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A Matrix Characterization for Multiplicative Exponential Linear Logic

Christoph Kreitz, Heiko Mantel
2004 Journal of automated reasoning  
We develop 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.  ... 
doi:10.1023/ fatcat:iw2ki256vjf6xfocfayaxwytgi

From linear proofs to direct logic with exponentials [chapter]

Enno Sandner
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.  ... 
doi:10.1007/3540634932_10 fatcat:fi62ng247fgghmcygtnfa6tgly

Connection-based proof construction in linear logic [chapter]

C. Kreitz, H. Mantel, J. Otten, S. Schmitt
1997 Lecture Notes in Computer Science  
We present 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.  ... 
doi:10.1007/3-540-63104-6_20 fatcat:ecyktsdfyndlvg4h6accwc544u

A Transfer Function Model for Ternary Switching Logic Circuits

M. A. Thornton
2013 2013 IEEE 43rd International Symposium on Multiple-Valued Logic  
The use of transfer matrices 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.  ... 
doi:10.1109/ismvl.2013.10 dblp:conf/ismvl/Thornton13 fatcat:ezkcti7pkfdynpn2rb5jekvemy

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]

Heiko Mantel, Jens Otten
1999 Lecture Notes in Computer Science  
linTAP is 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.  ... 
doi:10.1007/3-540-48754-9_20 fatcat:tdwsc7dc4vftzawqopz3tdcepi

Spectral Response of Ternary Logic Netlists

M. A. Thornton, T. W. Manikas
2013 2013 IEEE 43rd International Symposium on Multiple-Valued Logic  
Past methods 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  ... 
doi:10.1109/ismvl.2013.52 dblp:conf/ismvl/ThorntonM13 fatcat:5inbxbp3cbc2zbvo7usi5qz4um

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

Efren Vazquez Silva, Rosa Isabel Urquiza Salgado, Mark Leonard Gordon, Acacio da Conceicao de Jesus Domingos
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 linear switched systems dependent on a continuous or discrete  ...  Such a panoramic study follows a bidirectional path.  ...  and Fuzzy Logic.  ... 
doi:10.12988/ams.2014.48673 fatcat:jovjkv3hzffgvly5am6jhu4rqy

Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results

Hai Lin, Panos J. Antsaklis
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.  ... 
doi:10.1109/tac.2008.2012009 fatcat:k5aa5khwszbb7in5jax35lv6ry

Cumulative subject index

1978 Information and Control  
describing growth, 37, 280 Filing systems combinatorial 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  ... 
doi:10.1016/s0019-9958(78)90707-6 fatcat:3g6qa5hi2zc2lgyyvndbar65di

Computational Complexity of Deciding Provability in Linear Logic and its Fragments [article]

Florian Chudigiewitsch
2021 arXiv   pre-print
We prove an original complexity 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  ... 
arXiv:2110.00562v1 fatcat:a6sidawnbjh5jpf2cvrermfrcy

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.  ... 

Logical Inference Algorithms and Matrix Representations for Probabilistic Conditional Independence [article]

Mathias Niepert
2012 arXiv   pre-print
The validation algorithm represents each set of CI statements as 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.  ... 
arXiv:1205.2621v1 fatcat:tote7hasj5hdjpxsu33ctrqrpy
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