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Independence-friendly cylindric set algebras

A. L. Mann
2009 Logic Journal of the IGPL  
We define independence-friendly cylindric set algebras and prove two main results. First, every independence-friendly cylindric set algebra over a structure has an underlying Kleene algebra.  ...  Second, every one-dimensional independence-friendly cylindric set algebra over a structure has an underlying monadic Kleene algebra.  ...  An independence-friendly cylindric set algebra (or IFG-algebra, for short) is any subalgebra of an independence-friendly cylindric power set algebra.  ... 
doi:10.1093/jigpal/jzp029 fatcat:plijbqwbfbbslll4zh54i46754

Cylindric Set Algebras and IF Logic [chapter]

Allen L. Mann
2013 Bolyai Society Mathematical Studies  
friendly cylindric set algebra, see IF algebra independence-friendly logic, see IF logic Kalman, J.  ...  A DF α cylindric set algebra (or DF α algebra) is a DF cylindric set algebra of dimension α. Independence-friendly cylindric set algebras (IF algebras) were defined in [20, Definition 2.1].  ...  , 11 K three-element Kleene algebra, 11 M centered four-element De Morgan algebra, 11 ϕ ∧ J ψ DF conjuction, 3 ϕ ∨ J ψ DF disjunction, 3 a ≈ J b a and b are indistinguishable on J, 4 a(n : b) assignment  ... 
doi:10.1007/978-3-642-35025-2_17 fatcat:ad4qepyhtbfvfk5sty3wdekra4

In Memoriam: Leon Albert Henkin 1921–2006

J. Donald Monk
2009 Bulletin of Symbolic Logic  
Concrete cylindric algebras, corresponding to fields of sets for Boolean algebras, are algebras of sets of sequences, corresponding to satisfaction sets for formulas.  ...  Hintikka's independence friendly logic can be considered as an elaboration of this idea. A problem which Henkin formulated in JSL, vol. 17, has led to an important field of research in logic.  ... 
doi:10.2178/bsl/1246453978 fatcat:qfwwyh3tb5dfdmhzdglsaq73au

Page 750 of Mathematical Reviews Vol. , Issue 99b [page]

1991 Mathematical Reviews  
The authors of this article advocate a system called “independence friendly (IF) first-order logic”, in which one can express independence among the quantifiers and connectives.  ...  Collins and Hoon Hong, Partial cylindrical algebraic decomposition for quantifier elimination (174-200); Hoon Hong, Simple solution formula construction in cylindrical algebraic de- composition based quantifier  ... 

Perfect IFG-Formulas

Allen L. Mann
2008 Logica Universalis  
We use the answer to show that the ordinary cylindric set algebra over a structure can be embedded into a reduct of the IFG-cylindric set algebra over the structure.  ...  IFG logic is a variant of the independence-friendly logic of Hintikka and Sandu. We answer the question: "Which IFG-formulas are equivalent to ordinary first-order formulas?"  ...  An IFG-cylindric set algebra (or IFG-algebra, for short) is any subalgebra of an IFG-cylindric power set algebra.  ... 
doi:10.1007/s11787-008-0037-z fatcat:b45jdilicnbeblsjzeryncnkaq

"Iff" is not expressible in independence-friendly logic [article]

Allen L. Mann
2008 arXiv   pre-print
We prove that independence-friendly logic does not have this property.  ...  An IFG-cylindric set algebra (or IFG-algebra, for short) is any subalgebra of an IFG-cylindric power set algebra.  ...  IFG-cylindric set algebras. We introduced IFG-cylindric set algebras in [11, 12] as a way to study the algebra of IFG logic.  ... 
arXiv:0806.4785v1 fatcat:cb4fxoakczgj7nflwiqamtwzyi

Cylindric Versions of Specialised Macdonald Functions and a Deformed Verlinde Algebra

Christian Korff
2012 Communications in Mathematical Physics  
We define cylindric generalisations of skew Macdonald functions when one of their parameters is set to zero.  ...  The resulting cylindric Macdonald functions appear in the coproduct of a commutative Frobenius algebra, which is a particular quotient of the spherical Hecke algebra.  ...  In particular the g r 's are all algebraically independent and, thus, theg r also form an algebraically independent set (note that g n+r and g r have different degree).  ... 
doi:10.1007/s00220-012-1630-9 fatcat:v7otgoq26rdohfuibkl2norqqa

Loop quantum geometry: a primer

Alejandro Corichi
2005 Journal of Physics, Conference Series  
The purpose of the written contribution is to provide a Primer version, that is, a first entry into Loop Quantum Gravity and to present at the same time a friendly guide to the existing pedagogical literature  ...  The other characterization is more algebraic. It is based on the observation that the (Abelian) algebra of cylindrical functions Cyl can be extended to a C * -algebra Cyl with unit.  ...  This has to be so if we want to have a fully background independent classical algebra for the quantization. A remark is in order.  ... 
doi:10.1088/1742-6596/24/1/001 fatcat:u5frufwfkrcpbl7b5bekv7m7y4

On the superselection theory of the Weyl algebra for diffeomorphism invariant quantum gauge theories [article]

Hanno Sahlmann, Thomas Thiemann
2003 arXiv   pre-print
As an important tool which is also interesting in its own right, we introduce a C*-algebra which is very similar to the Weyl algebra used in the canonical quantization of free quantum field theories.  ...  Most notably, a diffeomorphism invariant representation of the algebra of basic observables of the theory, the Ashtekar-Lewandowski representation, has been constructed.  ...  Acknowledgments We thank the Erwin -Schrödinger Institute for providing a friendly hospitality and a challenging research environment during the 'Quantum field theory on curved spacetimes' workshop, where  ... 
arXiv:gr-qc/0302090v2 fatcat:xu66dscnibbx3glkj6cnkpdj24

Cylindric plane partitions, Lambda determinants, Commutants in semicircular systems [article]

Robin Langer
2021 arXiv   pre-print
Semicircular systems were first introduced by Voiculescu as a part of his study of von Neumann algebras.  ...  Cylindric plane partitions may be thought of as a natural generalization of reverse plane partitions.  ...  The Borel σ-algebra of R is the smallest σ algebra on R which is generated by the open sets of R.  ... 
arXiv:2110.12629v1 fatcat:2kxjc7bysrhtlh3c7t7rq5r6lm

Computer facilitated generalized coordinate transformations of partial differential equations with engineering applications

A. Elkamel, F.H. Bellamine, V.R. Subramanian
2011 Computer Applications in Engineering Education  
In our opinion, the use of Maple or similar computer algebraic systems (e.g.  ...  We illustrate this by considering a number of engineering problems governed by PDEs in different coordinate systems such as the bipolar, elliptic cylindrical, and prolate spheroidal.  ...  ð10Þ This form of writing the relationship between the ''old'' set of coordinates, that is, x, y and the ''new'' set of coordinates u, v provides us a further insight since we can notice that Equations  ... 
doi:10.1002/cae.20318 fatcat:irlqnkmyabaxtm5qi2e2wwepbi

Exhaustive Synthesis and Realization of Extended-Box Topologies With Dispersive Couplings

Yan Zhang, Fabien Seyfert, Ke-Li Wu
2021 2021 IEEE MTT-S International Microwave Filter Workshop (IMFW)  
Following [8] and preceding section, the algebraic set of equation characterising all congruent transformations passing from former circuital realisation to our target topology is the following:    ...  The input and output couplings B S,k and B k,L are supposed to be frequency-independent.  ... 
doi:10.1109/imfw49589.2021.9642326 fatcat:6ydocwbst5cenirtvccssfafwi

Distributed UAV-enabled zero-forcing cooperative jamming scheme for safeguarding future wireless networks [article]

X. A. Flores Cabezas, D. P. Moya Osorio, M. Latva-aho
2021 arXiv   pre-print
The position of A is set at coordinates (0, 0) and B is located at coordinates (d AB , 0), so the cylindrical coordinates of both jammers become (R J , θ J1 , z J1 ) and (R J , θ J2 , z J2 ), respectively  ...  Analysing the region where ∆ > 1, for which jamming improves secrecy, basic algebraic derivation leads to the condition g INT > 0, which is always true.  ... 
arXiv:2109.13929v1 fatcat:57otzjfshve67kv3urgelxapqu

A Spatial Search Framework for Executing Perceptions and Actions in Diagrammatic Reasoning [chapter]

Bonny Banerjee, B. Chandrasekaran
2010 Lecture Notes in Computer Science  
We prove the correctness of our approach and show that it is more efficient than cylindrical algebraic decomposition, a well-known algebraic approach, by executing perceptions/actions in two army applications  ...  We observe that the domain/task-specific perceptions/actions can be transformed into domain/task-independent spatial problems.  ...  The enhanced algorithm is shown to be more efficient than cylindrical algebraic decomposition (CAD), a well-known algebraic approach, in executing perceptions/actions for two army applications.  ... 
doi:10.1007/978-3-642-14600-8_15 fatcat:evmdw7lbuzeljmfm7eft5e3wym

High-Speed GPU-Based Fully Three-Dimensional Diffuse Optical Tomographic System

Manob Jyoti Saikia, Rajan Kanhirodan, Ram Mohan Vasu
2014 International Journal of Biomedical Imaging  
They evaluated the performance of CULA (CULA is a set of GPU-accelerated linear algebra libraries utilizing the CUDA parallel computing architecture) [32] based algorithms for DOT.  ...  The domain over which the function ( , ) is defined is divided into a finite set of disjoint elements.  ... 
doi:10.1155/2014/376456 pmid:24891848 pmcid:PMC4003791 fatcat:3oegtrwva5gndoaj73eyqg4hg4
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