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Chu spaces as a semantic bridge between linear logic and mathematics

2003
*
Theoretical Computer Science
*

These create

doi:10.1016/s0304-3975(01)00169-4
fatcat:yakjakvagbga7elzfwx7bxmfam
*a**bridge**between**linear**logic**and**mathematics*by soundly*and*fully completely interpreting*linear**logic*while fully*and*concretely embedding*a*comprehensive range of concrete categories of ... We propose*a*sibling role for it*as**a**logic*of transformational*mathematics*via the self-dual category of*Chu**spaces*,*a*generalization of topological*spaces*. ... The interpretation of states of*a**Chu**space**as*evidence against*a*proposition was suggested to us by Gordon Plotkin. ...##
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Page 752 of Mathematical Reviews Vol. , Issue 2004b
[page]

2004
*
Mathematical Reviews
*

.”
2004b:03038 03B47 18B30 54B30
Pratt, Vaughan (1-STF-C; Stanford, CA)

*Chu**spaces**as**a**semantic**bridge**between**linear**logic**and**mathematics*. ... Girard’s)*linear**logic*. In the present paper the author emphasizes*a*role For the web version of*Mathematical*Reviews, see http: //www.ams.org/mathscinet ...##
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Author index

2003
*
Theoretical Computer Science
*

.,

doi:10.1016/s0304-3975(03)00024-0
fatcat:azmdpkkrxvcwplluu5qfnsxktm
*Chu**spaces**as**a**semantic**bridge**between**linear**logic**and**mathematics*(3) 439-471 Retor! ... Schalk, Glueing*and*orthogonality for models of*linear**logic*(1-2) 183-231 Joinet, J.-B., see V. Danos (3) 353-378 Kanovich, M.I., M. Okada*and**A*. ...##
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Page 7605 of Mathematical Reviews Vol. , Issue 2004j
[page]

2004
*
Mathematical Reviews
*

Summary: “The essential interaction

*between*classical*and*intu- itionistic features in the system of*linear**logic*is best described in the language of category theory. ... Disjunctive multisets are modeled*as*finite sets of multisets. The Li- Horn fragment of*linear**logic*, with the cut rule slightly restricted, is sound with respect to this*semantics*. ...##
###
Strategic directions in concurrency research

1996
*
ACM Computing Surveys
*

ACKNOWLEDGMENTS This report has benefited from helpful comments from Chris Hankin, Michael Loui, Jack Stankovic,

doi:10.1145/242223.242252
fatcat:4gu2wurduveqdhqqrhr27yaqjq
*and*Peter Wegner. ...*Chu**spaces*are of independent*mathematical*interest, forming*a*bicomplete self-dual closed category first studied by Barr*and**Chu*[Barr 1979 ] that has found applications elsewhere in proof theory, game ...*A**Chu**space*[Gupta*and*Pratt 1993 ] is an event-state-symmetric generalization of the notion of event structure consisting of*a*set of events,*a*set of states,*and**a*binary relation of occurrence*between*...##
###
Page 1037 of Mathematical Reviews Vol. , Issue 93b
[page]

1993
*
Mathematical Reviews
*

(ii) The difference

*between*the number of vertices in*A**and*the number of vertices in*A*is 0 if |V| is even,*and*is 1 if |V| is odd. ... linguistics 93b:68072 93b:68070 68R10 68Q20 Hsu, Su*Chu*(RC-NTHU-CS); Hsieh, Hsien Fen (RC-NTHU-CS); Huang, Shing Tsaan (RC-NTHU-CS)*A*fully-pipelined systolic algorithm for finding*bridges*on an undirected ...##
###
Induction and recursion on datatypes
[chapter]

1995
*
Lecture Notes in Computer Science
*

different theories occur frequently in

doi:10.1007/3-540-60117-1_14
fatcat:namzjvik6vapne363qzzvaqdlu
*mathematics**and**logic*-*between*syntax*and**semantics*of*a**logic*,*between*structures*and*power structures,*between*relations*and*relational algebras, to name just ... We organize the class of all binary relations*between*any pair of sets into*a*category whose morphisms transform rows covariantly*and*columns contravariantly, called the category*Chu*(2) of*Chu**spaces*over ... The use of this algebra is illustrated by derivations of*a*shortest path,*a*hamiltonian circuits,*and**a*sorting algorithm. All derivations are formal, understandable*and*concise. ...##
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A categorical semantics for polarized MALL

2007
*
Annals of Pure and Applied Logic
*

Barr in the late 1970's in abstract duality theory

doi:10.1016/j.apal.2006.09.001
fatcat:24zznvflczfu3eygvwieimxn2i
*and*more recently in work on game*semantics*for*linear**logic*. ... In this paper, we present*a*categorical model for Multiplicative Additive Polarized*Linear**Logic*MALLP, which is the*linear*fragment (without structural rules) of Olivier Laurent's Polarized*Linear**Logic*... Finally*a*special thanks to Olivier Laurent whose work on MALLP was the impetus for our work,*and*who has spent considerable time in discussions with us. P. ...##
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Editors' Introduction: The Third Life of Quantum Logic: Quantum Logic Inspired by Quantum Computing

2013
*
Journal of Philosophical Logic
*

We discuss our own work connecting quantum

doi:10.1007/s10992-013-9273-7
fatcat:manoyqxk6rh2tnt23q543txmlm
*logic*to quantum computation (viewing quantum*logic**as*the*logic*of quantum registers storing qubits), make some speculations about*mathematics*based on quantum ... The second life has to do with attempt to understand quantum*logic**as**logic*that began in the late 1950's*and*blossomed in the 1970's. ... In*a*broad sense Samson Abramsky's "Coalgebras,*Chu**spaces*,*and*representations of physical systems" is on the same general topic*as*Gudder's*and*Harding's papers:*mathematical*representations of quantum ...##
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Integral biomathics: A post-Newtonian view into the logos of bios

2010
*
Progress in Biophysics and Molecular Biology
*

This work is an attempt for

doi:10.1016/j.pbiomolbio.2010.01.005
pmid:20146929
fatcat:ukagr4ftyjaqvknyjorvewxavm
*a*state-of-the-art survey of natural*and*life sciences with the goal to define the scope*and*address the central questions of an original research program. ... It is focused on the phenomena of emergence, adaptive dynamics*and*evolution of self-assembling, self-organizing, self-maintaining*and*self-replicating biosynthetic systems viewed from*a*newly-arranged ... complex,*semantically*enfolded relationships within*and**between*the formalisms*as*"musico-*logical*offerings" (Hofstadter, 1999) . ...##
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Hammering towards QED

2014
*
Journal of Formalized Reasoning
*

They give the authors of formal proofs

doi:10.6092/issn.1972-5787/4593
dblp:journals/jfrea/BlanchetteKPU16
fatcat:zw4fz3wjrbfm3acuk4f576mzxm
*a*strong "one-stroke" tool for discharging difficult lemmas without the need for careful*and*detailed manual programming of proof search. ... The main ingredients underlying this approach are efficient automatic theorem provers that can cope with hundreds of axioms, suitable translations of richer*logics*to their formalisms, heuristic*and*learning ... · 37*and*Hardening the Hammer (grants Ni 491/14-1). Kaliszyk is supported by the Austrian Science Fund grant (FWF):P26201. ...##
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Introduction to linear bicategories

2000
*
Mathematical Structures in Computer Science
*

These compositions provide

doi:10.1017/s0960129520003047
fatcat:5yavjnjpkrgq7m45gdnydnugmm
*a**semantic*model for the tensor*and*par of*linear**logic*: in particular,*as*composition is fundamentally noncommutative, they provide*a*suggestive source of models for noncommutative ... In*a**linear*bicategory, the*logical*notion of complementation becomes*a*natural*linear*notion of adjunction. ... So for example, in the * -autonomous context*A*B ⊥ will act*as**a*"co-function*space*" for ,*as*(in the dual way)*A*⊥ B is*a*"function*space*" for . ...##
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Can Practitioners Neglect Theory and Theoreticians Neglect Practice?

2011
*
Computer
*

Acknowledgments I thank Benedikt Hauptmann

doi:10.1109/mc.2011.305
fatcat:q5ssxn747nadnfqjosamnkdsty
*and*Holger Pfeifer for reading*and*commenting on drafts of this article. ... There is*a*close relationship*between*computing*and**mathematical**logic*,*and*many software engineering issues are closely related to*logic*. ...*Chu**spaces*proved to be useless in practice, in the end contributing nothing to resolving engineering challenges. ...##
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Semantic Measures for the Comparison of Units of Language, Concepts or Instances from Text and Knowledge Base Analysis
[article]

2016
*
arXiv
*
pre-print

(e.g., Cognitive Sciences, Linguistics,

arXiv:1310.1285v3
fatcat:z2eipgghvvd7fawumejfnz4poa
*and*Artificial Intelligence to mention*a*few). ...*Semantic*measures are widely used today to estimate the strength of the*semantic*relationship*between*elements of various types: units of language (e.g., words, sentences, documents), concepts or even ... This reflects the difficulty to limit the*semantic*similarity,*as*detected by humans, inside formal (*and*partial)*logical**mathematical*models. ...##
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Assertions, Hypotheses, Conjectures, Expectations: Rough-Sets Semantics and Proof Theory
[chapter]

2014
*
Trends in Logic
*

This conceptual clarification not only gives

doi:10.1007/978-94-007-7548-0_10
fatcat:z5fsme3hlbdrtjgn6i2rcyxdam
*a*more convincing characterization of the*logic*in [5]*as**a*treatment of assertions*and*hypotheses, but also opens the way to distinct representations of conjectures ... both in the epistemic S4*semantics**and*rough sets interpretation. ... back at least to D.Nelson [38]*and*comes up in various contexts related to game*semantics**and*in particular the construction of*Chu**spaces*. ...
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