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Citations: Semantics for substructural logics - Ono (ResearchIndex)   (Site not responding. Last check: 2007-11-06) Pretopology Semantics for Bimodal Intuitionistic Linear Logic - Hartonas (1997) Ono, Semantics for Substructural Logics, in [9], 259-291. Ono, Semantics for Substructural Logics, in [13], 259-291. citeseer.ist.psu.edu /context/19481/0   (2405 words)

Substructural Logics   (Site not responding. Last check: 2007-11-06) Substructural logics are non-classical logics weaker than classical logic, notable for the absence of structural rules present in classical logic. In addition, techniques from substructural logics are useful in the study of traditional logics such as classical and intuitionistic logic. For logics, such as linear logic, without the distribution axiom, the semantics must be more complex, with a different clause for disjunction required to invalidate the inference of distribution. www.science.uva.nl /~seop/archives/spr2004/entries/logic-substructural   (2915 words)

Alasdair Urquhart - 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. camel.math.ca /Events/winter99/abstracts/node50.e?nomenu=1   (149 words)

Substructural Logic Page This is an account of the semantics of a family of logics whose paradigm member is the relevant logic R of Anderson and Belnap. Our further goal is to put these logics in the service of practical reasoning systems, since the basic concept of our treatment is that of an agent a reasoning to conclusions using as assumptions the theory of agent b, where a and b may or may not be the same. This is an essay in logic in the traditional sense: the formal theory of inference. users.rsise.anu.edu.au /~jks/substructural.html   (1039 words)

Relevance Logic Our exposition of relevant logic is backwards to most found in the literature We will begin, rather than end, with the semantics, since most philosophers at present are semantically inclined. Linear logics, a branch of logic discoverd by the French logician Girard, is a logic of computational resources. Linear logic is, in fact, a weak relevant logic with the addition of two operators. plato.stanford.edu /entries/logic-relevance/index.html   (2543 words)

Oxford University Press: Substructural Logics: Kosta Dosen   (Site not responding. Last check: 2007-11-06) Substructural logics comprise a family of nonclassical logics that arose in response to problems in theoretical computer science, mathematical linguistics, and category theory. This important volume--the first to bring together the disparate strands of work in substructural logics--will be welcomed by student and professional logicians, theoretical computer scientists, theoretical linguists, philosophers, and mathematicians working in category theory and universal algebra. Covering propositional logic, first-order logic, and second-order logic, as well as proof theory, computability theory, and model theory, the text also contains numerous carefully graded exercises and is ideal for a first or refresher course. www.oup.com /us/catalog/general/subject/Linguistics/TheoreticalDescriptiveLinguistic/?view=usa&ci=0198537778   (290 words)

Logical Pluralism | Log This situation has the absurd consequence that one might concede that the conclusion of an argument was true (since the argument had true premises and was truth-preserving); yet should refuse to infer the conclusion from the premises, in the absence of demonstration of the relevance of the premises to the conclusion. His paper on the role of logic in AI is very clear, and contains an excellent discussion of the role of logic as a determiner of valdi inference, as opposed to logic as a tool for constructing or analysing derivations. Different logics are given by choosing different syntactic units (is identity one of them? is necessity?) or by choosing different fixed interpretations of the syntactic units so chosen. pluralism.pitas.com   (9922 words)

Algebra & Substructural Logics   (Site not responding. Last check: 2007-11-06)    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. By a fortunate coincidence, the interest in algebraic structures related to substructural logics is also undergoing a revival among algebraists. www.jaist.ac.jp /%7Ekowalski/workshop.html   (194 words)

Substructural logic -- Facts, Info, and Encyclopedia article   (Site not responding. Last check: 2007-11-06) They differ in having fewer structural rules available: the concept of structural rule is based on the (Click link for more info and facts about sequent) sequent presentation, rather than the (Click link for more info and facts about natural deduction) natural deduction formulation. Two of the more significant substructural logics are (Click link for more info and facts about relevant logic) relevant logic and (Click link for more info and facts about linear logic) linear logic. They occur naturally in proof theory, and were first noticed there (before receiving a name). www.absoluteastronomy.com /encyclopedia/s/su/substructural_logic.htm   (293 words)

Nak Lab. SIG-TH : Linear Logic   (Site not responding. Last check: 2007-11-06) A system of logic consists of how to write formula (this is called formation rule) and the rule what kind of formula is gained from what kind of formulas (this is called inference rule). When a inference rule is applied, linear logic controls the change of the number of atomic formulas in the sequents referring to the logical operator. Many researches regarding linear logic semantics, proof theory, complexity, and expressiveness are made in these days. www.nak.ics.keio.ac.jp /groups/th/linearlogic.html   (450 words)

Wadler: Linear Logic   (Site not responding. Last check: 2007-11-06) This paper introduces a new way of attaching proof terms to proof trees for classical linear logic, which bears a close resemblance to the way that pattern matching is used in programming languages. It equates the same proofs that are equated by proof nets, in the formulation of proof nets introduced by Dominic Hughes and Rob van Glabbeek; and goes beyond that formulation in handling exponentials and units. The presentation of linear logic is simplified by basing it on the Logic of Unity. cm.bell-labs.com /cm/cs/who/wadler/topics/linear-logic.html   (1065 words)

Substructural Logics   (Site not responding. Last check: 2007-11-06) A comprehensive bibliography on relevant logic was put together by Robert Wolff and can be found in the second volume of Entailment (Anderson, Belnap and Dunn 1992). The bibliography in An Introduction to Substructural Logics is not as comprehensive as Wolff’s, but it does include material up to the last part of the 1990s. Restall, Greg, 2000, An Introduction to Substructural Logics, Routledge. www.science.uva.nl /~seop/archives/win2000/entries/logic-substructural   (2771 words)

OUP: Substructural Logics: Dosen Substructural logics are nonclassical logics, which arose in response to problems in foundations of mathematics and logic, theoretical computer science, mathematical linguistics, and category theory. Substructural logics differ from classical logics, and from each other, in their presuppositions about Gentzen's structural rules, although their presuppositions about the deductive role of logic constants are invariant. Substructural logics have been a subject of study for logicians during the last sixty years. www.oup.co.uk /isbn/0-19-853777-8   (550 words)

Amazon.de: English Books: An Introduction to Substructural Logics   (Site not responding. Last check: 2007-11-06) An introduction to 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. This text systematically surveys the results and the important impact that this class of logics has had on wide ranging fields. www.amazon.de /exec/obidos/ASIN/041521534X/geometrynet01-21   (215 words)

Substructural Logics   (Site not responding. Last check: 2007-11-06) Belnap Theorems in Classical Logic are Instances of Theorems in Condensed BCI Logic M.W. Bunder Partial Gaggles Applied to Logics with Restricted Structural Rules J.M. Dunn A General Theory of Structured Consequence Relations D.M. Gabbay Decidability and Interpolation for a First-Order Relevance Logic A. Lambek The Semantics of Entailment 0 R.K. Meyer and E.D. Mares Semantics for Substructural Logics H. Soloviev Tutorial on Linear Logic A.S. Troelstra The Landscape of Deduction J. www.cis.upenn.edu /~bcpierce/types/archives/1994/msg00048.html   (194 words)

Introduction to Linear Logic   (Site not responding. Last check: 2007-11-06) Linear Logic was introduced by J.-Y. Girard in 1987 and it has attracted much attention from computer scientists, as it is a logical way of coping with resources and resource control. The focus of this technical report will be on proof-theory and computational interpretation of proofs, that is, we will focus on the question of how to interpret proofs as programs and reduction (cut-elimination) as evaluation. Cut-elimination for Classical Logic is highly non-deterministic; it is shown how this can be remedied either by moving to Intuitionistic Logic or to Linear Logic. www.brics.dk /LS/96/6/BRICS-LS-96-6/BRICS-LS-96-6.html   (210 words)

Linear Logic as a good logical foundation for computer science.   (Site not responding. Last check: 2007-11-06) Research in linear logic has been the thrust behind the development of a closer relationship between logic and computer science, as evid enced for example by natural characterizations of major complexity classes in terms of natural fragments of linear logic (Lincoln, Mitchell, Scedrov, Shankar, Kanovich, Lafont). Direct connections have been established between linear logic and various models of concurrency like Petri nets (Asperti, Brown, Meseguer, Gunter), games (Blass, Abramsky, Lamarche), stochastic Petri nets, Dijkstra's guarded commands (Kanovich); all this shows linear logic to be a good logical foundation for the theory of computational processes that may consume resources. Another important aspect is that linear logic provides not only basic input/output specifications (types, or formulas), but also a setting for well-typed programs (terms, or formal proofs), as well as a means of executing well-typed programs by means of term reduction or normalization (Girard, Regnier, Danos). www.univ-paris12.fr /lacl/lundi/kanovitch.html   (507 words)

UvA DARE Decidability and finite model property of substructural logics Hiroakira Ono In this paper, we will give a short survey of results on decision problems and the finite model property of substructural logics. The paper is far from a complete list of these results, since a lot of results have been obtained already in some restricted classes of substructural logics, like relevant logics, and therefore it is impossible to cover all of them. Our aim of the present paper is to try to compare results from different classes of substructural logics with each other and discuss them as a whole, in order to get a perspective of them. dare.uva.nl /record/114316   (144 words)

Substructural Logics   (Site not responding. Last check: 2007-11-06) Substructural logics are typically obtained by dropping structural rules such as weakening, contraction or interchange from the standard Gentzen calculus of classical logic. In a multiple conclusion Gentzen calculus, structural rules can be stated left of the turnstile as well as right of the turnstile. Most of the substructural logics seem to bias towards dropping structural rules to the left of the turnstile but keep right structural rules the same or keep the calculus in a single conclusion setting. www.philo.at /phlo/199903/msg00045.html   (111 words)

On Matrix Characterizations for Propositional Substructural Logics (ResearchIndex) This paper provides a unified approach for matrix characterizations for propositional substructural logics, whereby the focus is laid on a uniform representation of different validity concepts in matrices. Starting from a restricted validity concept for matrices called basic-validity, where a matrix is considered as valid if each literal is connected exactly once, we use rewrite rules to obtain a wider class of validity concepts. 20 Semantics for Substructural Logics (context) - Ono - 1993 citeseer.ist.psu.edu /389009.html   (337 words)

Linear Logic papers of Andreas R. Blass   (Site not responding. Last check: 2007-11-06) This talk is a survey of two topics of recent interest in mathematical logic, namely linear logic and cardinal characteristics of the continuum. We discuss the extent to which game semantics is implicit in the formalism of linear logic and in the intuitions underlying linear logic. A category used by de Paiva to model linear logic also occurs in Vojtas's analysis of cardinal characteristics of the continuum. www.math.lsa.umich.edu /~ablass/ll.html   (356 words)

1Up Science > Links Directory > Math: Logic and Foundations: Nonstandard Logics and Extensions: Substructural ... Article by Samson Abramsky which proposes a formulae-as-types correspondence first for intuitionsitic linear logic, and then for classical linear logic. Introductory course on linear logic by Vincent Danos and Roberto Di Cosmo. Article by V. Danos, J.-B. Joinet and H. Schellinx outlining how linear logic can function as a `mark-up logic' allowing the embedding of a large class of logics in a manner that respects their underlying proof semantics (cf. www.1upscience.com /links/substructural-logics-linear-logic.html   (303 words)

Labelled Natural Deduction for Substructural Logics - Broda, Finger, Russo (ResearchIndex)   (Site not responding. Last check: 2007-11-06) Abstract: In this paper a uniform methodology to perform Natural Deduction over the family of linear, relevance and intuitionistic logics is proposed. In the system described here, labels are either ground terms or variables of a given labelling language and inference rules manipulate formulas and labels... The idea of labelled deduction also appeared outside the context of modal logic, namely for finite many valued logics where it... citeseer.lcs.mit.edu /broda97labelled.html   (485 words)

Open Directory - Science: Math: Logic and Foundations: Nonstandard Logics and Extensions: Substructural Logics: Linear ...   (Site not responding. Last check: 2007-11-06) Computational Interpretations of Linear Logic (1993) - Article by Samson Abramsky which proposes a formulae-as-types correspondence first for intuitionsitic linear logic, and then for classical linear logic. Linear Logic as a Good Logical Foundation for Computer Science - A brief analysis of the computational aspects of linear logic by Max Kanovich. A New Deconstructive Logic: Linear Logic (1997) - Article by V. Danos, J.-B. Joinet and H. Schellinx outlining how linear logic can function as a `mark-up logic' allowing the embedding of a large class of logics in a manner that respects their underlying proof semantics (cf. dmoz.org /Science/Math/Logic_and_Foundations/Nonstandard_Logics_and_Extensions/Substructural_Logics/Linear_Logic   (388 words)

Relevance Principle for Substructural Logics with Mingle and Strong Negation -- Kamide 12 (6): 913 -- Journal of Logic ... Relevance Principle for Substructural Logics with Mingle and Strong Negation -- Kamide 12 (6): 913 -- Journal of Logic and Computation Relevance Principle for Substructural Logics with Mingle and Strong Negation hold for substructural logics with mingle and usual negation, logcom.oxfordjournals.org /cgi/content/abstract/12/6/913   (111 words)

A Pragmatic Interpretation Of Substructural Logics (ResearchIndex) 85 Linear logic: its syntax and semantics - Girard - 1995 58 A term calculus for intuitionistic linear logic - Benton, Bierman et al. Planar and Braided Proof-Nets for Multiplicative Linear Logic.. citeseer.ist.psu.edu /445146.html   (293 words)

Citations: editors: Substructural Logics - Schroeder-Heister, Dosen (ResearchIndex) Schroeder-Heister, P Dosen K., editors: Substructural Logics, Oxford Science Publications, Clarendon Press, Oxford, 1993. Since classical logic is already strongly complete, CP H is exactly classical logic. This consequence relation can very naturally be defined by using the standard Hilbert type formulations of these logics: A 1 ; A n.... citeseer.ist.psu.edu /context/197408/0   (252 words)

A Syntactic Approach to Maksimova's Principle of Variable Separation for Some Substructural Logics, H. Naruse Bayu ... In the present paper, a proof-theoretic approach to this principle in some substructural logics is given, which analyzes a given cut-free proof of the formula 381--91 in Entailment: The Logic of Relevance and Necessity, vol. [14] Ono, H., ``Semantics for substructural logics,'' pp. projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.ndjfl/1039293022   (408 words)

Information About Substructural Logics Web Sites   (Site not responding. Last check: 2007-11-06) Top: Science: Math: Logic and Foundations: Nonstandard Logics and Extensions: Substructural Logics Substructural and Paraconsistent Logics - A section of the SWIF map of logic on the WWW. Substructural Logics - Survey from the Stanford Encyclopedia of Philosophy by Greg Restall. www.worldcrawl.com /Science/Math/LogicandFoundations/NonstandardLogicsandExtensions/SubstructuralLogics   (60 words)

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