsistent Logics
A section of the SWIF map of logic on the WWW. Resources are in English and Italian.
http://lgxserver.uniba.it/lei/logica/lglin_lo.htm
Substructural Logics

Survey from the Stanford Encyclopedia of Philosophy by Greg Restall.
http://plato.stanford.edu/entries/logic-substructural/
Science Directory

22. Substructural Logics
Contents Preface A Historical Introduction to Substructural logics K. Do\v{s}en Life in the Undistributed Middle N. Belnap Theorems in Classical Logic are
http://www.cis.upenn.edu/~bcpierce/types/archives/1994/msg00048.html
##### Substructural Logics

23. CiteULike: Tag Substructural-logics [2 Articles]
posted to affinelogic cirquent-calculus computability-logic linear-logic logic proof-theory resource-semantic sequent-calculus Substructural-logics by
http://www.citeulike.org/tag/substructural-logics
##### Tag substructural-logics [2 articles]
Recent papers classified by the tag substructural-logics.
• Relevant and substructural logics by G Restall posted to logic substructural-logics by tautologico on 2005-03-20 03:26:11 as Introduction to Cirquent Calculus and Abstract Resource Semantics (27 Jun 2005) by Giorgi Japaridze posted to affine-logic cirquent-calculus computability-logic linear-logic ... substructural-logics by Anyzev on 2005-11-29 06:19:54 as along with 1 person
RIS
##### Related Tags
Tags related to: substructural-logics Filter: affine-logic cirquent-calculus computability-logic linear-logic ... sequent-calculus CiteULike organises scholarly (or academic) papers or literature and provides bibliographic (which means it makes bibliographies) for universities and higher education establishments. It helps undergraduates and postgraduates. People studying for PhDs or in postdoctoral (postdoc) positions. The service is similar in scope to EndNote or RefWorks or any other reference manager like BibTeX, but it is a social bookmarking service for scientists and humanities researchers.

 24. Residuated Lattices An Algebraic Glimpse At Substructural Logics Residuated Lattices An Algebraic Glimpse at Substructural logics, 151 Support contact About Elsevier Select your view Advertisers and sponsorshttp://elsevier.net/wps/find/submitbook.authors/711437?navopenmenu=5

 25. Residuated Lattices: An Algebraic Glimpse At Substructural Logics Is Available F Residuated Lattices an Algebraic Glimpse at Substructural logics only \$130.37, get the Residuated Lattices an Algebraic Glimpse at Substructural logicshttp://www.bestprices.com/cgi-bin/vlink/0444521410?id=nsession

 26. CAT.INIST Logic for two The semantics of distributive Substructural logics. J SLANEY, R MEYER Lecture notes in computer science, 554567, Springer-Verlag.http://cat.inist.fr/?aModele=afficheN&cpsidt=2731769

27. DBLP: Norihiro Kamide
4, Norihiro Kamide Kripke Semantics for Modal Substructural logics. 2 EE, Norihiro Kamide A Canonical Model Construction for Substructural logics
http://www.informatik.uni-trier.de/~ley/db/indices/a-tree/k/Kamide:Norihiro.html
##### Norihiro Kamide
List of publications from the DBLP Bibliography Server FAQ Coauthor Index - Ask others: ACM DL Guide CiteSeer CSB ... EE Norihiro Kamide: Synthesized substructural logics. Math. Log. Q. 53 EE Norihiro Kamide: Foundations of Paraconsistent Resolution. Fundam. Inform. 71 EE Norihiro Kamide: Phase Semantics and Petri Net Interpretation for Resource-Sensitive Strong Negation. Journal of Logic, Language and Information 15 EE Norihiro Kamide: Linear and affine logics with temporal, spatial and epistemic operators. Theor. Comput. Sci. 353 EE Norihiro Kamide: Linear Logics with Communication-merge. J. Log. Comput. 15 Norihiro Kamide: Natural deduction systems for Nelson's paraconsistent logic and its neighbors. Journal of Applied Non-Classical Logics 15 EE Norihiro Kamide: A spatial modal logic with a location interpretation. Math. Log. Q. 51 EE Norihiro Kamide: On a logic of involutive quantales. Math. Log. Q. 51 EE Norihiro Kamide: Gentzen-Type Methods for Bilattice Negation. Studia Logica 80 EE Norihiro Kamide: Combining Soft Linear Logic and Spatio-temporal Operators. J. Log. Comput. 14

28. T.Suzuki
A relational sematics for distributive Substructural logics and the topological Kripke completeness of some distributive Substructural logics.
http://www.cs.le.ac.uk/~ts119/
##### computerÂ science
HOME MAP CONTACT
Ph.D research student Charles Wilson Building 303Â
Department of Computer Science,
University of Leicester,
Leicester,
T: +44 (0)116 252 1371
E: ts119 'at' mcs.le.ac.uk
##### Research Interests
• Duality theory Coalgebraic logic
• Technical reports
• SUZUKI, Tomoyuki. A relational sematics for distributive substructural logics and the topological characterization of the descriptive frames (submitted). Tomoyuki Suzuki. Kripke completeness of some distributive substructural logics. Japan Advanced Institute of Science and Technology, March 2007. (supervised by H.Ono)
##### International
• A relational semantics for distributive substructural logics and the topological characterization of the descriptive frames, CALCO-jnr:CALCO Young Researchers Workshop in 2nd Conference on Algebra and Coalgebra in Computer Science, 20-24 August 2007, Bergen, Norway. Relational semantics for distributive substructural logics, Algebraic and Topological Methods in Non-Classical Logics III, 5-9 August, Oxford, UK.
##### Education
• Master of Science (Information Science), Japan Advanced Institute of Science and Technology, 2007.
• 29. Peter Suber, "Non-Standard Logics"
An Introduction to Substructural logics. Routledge, 2000. (Details.) SchroederHeister, Peter (ed.). Substructural logics. Oxford University Press, 1994.
http://www.earlham.edu/~peters/courses/logsys/nonstbib.htm
 A Bibliography of Non-Standard Logics Peter Suber Philosophy Department Earlham College In the kinds of non-standard logics included, this bibliography aims for completeness, although it has not yet succeeded. In the coverage of any given non-standard logic, it does not at all aim for completeness. Instead it aims to include works suitable as introductions for those who are already familiar with standard first-order logic. Looking at these non-standard logics gives us an indirect, but usefully clear and comprehensive idea of the usually hazy notion of "standardness". In standard first-order logics: Wffs are finite in length (although there may be infinitely many of them). Rules of inference take only finitely many premises. There are only two truth-values, "truth" and "falsehood". Truth-values of given proposition symbols do not change within a given interpretation, only between or across interpretations. All propositional operators and connectives are truth-functional. "p ~p" is provable even if we do not have p or ~p separately; that is, the principle of excluded middle holds.

 30. OUP: UK General Catalogue Substructural logics are nonclassical logics, which arose in response to problems in foundations of mathematics and logic, theoretical computer science,http://www.oup.com/uk/catalogue/?ci=9780198537779

31. Bibliography Of The Book "An Introduction To Substructural Logics"
Bibliography of the book An Introduction to Substructural logics . This bibliography is a part of the Computer Science Bibliography Collection.
http://liinwww.ira.uka.de/bibliography/Theory/isl.html
##### Bibliography of the book "An Introduction to Substructural Logics"
About Browse Statistics Number of references: Last update: April 20, 2000 Number of online publications: Supported: yes Most recent reference: Query: in any author title field
Publication year : in: , since: , before: (four digit years)
Options: Results as Citation Results in BibTeX 10 results per page 40 results per page 100 results per page 200 results per page sort by score year online papers only
You may use Lucene syntax , available fields are: ti (title), au (author), yr (publications year).
##### Information on the Bibliography
Author:
Greg Restall (email mangled to prevent spamming)
Department of Philosophy
Macquarie University
Sydney 2109
Australia
Abstract:
This is the bibliography of the book " An Introduction to Substructural Logics " by Greg Restall.
##### Bibliographic Statistics
Types:
article(442), book(204), incollection(141), unpublished(35), inproceedings(34), techreport(25), phdthesis(15), bibtex(3), misc(3), proceedings(2), booklet(1), mastersthesis(1)

 32. Substructural Logics Substructural logics are typically obtained by dropping structural rules such as weakening, contraction or interchange from the standard Gentzen calculus ofhttp://www.philo.at/phlo/199903/msg00045.html

 33. TR-ARP-1-94 John Slaney. The Crisis In Finite Mathematics Finite Models for some Substructural logics. 18 pages TRARP-5-94 Greg Restall. Displaying and Deciding Substructural logics 1 logics withhttp://ftp.rsise.anu.edu.au/techreports/index.txt

 34. Substructural Logics: A Primer - Logic Journals, Books & Online Media | Springer Substructural logics A Primer Logic. Substructural logics are by now one of the most prominent branches of the research field usually labelled ashttp://www.springer.com/west/home/new & forthcoming titles (default)?SGWID=4-403

 35. Publications LDS-Natural Deduction For Substructural Logics LDSNatural Deduction for Substructural logics. Krysia Broda, Marcelo Finger, Alessandra Russo. Journal Article 1996 Volume 4; Issue 3; pp.486Â489http://pubs.doc.ic.ac.uk/LDSSubstructural/

36. Proof Theory - Substructural Logics
A selection of articles related to Proof theory Substructural logics.
http://www.experiencefestival.com/proof_theory_-_substructural_logics
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##### A Wisdom Archive on Proof theory - Substructural logics
Proof theory - Substructural logics A selection of articles related to Proof theory - Substructural logics More material related to Proof Theory can be found here: Main Page
for

Proof Theory
Index of Articles ...
Proof theory - Substructu...
Proof theory, Proof theory - Consistency proofs, Proof theory - Formal and informal proof, Proof theory - History, Proof theory - Kinds of proof calculus, Proof theory - Ordinal analysis, Proof theory - Selected bibliography, Proof theory - Structural proof theory, Proof theory - Substructural logics, Proof theory - Tableau systems, Proof techniques, Intermediate logics, Proof-theoretic semantics
##### ARTICLES RELATED TO Proof theory - Substructural logics
Proof theory - Substructural logics: Encyclopedia II - Proof theory - History Although the formalisation of logic was much advanced by the work of such figures as Gottlob Frege, Peano, Russell and Dedekind, conventionally the story of modern proof theory is seen as being established by David Hilbert, who initiated what is called Hilbert's program in the Foundations of mathematics. Kurt GÂ¶del's seminal work on proof theory first advanced, then refuted this program: his completeness theorem seemed to bring Hilbert's problem of reducing all mathematics to a finitist formal system, then his incompleteness theorems showed that was unattainable. All of this work was carried out with the pr ...

37. Introduction To Substructural Logics ~ Greg Restall ~ EBookMall ~ EBook
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##### An Introduction to Substructural Logics eBook
by Greg Restall
An Introduction to Substructural Logics eBook
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##### An Introduction to Substructural Logics Summary
This book introduces an important group of logics that have come to be known under the umbrella term "susbstructural". Substructural logics have independently led to significant developments in philosophy, computing and linguistics. An Introduction to Substructural Logics is the first book to systematically survey the new results and the important impact that this class of logics has had on wide-ranging fields of study.
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38. Math: Logic And Foundations: Nonstandard Logics And Extensions: Substructural Lo
Substructural and Paraconsistent logics http//lgxserver.uniba.it/lei/logica/lglin_lo.htm http//plato.stanford.edu/entries/logicSubstructural/
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##### Math: Logic and Foundations: Nonstandard Logics and Extensions: Substructural Logics
the entire directory only this category Advanced Search Home Math Logic and Foundations ... Nonstandard Logics and Extensions : Substructural Logics CATEGORIES: Linear Logic Relevance Logic LINKS:
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39. Residuated Lattices: An Algebraic Glimpse At Substructural Logics - Blackwell On
Blackwell Residuated Lattices An Algebraic Glimpse at Substructural logics, Galatos, Nikolaos Jipsen, Peter Kowalski, Tomasz, Elsevier Science.
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##### Residuated Lattices: An Algebraic Glimpse at Substructural Logics
An Algebraic Glimpse at Substructural Logics
##### Galatos, Nikolaos Jipsen, Peter Kowalski, Tomasz
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Not currently stocked in Blackwell stores. Ask your local store to obtain this book for you. ISBN DEWEY edition What's this? Pages Publisher Elsevier Science Volumes Imprint SUN LITHO-PRINT Weight (grammes) Format Hardback Series ISSN Publication date 01 Jun 2007 Series title Library of Congress QA Height (mm) DEWEY Width (mm) Ch. 1

40. MASTER IN PURE AND APPLIED LOGIC
Master degree in pure and applied logic jointly offered by the University of of Substructural logics to computer science and computational linguistics),
http://www.ub.es/masterlogic/docto-e.html
 Castellano English Interuniversity Master UB UPC Index Introduction Academic structure Lecturers Courses ... Other activities Doctorate (PhD) News Related links For further information please contact jansana ub.edu DOCTORATE DEGREE (PhD) Students who successfully complete the research track of the Master in Pure and Applied Logic will be prepared to initiate a research career at an international level, in the area of Logic where they have specialized. The lecturers at the Master , as well as other researchers of their groups, can supervise research work leading to the Spanish official title of Doctor in the Official Postgraduate Programs (POP) of the catalan universities. Below you can see the research areas of these lecturers and researchers. The list of the relevant POPs is not completely determined yet, but it is expected that it will include at least the following ones: Computation (Technical University of Catalonia) Mathematics (University of Barcelona) Mathematics and Statistics (Technical University of Catalonia) Philosophy (University of Barcelona) According to the Spanish regulations presently in force, admittance to the

 41. Browse Books About Introductory Logic This book introduces an important group of logics that have come to be known under the umbrella term susbstructural . Substructural logics havehttp://www.routledge.com/shopping_cart/categories/categories_products.asp?parent

42. ICCL Summer School 2004
In this course, rather than examine decidability or complexity results for Substructural logics and their fragments, we concentrate on the practicalities of
http://www.computational-logic.org/iccl/events/SA-2004/

43. Chapters.indigo.ca: An Introduction To Substructural Logics: Restall: Books
This is the first book to systematically survey new areas of Substructural logics. This book is geared to introduce the topic to advanced students.
http://www.chapters.indigo.ca/books/An-Introduction-to-Substructural-Logics-Rest
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This is the first book to systematically survey new areas of substructural logics. This book is geared to introduce the topic to advanced students. An Introduction to Substructural Logicscovers the area of logic that is crucial to developments in computing, philosophy and linguistics.

44. Alasdair Urquhart - Complexity Problems For Substructural Logics
Alasdair Urquhart Complexity problems for Substructural logics.
http://www.math.ca/Events/winter99/abstracts/node50.html
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##### Alasdair Urquhart - Complexity problems for substructural logics
ALASDAIR URQUHART, Department of Philosophy, University of Toronto, Toronto, Ontario M5S 1A1 Complexity problems for substructural logics
Substructural logics are typically obtained by restricting the structural rules of contraction and weakening in propositional logic. They include logics (such as relevance logics) that were originally investigated for philosophical reasons, and logics such as linear logic that were inspired by ideas from category theory and computer science. A surprising feature of these logics is that the simple omission of the structural rules leads in many cases to a drastic increase in complexity. For example, propositional linear logic is undecidable. In other cases, such as linear logic with weakening, the propositional logic is decidable, but of a high intrinsic complexity. In this talk, I shall report on some recent results on the complexity of decidable substructural propositional logics, and explain some of the open questions in the area.
Next: Franck van Breugel - Up: Applied Logic / Logique Previous: Robert Seely - Semantics

45. 15-816 Linear Logic / Projects
A project might consist of some theoretical analysis, an implementation, or an encoding or explanation using linear or other Substructural logic.
http://www.cs.cmu.edu/~fp/courses/linear/projects.html
Home Schedule Assignments Projects ... Resources fp@cs Frank Pfenning
##### 15-816 Linear Logic Projects
This page contains some suggestions for projects for this course. You are encouraged to draw upon your own experience and judgment to develop other project ideas. Note that the given references are by no means exhaustive, but provide an entry point to the literature. Warning: The links to papers have not yet been checked for accuracy. A project might consist of some theoretical analysis, an implementation, or an encoding or explanation using linear or other substructural logic. The only constant requirement is that the project contain a term paper that explains the background, motivation, technical contribution, and draws some conclusion. I would expect the term papers to be at least about 10 pages long. The best term papers may be suitable for publication, depending on the chosen topic and results.
##### Classical Linear Logic
Give a judgmental explanation of linear logic in terms of three basic judgments: A is true, A is false, and contradiction. We have unrestricted and linear assumptions about the truth and falsehood of propositions, and our only goal is to derive a contradiction. From this we might be able to see clearly how intuitionistic linear logic is a generalization of classical linear logic by accomodating other goals besides contradiction. It might also be interesting to see if one can join both classical and intuitionistic logic consistently in the same system.

46. Marcelo Finger's Publications
`Algorithmic Correspondence Theory for Substructural Categorial Logic . Advances in Modal Logic 2000, Leipzig, Germany, 47 October 2000.
http://www.ime.usp.br/~mfinger/publications/
##### Marcelo Finger 's Publications
May 19, 2004 See also my papers in portuguese and my PhD thesis Bibfinder query results for Marcelo Finger can be found here Publications
• Sabine Broda, Luis Damas, Marcelo Finger, and Paulo Silva e Silva.
The decidability of a fragment of BB'IW -logic.
Theoretical Computer Science Available in gzip'ed PDF format Marcelo Finger and Renata Wassermann.
Approximate and limited reasoning: Semantics, proof theory, expressivity and control.
Journal of Logic And Computation Available in PDF format Andrei Goldchleger, Fabio Kon, Alfredo Goldman, Marcelo Finger, and Germano Capistrano Bezerra.
InteGrade: Object-Oriented Grid Middleware Leveraging Idle Computing Power of Desktop Machines.
Concurrency and Computation: Practice and Experience , 16:449-459, March 2004. Available in PDF format Marcelo Finger.
Towards polynomial approximations of full propositional logic.
Technical Report RT-2004-04, Department of Computer Science, IME/USP, 2004. Available in gzip'ed PDF format Marcelo Finger and Renata Wassermann.
The universe of approximations.

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