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Linear logical approximations

2008
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Proceedings of the 2009 ACM SIGPLAN workshop on Partial evaluation and program manipulation - PEPM '09
*

We show that, by specifying operational semantics in a bottom-up,

doi:10.1145/1480945.1480949
dblp:conf/pepm/SimmonsP09
fatcat:4fyzgv7asrguvlc77suhllkqem
*linear**logic*programming language -a technique we call substructural operational semantics (SSOS)manifestly sound program*approximations*... can be derived by simple and intuitive*approximations*of the*logic*program. ... at(p)*Linear**logical*algorithms In the example of the previous section we exploited*linear**logic*to represent state change and name generation, which then served as the basis for our*approximations*. ...##
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Approximations of Isomorphism and Logics with Linear-Algebraic Operators
[article]

2019
*
arXiv
*
pre-print

These equivalences first appeared in the study of rank

arXiv:1902.06648v2
fatcat:dmyz6u4rqnhv3olcegxtmfe4oq
*logic*, but in fact they can be used to delimit the expressive power of any extension of fixed-point*logic*with*linear*-algebraic operators. ... of fixed-point*logic*with*linear*-algebraic operators can capture PTIME, unless it includes such operators for all prime characteristics. ... The Invertible Map Equivalence and*Linear*-Algebraic*Logics*The invertible map equivalence relation was introduced by Dawar and Holm [14, 26] as a family of*approximations*of isomorphism. ...##
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Linear approximation of planar spatial databases using transitive-closure logic

2000
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Proceedings of the nineteenth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems - PODS '00
*

Furthermore, we introduce an extension of transitive-closure

doi:10.1145/335168.335215
dblp:conf/pods/GeertsK00
fatcat:yacih2vhkjbd5i3bspdfhvdi74
*logic*and show that this*logic*is complete for the computable queries on*linear*spatial databases. ... Motivated by applications in geographic information systems, we investigate*linear**approximations*of spatial databases and study in which language they can be expressed effectively. ... A formula in FO + Poly is a first-order*logic*formula ϕ(x1, . . . , xn, S1, . . . , Sm) built, using the*logical*connectives and quantifiers, from two kinds of atomic formulas: S ℓ (x, y) and p(x1, . . ...##
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Linear Approximation of Semi-algebraic Spatial Databases Using Transitive Closure Logic, in Arbitrary Dimension
[chapter]

2002
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Lecture Notes in Computer Science
*

Since both the encoding and decoding between a

doi:10.1007/3-540-46093-4_11
fatcat:q5uf5lnvgvdinhr6i4e2ob7kwu
*linear*spatial database and this finite representation are expressible in FO+TCS, we may conclude the completeness of this*logic*on*linear*spatial databases ... The completeness of this*logic*on all*linear*spatial databases, is then obtained using a finite representation of these databases given by Vandeurzen et al. [20]. ... Fig. 3 . 3 Illustration of the algorithm*Linearize*. Theorem 5 . 5 Rational*linearizations*of spatial databases are expressible in the transitive closure*logic*FO+TC. ...##
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Non-Uniform Random Number Generation Through Piecewise Linear Approximations

2006
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2006 International Conference on Field Programmable Logic and Applications
*

The architecture is based on a piecewise

doi:10.1109/fpl.2006.311219
dblp:conf/fpl/ThomasL06
fatcat:tjaa5rjglbdqxd3dmyvpk3uzee
*linear**approximation*, using just one table lookup, one comparison and one subtract operation to map from a uniform source to an arbitrary non-uniform distribution ... Customisation of the distribution is fully automatic, requiring less than a second of CPU time to*approximate*a new distribution, and around 1000 cycles to switch distributions at run-time. ... One method for calculating the best*approximation*is to use solve a system of*linear*equations, as used in a similar approach to*approximating*the Gaussian distribution [14] , but this was found to be ...##
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Approximate Controllability Results for Impulsive Linear Fuzzy Stochastic Differential Equations Under Nonlocal Conditions

2015
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International Journal of Fuzzy Logic Systems
*

In this paper, the

doi:10.5121/ijfls.2015.5403
fatcat:ewbjiewxvndohopwvalbrcpvh4
*approximate*controllability of impulsive*linear*fuzzy stochastic differential equations with nonlocal conditions in Banach space is studied. ... By using the Banach fixed point theorems, stochastic analysis, fuzzy process and fuzzy solution, some sufficient conditions are given for the*approximate*controllability of the system. ... It should be mentioned that there is no work done on the*approximate*controllability of*linear*fuzzy stochastic differential equations. ...##
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Approximations of Isomorphism and Logics with Linear-Algebraic Operators

2019

The

doi:10.18154/rwth-2019-06475
fatcat:fs5edha6xzfnrpgco3gjwnsjuq
*logic*LA ω (Q) = k∈ω LA k (Q) is then a natural upper bound on the expressive power of any extension of fixed-point*logics*by means of Q-*linear*-algebraic operators. ... These equivalences have first appeared in the study of rank*logic*, but in fact they can be used to delimit the expressive power of any extension of fixed-point*logic*with*linear*-algebraic operators. ... I C A L P 2 0 1 9 112:12*Approximations*of Isomorphism and*Logics*with*Linear*-Algebraic Operators Corollary 13 . 13 If Q = P, no extension of fixed-point*logic*with Q-*linear*algebraic operators captures ...##
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Logical approximation for program analysis

2011
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Higher-Order and Symbolic Computation
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sound program

doi:10.1007/s10990-011-9071-2
fatcat:ulpr2sclznafrpyoaxmm2mivt4
*approximations*can be derived by simple and intuitive transformations and*approximations*of the*logic*program. ... A secondary goal, which is the focus of this paper, is to leverage the*logical*basis to develop precise, yet tractable,*approximations*of the systems we specify. ...*Approximating*ordered*logic*programs as saturating*logic*programs Our*approximation*strategy is extremely simple: essentially, an*approximation*of an ordered or*linear**logical*specification is generated ...##
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Collection analysis for Horn clause programs
[article]

2007
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arXiv
*
pre-print

Central to this scheme is the use of

arXiv:0708.2230v1
fatcat:5lr5lmatufgxrfxofe42by5vwq
*linear**logic*as a omputational*logic*underlying the*logic*of Horn clauses. ... Such*approximations*can be used to provide partial correctness properties of*logic*programs. ...*Linear**logic*formulas for computing that*approximation*can be generated using the following*approximating*substitution. ...##
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Collection analysis for Horn clause programs

2006
*
Proceedings of the 8th ACM SIGPLAN symposium on Principles and practice of declarative programming - PPDP '06
*

Central to this scheme is the use of

doi:10.1145/1140335.1140357
dblp:conf/ppdp/Miller06
fatcat:ykekp4hkkraxpcaf46g5xmgr6i
*linear**logic*as a computational*logic*underlying the*logic*of Horn clauses. ... Such*approximations*can be used to provide partial correctness properties of*logic*programs. ...*Linear**logic*formulas for computing that*approximation*can be generated using the following*approximating*substitution. ...##
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Identification of Nonlinear Systems Using Nonparametric Training Method for Threshold Logic Learning Machine

閾値論理学習機械のノンパラメータ形訓練法を用いた非線形システムの同定

1975
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Transactions of the Society of Instrument and Control Engineers
*

閾値論理学習機械のノンパラメータ形訓練法を用いた非線形システムの同定

As the first step, the

doi:10.9746/sicetr1965.11.398
fatcat:oik5e4732fgdrm6whbnpuulvki
*approximate*solutions of the parameters of*linear*element are obtained by the nonparametric training procedure of the threshold*logic*learning machines, and then the*approximate*... The dynamics of the*linear*element is represented by the weighting coefficients derived from the impulse response and the characteristics of the zero-memory nonlinear element is*approximated*by the polynomial ... As the first step, the*approximate*solutions of the parameters of*linear*element are obtained by the nonparametric training procedure of the threshold*logic*learning machines, and then the*approximate*...##
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Logical approaches to imprecise probabilities

2008
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International Journal of Approximate Reasoning
*

The paper by Wilson presents a generic

doi:10.1016/j.ijar.2007.08.004
fatcat:zlenk5w55fey5juugthfvcq3rm
*logic*for reasoning with*linear*constraints that represent uncertain information. The approach is explored for several different underlying uncertainty*logics*. ... Editorial*Logical*approaches to imprecise probabilities This special issue of the International Journal of*Approximate*Reasoning (IJAR) collects several recent works in*logical*approaches to imprecise ... concentrates especially on a possibilistic*logic*representation of uncertain*linear*constraints, a lattice-valued possibilistic*logic*, an assumption-based reasoning formalism, and a Dempster-Shafer representation ...##
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A Little Logic Goes a Long Way
[chapter]

2008
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Human Reasoning and Cognitive Science
*

*logical*framework for partial matchmaking and Log-

*Linear*Description

*Logics*as a new combination of Description

*Logics*with (log-

*linear*) probabilistic models. ... We show that purely

*logical*matchmaking achieves results comparable with state of the art matchmaking systems that rely on similarity functions and present results that show that log-

*linear*description ...

*logical*framework for partial matchmaking and Log-

*Linear*Description

*Logics*as a new combination of Description

*Logics*with (log-

*linear*) probabilistic models. ...

##
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Page 5967 of Mathematical Reviews Vol. , Issue 2004h
[page]

2004
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Mathematical Reviews
*

Light

*linear**logic*, introduced by J.-Y. ...*Logic*120 (2003), no. 1-3, 65-102. Summary: “We introduce the new notion of additive ‘multibox’ for*linear**logic*proof-nets. ...##
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Information about the Society

1965
*
IEEE Transactions on Electronic Computers
*

*logic*Analog computer Random process Memory

*Linear*lumped parameter delay

*approximation*Rational spectrum noise Accession No. ... In addition to a bit-comparison

*logic*, other

*logical*operations (such as the correlation of rational spectrum noise (generated by passing white noise through a

*linear*NAND, NOR, AND, OR) can be implemented ...

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