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Chu spaces as a semantic bridge between linear logic and mathematics

Vaughan Pratt
2003 Theoretical Computer Science  
These create 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.  ... 
doi:10.1016/s0304-3975(01)00169-4 fatcat:yakjakvagbga7elzfwx7bxmfam

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  ... 

Author index

2003 Theoretical Computer Science  
., 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.  ... 
doi:10.1016/s0304-3975(03)00024-0 fatcat:azmdpkkrxvcwplluu5qfnsxktm

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

Rance Cleaveland, Scott A. Smolka
1996 ACM Computing Surveys  
ACKNOWLEDGMENTS This report has benefited from helpful comments from Chris Hankin, Michael Loui, Jack Stankovic, 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  ... 
doi:10.1145/242223.242252 fatcat:4gu2wurduveqdhqqrhr27yaqjq

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]

Henk Doornbos, Roland Backhouse
1995 Lecture Notes in Computer Science  
different theories occur frequently in 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.  ... 
doi:10.1007/3-540-60117-1_14 fatcat:namzjvik6vapne363qzzvaqdlu

A categorical semantics for polarized MALL

Masahiro Hamano, Philip Scott
2007 Annals of Pure and Applied Logic  
Barr in the late 1970's in abstract duality theory 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.  ... 
doi:10.1016/j.apal.2006.09.001 fatcat:24zznvflczfu3eygvwieimxn2i

Editors' Introduction: The Third Life of Quantum Logic: Quantum Logic Inspired by Quantum Computing

J. Michael Dunn, Lawrence S. Moss, Zhenghan Wang
2013 Journal of Philosophical Logic  
We discuss our own work connecting quantum 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  ... 
doi:10.1007/s10992-013-9273-7 fatcat:manoyqxk6rh2tnt23q543txmlm

Integral biomathics: A post-Newtonian view into the logos of bios

Plamen L. Simeonov
2010 Progress in Biophysics and Molecular Biology  
This work is an attempt for 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) .  ... 
doi:10.1016/j.pbiomolbio.2010.01.005 pmid:20146929 fatcat:ukagr4ftyjaqvknyjorvewxavm

Hammering towards QED

Jasmin C. Blanchette, Cezary Kaliszyk, Lawrence C. Paulson, Josef Urban
2014 Journal of Formalized Reasoning  
They give the authors of formal proofs 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.  ... 
doi:10.6092/issn.1972-5787/4593 dblp:journals/jfrea/BlanchetteKPU16 fatcat:zw4fz3wjrbfm3acuk4f576mzxm

Introduction to linear bicategories

J. R. B. COCKETT, J. KOSLOWSKI, R. A. G. SEELY
2000 Mathematical Structures in Computer Science  
These compositions provide 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 .  ... 
doi:10.1017/s0960129520003047 fatcat:5yavjnjpkrgq7m45gdnydnugmm

Can Practitioners Neglect Theory and Theoreticians Neglect Practice?

Manfred Broy
2011 Computer  
Acknowledgments I thank Benedikt Hauptmann 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.  ... 
doi:10.1109/mc.2011.305 fatcat:q5ssxn747nadnfqjosamnkdsty

Semantic Measures for the Comparison of Units of Language, Concepts or Instances from Text and Knowledge Base Analysis [article]

Sébastien Harispe, Sylvie Ranwez, Stefan Janaqi, Jacky Montmain
2016 arXiv   pre-print
(e.g., Cognitive Sciences, Linguistics, 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.  ... 
arXiv:1310.1285v3 fatcat:z2eipgghvvd7fawumejfnz4poa

Assertions, Hypotheses, Conjectures, Expectations: Rough-Sets Semantics and Proof Theory [chapter]

Gianluigi Bellin
2014 Trends in Logic  
This conceptual clarification not only gives 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.  ... 
doi:10.1007/978-94-007-7548-0_10 fatcat:z5fsme3hlbdrtjgn6i2rcyxdam
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