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A Matrix Characterization for Multiplicative Exponential Linear Logic

2004
*
Journal of automated reasoning
*

We develop

doi:10.1023/b:jars.0000029976.22387.ac
fatcat:iw2ki256vjf6xfocfayaxwytgi
*a**matrix**characterization*of*logical*validity in MELL, the*multiplicative*fragment of propositional*linear**logic*with*exponentials*and constants. ... Our*characterization*is based on concepts similar to*matrix**characterizations*proposed by Wallen*for*other non-classical*logics*. ... Acknowledgments We would like to thank Marcelo Correa*for*his useful feedback on the soundness and completeness proofs in Section 6. ...##
###
From linear proofs to direct logic with exponentials
[chapter]

1997
*
Lecture Notes in Computer Science
*

*For*

*a*well-chosen subclass of formulas of this

*logic*we provide

*a*

*matrix*-

*characterization*which can be used as

*a*foundation

*for*proof-search methods based on the connection calculus. ... Following the idea of

*Linear*Proofs presented in 4] we introduce the Direct

*Logic*14] with

*exponentials*(DLE). The

*logic*combines Direct

*Logic*with the

*exponentials*of

*Linear*

*Logic*. ... Then we present

*a*

*matrix*-

*characterization*

*for*

*a*subclass of DLE formulas. ...

##
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Connection-based proof construction in linear logic
[chapter]

1997
*
Lecture Notes in Computer Science
*

We present

doi:10.1007/3-540-63104-6_20
fatcat:ecyktsdfyndlvg4h6accwc544u
*a**matrix**characterization*of*logical*validity in the*multiplicative*fragment of*linear**logic*. ... They can be extended to further fragments of*linear**logic*once*a**matrix**characterization*has been found. ... Conclusion We have presented*a**matrix**characterization*of*logical*validity in the*multiplicative*fragment of*linear**logic*MLL. ...##
###
A Transfer Function Model for Ternary Switching Logic Circuits

2013
*
2013 IEEE 43rd International Symposium on Multiple-Valued Logic
*

The use of transfer matrices

doi:10.1109/ismvl.2013.10
dblp:conf/ismvl/Thornton13
fatcat:ezkcti7pkfdynpn2rb5jekvemy
*for**logic*network simulation are then developed that allow*for**multiple*output responses to be obtained through*a*single vector-*matrix*product calculation. ... Techniques*for*determination of the transfer*matrix*from*a**logic*switching model or directly from*a*netlist are provided. ...*matrix*as derived in the previous section allows*for**a*means to derive the system response*for*one or more*logic*network input vectors through*a*single vector-*matrix**multiplication*operation. ...##
###
Page 3945 of Mathematical Reviews Vol. , Issue 92g
[page]

1992
*
Mathematical Reviews
*

Although the lower bounds are

*for**a*more general model, they are as large as the known bounds*for*straight- line programs (even improving the known straight-line bounds*for**matrix**multiplication*) except ... Summary: “This paper establishes time-space tradeoffs*for*some algebraic problems in the branching program model, including con- volution of vectors, integer*multiplication*,*matrix*-vector products,*matrix*...##
###
linTAP : A Tableau Prover for Linear Logic
[chapter]

1999
*
Lecture Notes in Computer Science
*

linTAP is

doi:10.1007/3-540-48754-9_20
fatcat:tdwsc7dc4vftzawqopz3tdcepi
*a*tableau prover*for*the*multiplicative*and*exponential*fragment M?LL of Girards*linear**logic*. ... We present the tableau calculus used by linTAP, an algorithm*for*prefix unification in*linear**logic*, the linTAP implementation, and some experimental results obtained with linTAP. ...*Linear**logic*can be divided into the*multiplicative*, additive, and*exponential*fragment. ...##
###
Spectral Response of Ternary Logic Netlists

2013
*
2013 IEEE 43rd International Symposium on Multiple-Valued Logic
*

Past methods

doi:10.1109/ismvl.2013.52
dblp:conf/ismvl/ThorntonM13
fatcat:5inbxbp3cbc2zbvo7usi5qz4um
*for*computation of the spectrum of*a**multiple*-valued*logic*network usually rely on first*characterizing*the network in terms of*a*switching function, secondly in mapping the function values ... The spectral transfer function can then be used to compute either the*logic*network spectral response*for**a*specified input, or*for*computation of the entire Chrestenson spectrum. ...*For*example,*a*vector is*a*tensor of order one and is*characterized*by*a*single dimensional value while*a**matrix*is*a*tensor of order two and is*characterized*by*a*pair of dimensions whose values are the ...##
###
Page 3179 of Mathematical Reviews Vol. , Issue 2003e
[page]

2003
*
Mathematical Reviews
*

MLL of

*linear**logic*. ... The algorithms reconstruct sequent proofs in different types of sequent calculi from*matrix*proofs according to the*matrix**characterizations*of*logical*validity [L.*A*. ...##
###
Page 549 of American Mathematical Society. Bulletin of the American Mathematical Society Vol. 61, Issue 6
[page]

1955
*
American Mathematical Society. Bulletin of the American Mathematical Society
*

This paper presents

*a*general solution to an integral equation*characterizing*opti- mum time-variable*linear*filters which operate from*a*finite starting point in time. ... An analysis is made of*a*so-called “row-operation procedure”*for*the determina- tion of the inverse of*a*(nonsingular) nonsymmetric real*matrix*. ...##
###
Some results of studies on the stability and controlability properties of the switched systems of differential equations

2014
*
Applied Mathematical Sciences
*

The first deals with the study of the considered systems of differential equations with regards the pooling of the same in two clusters, namely

doi:10.12988/ams.2014.48673
fatcat:jovjkv3hzffgvly5am6jhu4rqy
*linear*switched systems dependent on*a*continuous or discrete ... Such*a*panoramic study follows*a*bidirectional path. ... and Fuzzy*Logic*. ...##
###
Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results

2009
*
IEEE Transactions on Automatic Control
*

*A*necessary and sufficient condition

*for*asymptotic stabilizability of switched

*linear*systems is described here. ... After

*a*brief review of the stability analysis under restricted switching and the

*multiple*Lyapunov function theory, the switching stabilization problem is studied, and

*a*variety of switching stabilization ... ACKNOWLEDGMENT The authors wish to thank the Associate Editor and the anonymous reviewers

*for*their insightful comments and suggestions. ...

##
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Cumulative subject index

1978
*
Information and Control
*

describing growth,
37, 280
Filing systems
combinatorial

doi:10.1016/s0019-9958(78)90707-6
fatcat:3g6qa5hi2zc2lgyyvndbar65di
*multiple*-valued,*for*multi- attribute queries, 36, 119 Filter . , bounding, simple solution to lack of exact*a*priori statistics, 39, 2t2 ... sharing pattern, 38, 21*Linear*stochastic system statistical properties, 39, 92*Logic*design,*multiple*-valued: method of Karpovsky, 39, 243 fuzzy and probability uncertainty, 38, 154 N Machines ...##
###
Computational Complexity of Deciding Provability in Linear Logic and its Fragments
[article]

2021
*
arXiv
*
pre-print

We prove an original complexity

arXiv:2110.00562v1
fatcat:a6sidawnbjh5jpf2cvrermfrcy
*characterization*of*a*fragment of the*logic*and present ideas*for**a*new, structural approach to the examination of provability in*linear**logic*. ... This interpretation makes*linear**logic**a*useful tool*for*formalisation in mathematics and computer science. ...*Multiplicative**Exponential**Linear**Logic*is TOWER-hard With the*multiplicative*-*exponential*fragment, we arrive at the most pressing complexitytheoretic question regarding*linear**logic*: it is not yet known ...##
###
Page 5218 of Mathematical Reviews Vol. , Issue 88j
[page]

1988
*
Mathematical Reviews
*

They introduce the notions of topo-

*logical*equivalence and structural stability, as well as*exponential*dichotomy and*multiplicative*separation. ... The authors consider the functional equation f(z +1) = zf(z)*for**matrix*functions. They give*a*survey of properties of the gamma function and its*characterizations*by means of functional equations. ...##
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Logical Inference Algorithms and Matrix Representations for Probabilistic Conditional Independence
[article]

2012
*
arXiv
*
pre-print

The validation algorithm represents each set of CI statements as

arXiv:1205.2621v1
fatcat:tote7hasj5hdjpxsu33ctrqrpy
*a*sparse 0-1*matrix**A*and validates instances of the implication problem by solving specific*linear*programs with constraint*matrix**A*. ... We will present an approximate*logical*inference algorithm which combines*a*falsification and*a*novel validation algorithm. ... Acknowledgments The author wants to thank Dirk Van Gucht and Marc Gyssens*for*helpful discussions, and the anonymous reviewers*for*their valuable comments and suggestions. ...
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