Linguistic truth-valued lattice-valued propositional logic system ?P(X) based on linguistic truth-valued lattice implication algebra

In the semantics of natural language, quantification may have received more attention than any other subject, and syllogistic reasoning is one of the main topics in many-valued logic studies on inference. Particularly, lattice-valued logic, a kind of important non-classical logic, can be applied to describe and treat incomparability by the incomparable elements in its truth-valued set. In this paper, we first focus on some properties of linguistic truth-valued lattice implication algebra. Secondly, we introduce some concepts of linguistic truth-valued lattice-valued propositional logic system ?P(X), whose truth-valued domain is a linguistic truth-valued lattice implication algebra. Then we investigate the semantic problem of ?P(X). Finally, we further probe into the syntax of linguistic truth-valued lattice-valued propositional logic system ?P(X), and prove the soundness theorem, deduction theorem and consistency theorem.     

Automata theory based on complete residuated lattice-valued logic (Ⅱ)

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, it demonstrates several basic equivalent characterizations on the retriev-ability of (?) valued automata. Finally, the connections of the homomorphisms between two (?) valued automata to continuous mappings and open mappings are clarified. So this paper establishes further the more profound fuzzy automata theory.     

Determination of α-resolution in lattice-valued first-order logic LF(X)

Key issues for resolution-based automated reasoning in lattice-valued first-order logic LF(X) are investigated with truth-values in a lattice-valued logical algebraic structure-lattice implication algebra (LIA). The determination of resolution at a certain truth-value level (called α-resolution) in LF(X) is proved to be equivalently transformed into the determination of α-resolution in lattice-valued propositional logic LP(X) based on LIA. The determination of α-resolution of any quasi-regular generalized literals and constants under various cases in LP(X) is further analyzed, specified, and subsequently verified. Hence the determination of α-resolution in LF(X) can be accordingly solved to a very broad extent, which not only lays a foundation for the practical implementation of automated reasoning algorithms in LF(X), but also provides a key support for α-resolution-based automated reasoning approaches and algorithms in LIA based linguistic truth-valued logics.     

A characterization of answer sets for logic programs

Checking if a program has an answer set, and if so, compute its answer sets are just some of the important problems in answer set logic programming. Solving these problems using Gelfond and Lifschitz's original definition of answer sets is not an easy task. Alternative characterizations of answer sets for nested logic pro- grams by Erdem and Lifschitz, Lee and Lifschitz, and You et al. are based on the completion semantics and various notions of tightness. However, the notion of tightness is a local notion in the sense that for different answer sets there are, in general, different level mappings capturing their tightness. This makes it hard to be used in the design of algorithms for computing answer sets. This paper proposes a characterization of answer sets based on sets of generating rules. From this char- acterization new algorithms are derived for computing answer sets and for per- forming some other reasoning tasks. As an application of the characterization a sufficient and necessary condition for the equivalence between answer set seman- tics and completion semantics has been proven, and a basic theorem is shown on computing answer sets for nested logic programs based on an extended notion of loop formulas. These results on tightness and loop formulas are more general than that in You and Lin's work.     

Self-adaptive differential evolution algorithm with α-constrained-domination principle for constrained multi-objective optimization

Real-world problems are inherently constrained optimization problems often with multiple conflicting objectives. To solve such constrained multi-objective problems effectively, in this paper, we put forward a new approach which integrates self-adaptive differential evolution algorithm with α-constrained-domination principle, named SADE-αCD. In SADE-αCD, the trial vector generation strategies and the DE parameters are gradually self-adjusted adaptively based on the knowledge learnt from the previous searches in generating improved solutions. Furthermore, by incorporating domination principle into α-constrained method, α-constrained-domination principle is proposed to handle constraints in multi-objective problems. The advantageous performance of SADE-αCD is validated by comparisons with non-dominated sorting genetic algorithm-II, a representative of state-of-the-art in multi-objective evolutionary algorithms, and constrained multi-objective differential evolution, over fourteen test problems and four well-known constrained multi-objective engineering design problems. The performance indicators show that SADE-αCD is an effective approach to solving constrained multi-objective problems, which is basically enabled by the integration of self-adaptive strategies and α-constrained-domination principle.     

Applications of fuzzy‐based linguistic patterns for the assessment of computer screen design quality

The main objective of this study was to develop a modeling framework which would unify different aspects of computer screen design and result in a quantitative criterion for an optimized computer screen format. The fuzzy set‐based linguistic design patterns were utilized as a tool to build this model. The linguistic patterns are based on categories of expressions related closely to natural language and truth values, which are close to a human designer's intuition. The proposed framework is capable of assessing the quality of computer screen design based on existing knowledge in human‐computer interface domain using the fuzzy‐based linguistic pattern approach. Exemplary patterns for an optimal screen density, information grouping, and some aspects of screen layout are presented, along with a sequence of calculations based on the exemplary screen format. This study showed that it is possible to achieve a rational and relatively easy to interpret assessment of different screen designs in the form of the degrees of truth. Such an evaluation criterion reflects the compatibility of a given screen design with the optimal one based on the current knowledge in the field. It is believed that the proposed methodological framework for computer screen design should significantly augment the efforts of human designers.     

Parallel Solutions for Large-Scale General Sparse Nonlinear Systems of Equations

In solving application problems,many large-scale nonlinear systems of equaions result in sparse Jacobian matrices.Such nonlinear systems are called sparse nonlinear systems.The irregularity of the locations of nonzrero elements of a general sparse matrix makes it very difficult to generally map sparse matrix computations to multiprocessors for parallel processing in a well balanced manner.To overcome this difficulty,we define a new storage scheme for general sparse matrices in this paper,With the new storage scheme,we develop parallel algorithms to solve large-scale general sparse systems of equations by interval Newton/Generalized bisection methods which reliably find all numerical solutions within a given domain.I n Section 1,we provide an introduction to the addressed problem and the interval Newton‘s methods.In Section 2,some currently used storage schemes for sparse systems are reviewed.In Section 3,new index schemes to store general sparse matrices are reported.In Section 4,we present a parallel algorithm to evaluate a general sparse Jacobian matrix.In Section 5,we present a parallel algorithm to solve the corresponding interval linear system by the all-row preconditioned scheme.Conclusions and future work are discussed in Section 6.     

The Convergence of TD(λ) for General λ

The method of temporal differences (TD) is one way of making consistent predictions about the future. This paper uses some analysis of Watkins (1989) to extend a convergence theorem due to Sutton (1988) from the case which only uses information from adjacent time steps to that involving information from arbitrary ones.It also considers how this version of TD behaves in the face of linearly dependent representations for states—demonstrating that it still converges, but to a different answer from the least mean squares algorithm. Finally it adapts Watkins' theorem that -learning, his closely related prediction and action learning method, converges with probability one, to demonstrate this strong form of convergence for a slightly modified version of TD.     

A predicate spatial logic for mobile processes

A modal logic for describing temporal as well as spatial properties of mobileprocesses, expressed in the asynchronous π-calculus, is presented. The logic has recur-sive constructs built upon predicate-variables. The semantics of the logic is establishedand shown to be monotonic, thus guarantees the existence of fixpoints. An algorithm isdeveloped to automatically check if a mobile process has properties described as formulasin the logic. The correctness of the algorithm is proved.     

A spatial logic for concurrency—II

We present a modal logic for describing the spatial organization and the behavior of distributed systems. In addition to standard logical and temporal operators, our logic includes spatial operations corresponding to process composition and name hiding, and a fresh name quantifier. In Part I of this work we study the fundamental semantic properties of our logic; the focus of the present Part II is on proof theory. The main contributions are a sequent-based proof system for our logic, and a proof of cut-elimination for its first-order fragment.     

Construction of quantum gates for concatenated Greenberger–Horne–Zeilinger-type logic qubit

Concatenated Greenberger–Horne–Zeilinger (C-GHZ) state is a kind of logic qubit which is robust in noisy environment. In this paper, we encode the C-GHZ state as the logic qubit and design two kinds of quantum gates for such logic qubit. The first kind is the single logic-qubit gate which contains the logic-qubit bit-flip gate and phase-flip gate. The second kind is the logic-qubit controlled-not (CNOT) gate. We exploit the single quantum gate for physical qubit, such as bit-flip gate and phase-flip gate, and two-qubit CNOT gate to realize the logic-qubit gate. We also calculated the success probability of such logic-qubit gate based on the imperfect physical quantum gate. This protocol may be useful for future quantum computation.     

K-Dimensional Optimal Parallel Algorithm for the Solution of a General Class of Recurrence Equations

This paper proposes a parallel algorithm,called KDOP (K-Dimensional Optimal Parallel algorithm),to solve a general class of recurrence equations efficiently.The KDOP algorithm partitions the computation into a series of subcomputations,each of which is executed in the fashion that all the processors work simultaneously with each one executing an optimal sequential algorithm to solve a subcomputation task.The algorithm solves the equations in O(N/P) steps in EREW PRAM model (Exclusive Read Exclusive Write Parallel Random Access Machine model) using p≤N^1-∈ processors,where N is the size of the problem,and ∈ is a given constant.This is an optimal algorithm (its sepeedup is O(p)) in the case of p≤N^1-∈.Such an optimal speedup for this problem was previously achieved only in the case of p≤N^0.5.The algorithm can be implemented on machines with multiple processing elements or pipelined vector machines with parallel memory systems.     

K-Dimensional Optimal Parallel Algorithm for the Solution of a General Class of Recurrence Equations

1IntroductionAlgorithmshavebeenproposedtosolvelinearrecurrencesinparallell1-13].Someofthemsupposeunlimitednumberofprocessorsbeingusedwhileothersuselimitednumberofprocessors.P-M.KoggeandH.S.Stoneproposedarecursivedou-blingalgorithmforthesolutionofageneraJclassofrecuxrenceequationsl1].Itisthefastestalgorithm(thetimeisO(log,N))whenthenumberofprocessingelemelltspiseqllaltoN.Howeveritisnotoptimalintermsofefficiency:itsspeedupisO(de),whileitsefficiencyisO(wt).TherecursivedoublingapproachcanPro…     

BRAVE—a parallel logic language for artificial intelligence

This paper presents the first results for the implementation of the logic language BRAVE on a parallel architecture. We explain the operational semantics of BRAVE with common programming examples and show how both and and or parallelism can be exploited and controlled using BRAVE syntax. The design of an abstract machine for the parallel execution of BRAVE is given along with the principles of compilation and example codings. Results are presented from running example programs on a three-processor prototype, using an interpreter for BRAVE written in C.     

Reformulation of LMI-based stabilisation conditions for non-linear systems in Takagi–Sugeno's form

This article addresses the stabilisation of non-linear systems represented by a discrete-time Takagi–Sugeno model. Based on an extended non-quadratic Lyapunov function and a non-parallel distributed compensation (non-PDC) law, some additional slack matrices are introduced. Compared with the existing methods, which collect the interactions among the subsystems into a sequence of collection matrices, the new method re-collects the newly introduced slack matrices into another collection matrix. In this way, a stability result more relaxed than some existing ones are obtained. Further, the convexity of the fuzzy blending rules is utilised, with a further improved result obtained. The corresponding robust stability results are also proposed. The effectiveness of the new results is validated by two simulation examples.     

Scheduling Algorithm of α-Planarization for Solving the Problem of Multiprocessor Scheduling

在分析多处理机调度问题的基础上,提出了α-平坦的概念,并将其引入到多处理机调度问题中;基于此,提出了一种新的基于α-平坦的求解多处理机调度问题的算法.算法首先对作业集合做平坦化处理,然后再对处理后所得的新问题进行求解,最终获得原调度问题的一个近似解.实验结果表明,通过该算法可以求得较好的结果,相对于其它启发式算法,该算法具有较好的稳定性.     

Adaptation of robot’s perception of fuzzy linguistic information by evaluating vocal cues for controlling a robot manipulator

This article proposes a method for adapting a robot’s perception of fuzzy linguistic information by evaluating vocal cues. The robot’s perception of fuzzy linguistic information such as “very little” depends on the environmental arrangements and the user’s expectations. Therefore, the robot’s perception of the corresponding environment is modified by acquiring the user’s perception through vocal cues. Fuzzy linguistic information related to primitive movements is evaluated by a behavior evaluation network (BEN). A vocal cue evaluation system (VCES) is used to evaluate the vocal cues for modifying the BEN. The user’s satisfactory level for the robot’s movements and the user’s willingness to change the robot’s perception are identified based on a series of vocal cues to improve the adaptation process. A situation of cooperative rearrangement of the user’s working space is used to illustrate the proposed system by a PA-10 robot manipulator.