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Planar and braided proof-nets for multiplicative linear logic with mix

1998
*
Archive for Mathematical Logic
*

We give

doi:10.1007/s001530050101
fatcat:d4jup33q2bac5ayzm5ud2wqemy
*two*characterization of such*proof*-nets, one representing*proof*-nets as CW-complexes in a*two*-*dimensional*disc,*the*other extending a characterization by Asperti. ... We consider a class of graphs embedded in R 2 as noncommutative*proof*-nets with an explicit*exchange**rule*. ... ., such that its removal yields*two*disconnected*proof*-*structures*. Then*the*induction hypothesis followed by a times*rule*concludes*the*case. ...##
###
The three dimensions of proofs

2006
*
Annals of Pure and Applied Logic
*

We give a 3-

doi:10.1016/j.apal.2005.12.012
fatcat:57h2no342zbrnpnpp5d6hxpvpm
*dimensional*generalization of Penrose diagrams*and*use it to provide several pictures of a*proof*. ... We prove that*the*free 3-category generated by this 3-polygraph describes*the**proofs*of classical propositional logic modulo*structural*bureaucracy. ... Hence,*the*SKS*proofs*are*the*rewriting paths generated by*the*inference*rules*, together with*the**structural**rules**and*their converse. ...##
###
An introduction to strategy-proof social choice functions

2001
*
Social Choice and Welfare
*

*The*associated social choice

*rule*is clearly strategy-

*proof*. In what follows, we'll describe other strategy-

*proof*

*rules*for

*exchange*economies. ...

*The*following

*and*last example describes a strategy-

*proof*

*rule*where di¨erent agents play di¨erent roles. Example 4. There are

*two*agents. Fix

*two*alternatives w 1

*and*w 2 , w 1 a w 2 . ...

##
###
Varieties of Cubical Sets
[article]

2017
*
arXiv
*
pre-print

We prove that all our sites are test categories in

arXiv:1701.08189v2
fatcat:eln74dav6fanvdkj4t6fcbhhby
*the*sense of Grothendieck, meaning that*the*corresponding presheaf categories of cubical sets model classical homotopy theory. ... Any opinions, findings*and*conclusions or recommendations expressed in this material are those of*the*authors*and*do not necessarily reflect*the*views of*the*AFOSR. ...*The*authors gratefully acknowledge*the*support of*the*Air Force Office of Scientific Research through MURI grant FA9550-15-1-0053. ...##
###
Ribbon Tensorial Logic

2018
*
Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science - LICS '18
*

Our main result is that

doi:10.1145/3209108.3209129
dblp:conf/lics/Mellies18
fatcat:j6idr7fbgnb6xber5xxzfrn7wi
*the*translation is also faithful:*two**proofs*are equal modulo*the*equational theory of ribbon tensorial logic if*and*only if*the*associated ribbon tangles are equal up to topological ...*The*translation is functorial: it is performed by exhibiting a correspondence between*the*notion of dialogue category in*proof*theory*and**the*notion of ribbon category in knot theory. ... д ∈ G n associated for each conversion*rule*π 1 ↭ π 2*and*for each*exchange**rule*appearing in*the*derivation trees π 1*and*of π 2 . ...##
###
Two polygraphic presentations of Petri nets

2006
*
Theoretical Computer Science
*

*The*first one sees places as generators of a commutative monoid

*and*transitions as rewriting

*rules*on it: this setting is totally equivalent to Petri nets, but lacks any graphical intuition. ... This document gives an algebraic

*and*

*two*polygraphic translations of Petri nets, all three providing an easier way to describe reductions

*and*to identify some of them. ... Acknowledgements I wish to thank Albert Burroni

*and*Yves Lafont for many discussions

*and*advices

*and*

*the*referees for their comments that have helped to improve this document. ...

##
###
Structural analysis of fuzzy controllers with nonlinear input fuzzy sets in relation to nonlinear PID control with variable gains

2004
*
Automatica
*

In

doi:10.1016/j.automatica.2004.03.019
fatcat:z5ux4dzs2fhrrcldr3rqluksly
*the*present paper, we study*the*analytical*structure*of an important class of*two*-*and*three-*dimensional*fuzzy controllers. ... Our*structural*results are thus more general*and*contain*the*existing ones as special cases.*Two*concrete examples are provided to illustrate*the*usefulness of*the*new results. ? ... Fuzzy*rules*for*the**two*-*dimensional*controllers are IF E(n) is P*AND*R(n) is P THEN u(n) (or u(n)) is P (*Rule*1) IF E(n) is P*AND*R(n) is N THEN u(n) (or u(n)) is Z (*Rule*2) IF E(n) is N*AND*R(n) is P ...##
###
Structural analysis of fuzzy controllers with nonlinear input fuzzy sets in relation to nonlinear PID control with variable gains*1

2004
*
Automatica
*

In

doi:10.1016/s0005-1098(04)00116-5
fatcat:4fynntb4s5d2xgfwlfzugadori
*the*present paper, we study*the*analytical*structure*of an important class of*two*-*and*three-*dimensional*fuzzy controllers. ... Our*structural*results are thus more general*and*contain*the*existing ones as special cases.*Two*concrete examples are provided to illustrate*the*usefulness of*the*new results. ? ... Fuzzy*rules*for*the**two*-*dimensional*controllers are IF E(n) is P*AND*R(n) is P THEN u(n) (or u(n)) is P (*Rule*1) IF E(n) is P*AND*R(n) is N THEN u(n) (or u(n)) is Z (*Rule*2) IF E(n) is N*AND*R(n) is P ...##
###
Page 5249 of Mathematical Reviews Vol. , Issue 2000g
[page]

2000
*
Mathematical Reviews
*

Anallocation

*rule*y is strategy*proof*if no player can take profit from misrepresenting his preferences. ...*the*common behavior of*the**two*identical players. ...##
###
Page 491 of Mathematical Reviews Vol. , Issue 2003A
[page]

2003
*
Mathematical Reviews
*

*and*allow one to construct

*two*-

*dimensional*symmetric vectors. In particular, given a standard basis eo, e; in R? ... Summary: “Inspired by

*the*‘

*two*envelopes

*exchange*paradox’, a finitely additive probability measure m on

*the*natural numbers is introduced. ...

##
###
Independent magnon states on magnetic polytopes

2001
*
European Physical Journal B : Condensed Matter Physics
*

However, we find that for certain coupling topologies, including recently synthesised icosidodecahedral

doi:10.1007/s10051-001-8701-6
fatcat:d25bvp4icbarxbfwtqmz7elpfi
*structures*this*rule*is violated for high total spins. ... spin quantum number S, a property which is also known as Lande interval*rule*. ... Richter*and*J. Schulenburg thank*the*Deutsche Forschungsgemeinschaft for support (project Ri 615/10-1). ...##
###
Local linear logic for locality consciousness in multiset transformation
[chapter]

1995
*
Lecture Notes in Computer Science
*

*The*semantics improves on

*the*existing

*structured*operational semantics (SOS) of

*the*language by highlighting Gamma's inefficiencies, which were hidden by

*the*SOS. ... We show how

*the*new semantics also gives us a better understanding of parallel Gamma

*and*its implementation,

*and*offers insight into

*the*nature of chemicalreaction based computational models in general ... We would also like to thank

*the*anonymous PLILP referees for their helpful suggestions. ...

##
###
One-dimensional Substitution Tilings with an Interval Projection Structure
[article]

2006
*
arXiv
*
pre-print

We also provide a complete description of all tilings of

arXiv:math/0601187v1
fatcat:imldvxftevgvdc7vfpuvrhhtbq
*the*line*and*half line with an interval projection*structure*that are fixed by a substitution*rule*. ... We obtain a geometric characterisation of all interval projection tilings that admit substitution*rules**and*describe*the*set of substitution*rules*for each such a tiling. ... Acknowledgements EOH*and*JSWL gratefully acknowledge*the*support of*the*UK Engineering*and*Physical Sciences Research Council (EPSRC). ...##
###
Coherence for Frobenius pseudomonoids and the geometry of linear proofs
[article]

2018
*
arXiv
*
pre-print

We argue that traditional

arXiv:1601.05372v4
fatcat:uknph4zxhvcs5d3alw3i3q6jzm
*proof*nets are*the*2d projections of these 3d diagrams. ... As a consequence we obtain a 3d notation for*proofs*in nonsymmetric multiplicative linear logic, with a geometrical notion of equivalence,*and*without*the*need for a global correctness criterion or thinning ... of surface*proofs*for multiplicative linear logic with units,*and*without*the**exchange**rule*. ...##
###
DeepVentilation: Learning to Predict Physical Effort from Breathing

2020
*
Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence
*

DeepVentilation has been trained on input signals of expansion

doi:10.24963/ijcai.2020/730
dblp:conf/ijcai/Todo20
fatcat:w43fsp4qhreozhfgxvrycsha34
*and*contraction of*the*rib-cage obtained using a non-invasive respiratory inductance plethysmography sensor to predict minute ventilation ...*The*system is used to track physical effort closely matching our perception of actual exercise intensity.*The*source code for*the*demo is available here: https://github.com/simula-vias/DeepVentilation ... Acknowledgments This work was partially supported by JSPS Kakenhi Grant Numbers JP17H04695*and*JP20H00587.*The*author thanks all*the*co-authors, collaborators,*and*discussants. ...
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