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Logic-driven fuzzy modeling with fuzzy multiplexers

Witold Pedrycz
2004 Engineering applications of artificial intelligence  
The two general design methodologies are studied and contrasted. The first is based on gradient-based learning and helps carry out parametric optimization.  ...  We introduce a concept of a fuzzy multiplexer, discuss its use in the design of logic networks and elaborate on the role of such networks in fuzzy modeling.  ...  Consider a two-variable Boolean function f (x 1 , x 2 ).  ... 
doi:10.1016/j.engappai.2004.04.011 fatcat:owc4652dx5gibjslx3xhvzfr7q

Validation of the control quality of characteristic field based fuzzy controllers

Rainer Hampel, Nasredin Chaker
2001 European Society for Fuzzy Logic and Technology  
We will demonstrate that one should define two restrictions for the characteristic field: continuity without local extrema and differentiability.  ...  With this background, the paper describes the quality of a two dimensional Fuzzy Controller characteristic field in connection with the necessary deformation for the compensation of non-linear effects.  ...  Cascading High-dimensional Fuzzy Controllers The cascading of multi-dimensional Fuzzy systems consists of a structure transformation into a cascade of two-dimensional systems.  ... 
dblp:conf/eusflat/HampelC01 fatcat:pwsek4apbbfidlw5xsavuvuhqu

Three-dimensional lattice logic circuits, Part III: Solving 3D volume congestion problem

Anas Al-Rabadi
2005 Facta universitatis - series Electronics and Energetics  
The synthesis of regular two-dimensional circuits using ISID has been introduced previously, and the synthesis of area-specific circuits using ISID has been demonstrated.  ...  The new multiple-valued ISID algorithm can have several applications such as: (1) multi-stage decompositions of multiplevalued logic functions for various lattice circuit layout optimizations, and (2)  ...  has been used (namely 2-to-1 multiplexer) to "semiregular" structure where many different logic primitives have been used, namely 2-to-1 multiplexer, AND, and OR gates.  ... 
doi:10.2298/fuee0501029a fatcat:qt3qrx6lwbamjbnmo5obkqkzam

One-Dimensional Guarded Fragments

Emanuel Kieronski, Michael Wagner
2019 International Symposium on Mathematical Foundations of Computer Science  
two free variables need not be guarded, and which thus may be seen as a unification of GF and the two-variable fragment, FO 2 .  ...  We call a first-order formula one-dimensional if every maximal block of existential (or universal) quantifiers in it leaves at most one variable free.  ...  Indeed, using an n-ary predicate and two fixed variables one can build 2 n atoms which then can be used to form 2 2 n different 2-types. Let A be a structure, and let a, b ∈ A be such that a = b.  ... 
doi:10.4230/lipics.mfcs.2019.16 dblp:conf/mfcs/Kieronski19 fatcat:h4yzat4tbfgythswdklitrcqf4

On the uniform one-dimensional fragment [article]

Antti Kuusisto
2016 arXiv   pre-print
The uniform one-dimensional fragment of first-order logic, U1, is a recently introduced formalism that extends two-variable logic in a natural way to contexts with relations of all arities.  ...  We also define a description logic version of a variant of U1 and prove a range of new results concerning the expressivity of U1 and related logics.  ...  Research on extensions and variants of two-variable logic is currently very active.  ... 
arXiv:1604.01673v2 fatcat:bq6bg7pqxrhynmyh2ogegsufzy

Concurrent Ternary Galois-based Computation using Nano-apex Multiplexing Nibs of Regular Three-dimensional Networks, Part III: Layout Congestion-free Effectuation

Anas N. Al-Rabadi
2021 Zenodo  
The developed nano-based implementations are performed in three dimensions to perform the required concurrent computations for which two-dimensional implementations are a special case.  ...  Since the concept of symmetry indices has been related to regular logic design, a more general method called Iterative Symmetry Indices Decomposition that produces regular three-dimensional lattice networks  ...  A two-dimensional Shannon lattice network. One notes that the two-dimensional lattice network in Fig. 6 is made up of 15 two-to-one multiplexers.  ... 
doi:10.5281/zenodo.4451781 fatcat:fhgfeg5q3jfwfiuoarjwrm4id4

Dialectical Logic K-Model: the Discrete Time Dynamical Sampling System, Multidimensional Logic Variable and Associate Database(ADB)

Yaozhi Jiang
2018 Journal of Mathematics Research  
logic variable via discrete Fourier transformation are explained; the second is the graph expression and matrices expression for the multidimensional logic variables in dialectical logic K-model.  ...  Multidimensional logic variable is important that can be used in multidimensional contradictions and in multiple-person games.  ...  , 1 , , 2 2 , 2 1 , 2 , 1 2 , 1 1 , 1 , in this paper are for 2-dimensional logic variable and 3-dimensional logic variable separately.One general definition for multidimensional  ... 
doi:10.5539/jmr.v10n2p88 fatcat:6iyxue4ggng4vbad5wzuulxgcq

Prediction of protein β-residue contacts by Markov logic networks with grounding-specific weights

Marco Lippi, Paolo Frasconi
2009 Computer applications in the biosciences : CABIOS  
On a non-redundant data set, our method achieves 44.9% F 1 measure, with 47.3% precision and 42.7% recall, which is significantly better (p < 0.01) than previously reported performance obtained by two-dimensional  ...  Motivation: Accurate prediction of contacts between β-strand residues can significantly contribute towards ab-initio prediction of the three-dimensional structure of many proteins.  ...  Multi-task learning can be easily implemented using Markov logic.  ... 
doi:10.1093/bioinformatics/btp421 pmid:19592394 fatcat:qxzgyqmb7nhwpiu274lv7a64tu

Three-dimensional lattice logic circuits, Part I: Fundamentals

Anas Al-Rabadi
2005 Facta universitatis - series Electronics and Energetics  
Although the current technology does not offer a menu for the immediate physical implementation of the proposed three-dimensional circuits, this paper deals with three-dimensional logic circuit design  ...  from a fundamental and foundational level for a rather new possible future directions in designing digital logic circuits.  ...  be conducted on the corresponding Galois field (GF) algebraic structures.  ... 
doi:10.2298/fuee0501001a fatcat:zzdewmocarfbxk6mp4dmljw7o4

The algorithm for minimizing Boolean functions using a method of the optimal combination of the sequence of figurative transformations

Volodymyr Riznyk, Mykhailo Solomko, Petro Tadeyev, Vitalii Nazaruk, Liudmyla Zubyk, Volodymyr Voloshyn
2020 Eastern-European Journal of Enterprise Technologies  
Встановлена відповідність інтервалів I(α, β) у булевому просторі n , які задаються парою булевих векторів α і β, таких, що α β з повною комбінаторною системою з повторенням 2-(n, b)-блоксхем (англ. 2-(  ...  При цьому спрощується алгоритмізація пошуку системи 2-(n, b)-design у структурі таблиці істинності заданої логічної функції, що правитиме інструментарієм для подальшої автоматизації пошуку системи 2-(n  ...  Two 1-dimensional single cubes, whose corresponding vertices are located at a distance equal to unity, forms a 2-dimensional single cube, two 2-dimensional single cubes form a 3-dimensional single cube  ... 
doi:10.15587/1729-4061.2020.206308 fatcat:jfrqapfg6be6tbvgh26zmwhpc4

The Glory of the Past and Geometrical Concurrency [article]

Cristian Prisacariu
2012 arXiv   pre-print
One is the fact that the geometrical aspect of HDAs makes it possible to use for capturing the hh-bisimulation, a standard modal logic that does not employ event variables, opposed to the two logics (over  ...  Besides, we try to understand better the above issues by introducing a related model that we call ST-configuration structures, which extend the configuration structures of van Glabbeek and Plotkin.  ...  Acknowledgements: The ST-configuration structures arose from a discussion with Luca Aceto.  ... 
arXiv:1206.3136v1 fatcat:l2l4sk7zfnfg7kccyp6jmgldqq

Variant Logic Construction Under Permutation and Complementary Operations on Binary Logic [chapter]

Jeffrey Zheng
2018 Variant Construction from Theoretical Foundation to Applications  
Different global coding schemes are discussed and typical two-variable cases of logic functionals are illustrated.  ...  The entire framework is described using 4 levels of hierarchy: n variables, 2 n states, 2 2 n functions, and 2 n !2 2 n logic functionals.  ...  Four schemes are described, in which one of them is in one-dimensional representation and other three schemes are two-dimensional representations.  ... 
doi:10.1007/978-981-13-2282-2_1 fatcat:g3gssu2d5fdbvjumn72lqme7ji

Characterising Choiceless Polynomial Time with First-Order Interpretations

Erich Gradel, Wied Pakusa, Svenja Schalthofer, Lukasz Kaiser
2015 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science  
Choiceless Polynomial Time (CPT) is one of the candidates in the quest for a logic for polynomial time.  ...  We also analyse the structure of PIL and show that many of the logical formalisms or database languages that have been proposed in the quest for a logic for polynomial time reappear as fragments of PIL  ...  On the other side, already two-dimensional interpretations suffice for the full power of PIL. Theorem 16. two-dimensional PIL ≡ two-dimensional PIL * ≡ PIL Proof.  ... 
doi:10.1109/lics.2015.68 dblp:conf/lics/GradelPSK15 fatcat:o6zudj655jdxzk54icw22ulauu

One-dimensional guarded fragments [article]

Emanuel Kieronski
2019 arXiv   pre-print
We call a first-order formula one-dimensional if its every maximal block of existential (universal) quantifiers leaves at most one variable free.  ...  two free variables need not be guarded, and which thus may be seen as a unification of GF and the two-variable fragment, FO2.  ...  (ii) The satisfiability (= finite satisfiability) problem for GF 1 with constants (with or without equality) is 2 -ExpTime-complete.  ... 
arXiv:1904.04572v2 fatcat:hne4ynke3nh6xa56hwzpl75cju

A Method of Majority Logic Reduction for Quantum Cellular Automata

R. Zhang, K. Walus, W. Wang, G.A. Jullien
2004 IEEE transactions on nanotechnology  
majority logic.  ...  We describe a novel method for using these standard functions to convert the sum-of-products expression to majority logic.  ...  Example 2: In Fig. 5 (b), the vertices of form a one-dimensional subspace of the function, described by an edge .  ... 
doi:10.1109/tnano.2004.834177 fatcat:a3jgxpxo7bcbjh7htiv5frexea
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