Due to the demand of high computational speed for processing big data that requires complex data manipulations in a timely manner,the need for extending classical logic to construct new multi-valued optical models bec...
Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant Nos. 91224006 and 61173063) and the Ministry of Science and Technology (201303107).
A B4-valued propositional logic will be proposed in this paper which there are three unary logical connectives ~1, ~2, ┐ and two binary logical connectives A, v, and a Gentzen-typed deduction system will be given s...
Residue Number System (RNS) has proved shaping the Digital Signal Processing (DSP) units into highly parallel, faster and secured entities. The computational complexity of the multiplication process for a RNS based de...
Description logics (DLs) are a family of logic-based knowledge representation formalisms with a number of computer science applications. DLs are especially well-known to be valuable for obtaining logical foundations o...
supported by the Assistance Grant of the Hoso Bunka Foundation.
We discuss the nature of complex number and its effect on complex-valued neural networks(CVNNs).After we review some examples of CVNN applications,we look back at the mathematical history to elucidate the features of ...
the National Natural Science Foundation of China (No.60274010, 60343001, 60221301, 60334040)
This paper gives a matrix expression of logic. Under the matrix expression, a general description of the logical operators is proposed. Using the semi-tensor product of matrices, the proofs of logical equivalences, im...
the National Natural Science Foundation of China (60274016);the Project of Scientific Research in Hight Education Bureau Liaoning Province (2023901018).
In this paper, we introduce the concept of fuzzifying topological linear space and discuss the structures and properties of the balanced neighborhood system of zero element. We also give the algebraic properties and t...
This work was supported by the National Foundation for Distinguished Young Scholars (Grant No. 69725004);the National Key Project for Basic Research (Grant No. 1998030509).
It reveals some equivalences between automata based on complete residuated lattice-valued logic (called (?) valued automata) and the truth-value lattice of the underlying logic (i.e. residuated lattice). In particular...
This work was supported by the National Foundation for Distinguished Young Scholars (Grant No. 69725004); the National Key Project for Basic Research (Grant No.1998030509) ; the National Natural Science Foundation of China (Grant No. 69823001).
This paper establishes a fundamental framework of automata theory based on complete residuated lattice-valued logic. First it deals with how to extend the transition relation of states and par-ticularly presents a cha...
In this paper we add some new corcollary and theorems to [1],in particular,we show the fundamental theorem of ultraproducts in lattice valued model for L α logic. As a corollary,we get the α compactness theorem for...