Causality Is Logically Definable—Toward an Equilibrium-Based Computing Paradigm of Quantum Agent and Quantum Intelligence (QAQI) (Survey and Research)

A survey on agents, causality and intelligence is presented and an equilibrium-based computing paradigm of quantum agents and quantum intelligence (QAQI) is proposed. In the survey, Aristotle’s causality principle and its historical extensions by David Hume, Bertrand Russell, Lotfi Zadeh, Donald Rubin, Judea Pearl, Niels Bohr, Albert Einstein, David Bohm, and the causal set initiative are reviewed;bipolar dynamic logic (BDL) is introduced as a causal logic for bipolar inductive and deductive reasoning;bipolar quantum linear algebra (BQLA) is introdused as a causal algebra for quantum agent interaction and formation. Despite the widely held view that causality is undefinable with regularity, it is shown that equilibrium-based bipolar causality is logically definable using BDL and BQLA for causal inference in physical, social, biological, mental, and philosophical terms. This finding leads to the paradigm of QAQI where agents are modeled as quantum enssembles;intelligence is revealed as quantum intelligence. It is shown that the enssemble formation, mutation and interaction of agents can be described as direct or indirect results of quantum causality. Some fundamental laws of causation are presented for quantum agent entanglement and quantum intelligence. Applicability is illustrated;major challenges are identified in equilibriumbased causal inference and quantum data mining.

Fuzzy Logic and Zadeh Algebra

In this work we create a connection between AFS (Axiomatic Fuzzy Sets) fuzzy logic systems and Zadeh algebra. Beginning with simple concepts we construct fuzzy logic concepts. Simple concepts can be interpreted semantically. The membership functions of fuzzy concepts form chains which satisfy Zadeh algebra axioms. These chains are based on important relationship condition (1) represented in the introduction where the binary relation Rm of a simple concept m is defined more general in Definition 2.10. Then every chain of membership functions forms a Zadeh algebra. It demands a lot of preliminaries before we obtain this desired result.

逻辑代数在设计三相异步电动机控制线路中的应用

电力拖动自动控制设备的控制对象为各类电动机或其他执行电器,控制原理为通过对控制对象的起动、停止、正反转、调速、制动等的运行方式采用电气控制的方法实现控制,进而在生产过程中实现自动化控制。为了更好地控制电动机的运行,需要设计相应的控制线路。从逻辑代数的基本概念入手,探讨逻辑代数在设计三相异步电动机控制线路中的应用,针对三相异步电动机连续运转和正反转控制线路设计进行详细介绍。

A Hierarchy of Compatibility and Comeasurability Levels in Quantum Logics with Unique Conditional Probabilities

In the quantum mechanical Hilbert space formalism, the probabilistic interpretation is a later ad-hoc add-on, more or less enforced by the experimental evidence, but not motivated by the mathematical model itself. A model involving a clear probabilistic interpretation from the very beginning is provided by the quantum logics with unique conditional probabilities. It includes the projection lattices in von Neumann algebras and here probability conditionalization becomes identical with the state transition of the Lueders-von Neumann measurement process. This motivates the definition of a hierarchy of five compatibility and comeasurability levels in the abstract setting of the quantum logics with unique conditional probabilities. Their meanings are： the absence of quantum interference or influence, the existence of a joint distribution, simultaneous measurability, and the independence of the final state after two successive measurements from the sequential order of these two measurements. A further level means that two elements of the quantum logic （events） belong to the same Boolean subalgebra. In the general case, the five compatibility and comeasurability levels appear to differ, but they all coincide in the common Hilbert space formalism of quantum mechanics, in von Neumann algebras, and in some other cases.

The Monty Hall Problem and beyond: Digital-Mathematical and Cognitive Analysis in Boole’s Algebra, Including an Extension and Generalization to Related Cases

The Monty Hall problem has received its fair share of attention in mathematics. Recently, an entire monograph has been devoted to its history. There has been a multiplicity of approaches to the problem. These approaches are not necessarily mutually exclusive. The design of the present paper is to add one more approach by analyzing the mathematical structure of the Monty Hall problem in digital terms. The structure of the problem is described as much as possible in the tradition and the spirit—and as much as possible by means of the algebraic conventions—of George Boole’s Investigation of the Laws of Thought (1854), the Magna Charta of the digital age, and of John Venn’s Symbolic Logic (second edition, 1894), which is squarely based on Boole’s Investigation and elucidates it in many ways. The focus is not only on the digital-mathematical structure itself but also on its relation to the presumed digital nature of cognition as expressed in rational thought and language. The digital approach is outlined in part 1. In part 2, the Monty Hall problem is analyzed digitally. To ensure the generality of the digital approach and demonstrate its reliability and productivity, the Monty Hall problem is extended and generalized in parts 3 and 4 to related cases in light of the axioms of probability theory. In the full mapping of the mathematical structure of the Monty Hall problem and any extensions thereof, a digital or non-quantitative skeleton is fleshed out by a quantitative component. The pertinent mathematical equations are developed and presented and illustrated by means of examples.

A New Branch of the Pure Algebra: BCL-Algebras

The BCK/BCI/BCH-algebras finds general algebra system than Boolean algebras system. This paper presents a novel class of algebras of type (2, 0) called BCL-algebras. We found the BCL-algebras to be more extensive class than BCK/BCI/BCH-algebras in the abstract algebra. The BCL-algebras as a class of logical algebras are the algebraic formulations of the set difference together with its properties in set theory and the propositional calculus in logical systems. It is important that the BCL-algebras play an independent role in the axiom algebra system.

Researches on Six Lattice-Valued Logic

Based on the direct product of Boolean algebra and Lukasiewicz algebra, six lattice-valued logic is put forward in this paper. The algebraic structure and properties of the lattice are analyzed profoundly and the tautologies of six-valued logic system L6P(X) are discussed deeply. The researches of this paper can be used in lattice-valued logic systems and can be helpful to automated reasoning systems.

Conditional Events and Quantum Logic

This paper begins with an overview of quantum mechanics, and then recounts a relatively recent algebraic extension of the Boolean algebra of probabilistic events to “conditional events” (order pairs of events). The main point is to show that a so-called “superposition” of two (or more) quantum events (usually with mutually inconsistent initial conditions) can be represented in this algebra of conditional events and assigned a consistent conditional probability. There is no need to imagine that a quantum particle can simultaneously straddle two inconsistent possibilities.

On BCL⁺-Algebras

This paper presents the BCL+-algebras, which is derived the fundamental properties. Results are generalized with version of BCL-algebras [5], using some unusual for a binary relation * and a constant 1 (one) in a non-empty set X, one may take different axiom systems for BCL+-algebras.

Closure Operators of Lattice-valued Propositional Logic LP(X)

In this paper, closure operators of lattice-valued propositional logic LP（X） are studied. A family of classical closure operators are defined and the relation between them and closure operators of LP（X） is investigated. At the same time, a tool for checking compactness of LP（X） is given.

Syntactic Extension of Lattice-valued Propositional Logic LP(X)

We have given a semantic extension of lattice-valued propositional logic LP（X） in [6]. In this paper, we investigate its corresponding syntactic extension of LP（X） and give the relations between these two extensions.

The Lattice of（∈,∈∨qk）-fuzzy Filters in a Given R0-algebra

The purpose of this paper is to further study the(∈,∈∨q_k)-fuzzy filter theory in R_0-algebras. Some new properties of(∈, ∈∨ q_k)-fuzzy filters are given. Representation theorem of(∈,∈∨q_k)-fuzzy filter which is generated by a fuzzy set is established. It is proved that the set consisting of all(∈, ∈∨q_k)-fuzzy filters on a given R_0-algebra, under the partial order, forms a complete distributive lattice.

Logic and Sense

In the paper, original formal-logical conception of syntactic and semantic： intensional and extensional senses of expressions of any language L is outlined. Syntax and bi-level intensional and extensional semantics of language L are characterized categorically： in the spirit of some Husserl＇s ideas of pure grammar, Le^niewski-Ajukiewicz＇s theory syntactic/semantic categories and in accordance with Frege＇s ontological canons, Bochefiski＇s famous motto--syntax mirrors ontology and some ideas of Suszko： language should be a linguistic scheme of ontological reality and simultaneously a tool of its cognition. In the logical conception of language L, its expressions should satisfy some general conditions of language adequacy. The adequacy ensures their unambiguous syntactic and semantic senses and mutual, syntactic, and semantic compatibility, correspondence guaranteed by the acceptance of a postulate of categorial compatibility syntactic and semantic （extensional and intensional） categories of expressions of L. From this postulate, three principles of compositionality follow： one syntactic and two semantic already known to Frege. They are treated as conditions of homomorphism partial algebra of L into algebraic models of L： syntactic, intensional, and extensional. In the paper, they are applied to some expressions with quantifiers. Language adequacy connected with the logical senses described in the logical conception of language L is, of course, an idealization, but only expressions with high degrees of precision of their senses, after due justification, may become theorems of science.

Reliability Measures for Tele-Communication System with Redundant Transferring Machine by Using Algebraic Method

There are so many existing methods to obtain system reliability like re-generating point function technique, supplementary variables technique etc., but all these techniques are full of complicated calculations. Keeping above these facts in mind, the authors in this paper have evaluated some reliability parameters for tele-communication system by using Boolean functions technique and algebraic method. Reliability of considered tele-communication system has been evaluated by considering the fact that failures follow arbitrary time distribution. In particular, the reliability expression has also been calculated for Exponential and Weibull distributions. Further, an important reliability parameter namely M.T.T.F. (mean time to failure) has also been calculated. A numerical example with graphical illustrations has been appended at the end to highlight the important results and practical utility of the model.

Resolution Method of Six-Element Linguistic Truth-Valued First-Order Logic System

Based on 6-elements linguistic truth-valued lattice implication algebras this paper discusses 6-elements linguistic truth-valued first-order logic system. With some special properties of 6-elements linguistic truth-valued first-order logic, we discussed the satisfiable problem of 6-elements linguistic truth-valued first-order logic and proposed a resolution method of 6-elements linguistic truth-valued firstorder logic. Then the resolution algorithm is presented and an example illustrates the effectiveness of the proposed method.

布尔逻辑思想初探

以布尔命名的“布尔代数”作为数学分支,在现今计算机科学领域蓬勃发展,那么布尔本人的逻辑思想在逻辑史上的地位应重新审视。从布尔对莱布尼茨的发展,布尔逻辑的形式和形式化的区分以及布尔和直言三段论的关系三个角度展开的分析,是凸显布尔逻辑思想当代价值的关键。

变电站备自投的配置与简化方案

变电站备自投运行方式多达数十种,采用“穷举”运行方式的方法实现变电站备自投是复杂且困难的。提出了110 kV变电站备自投由1个高压侧备自投和1个中压侧备自投、1~3个低压侧备自投组成110 kV变电站备自投的简化方案,简单、易于实施;阐述了高压侧备自投、中压侧备自投与各低压侧备自投之间的配合关系和要求。以最简单的内桥接线变电站为例,通过逻辑代数为理论分析工具,对该变电站备自投运行方式进行理论分析,与穷举的该变电站备自投运行方式结果一样、运行效果一致,证明了该内桥接线备自投的配置与简化是成立的,该分析方法同样适用于其他接线变电站备自投的理论分析。

Fuzzy蕴涵代数及其理想理论

模糊逻辑代数分析是模糊逻辑研究领域的热点问题之一。运用代数学和格论的方法及原理,深入研究了Fuzzy蕴涵代数及其理想问题。首先,利用伪补算子给出了Fuzzy蕴涵代数的若干新性质。其次,在Fuzzy蕴涵代数中引入理想和生成理想的概念并考察其性质特征和等价刻画。最后,讨论了由给定Fuzzy蕴涵代数全体理想构成的集合的格论特征,证明了该集合关于集合包含序构成分配的连续(代数)格,特别地构成完备Heyting代数,进而构成Frame的重要结论。

MTL代数的直觉模糊理想

将直觉模糊集与理想概念相结合,在MTL代数中引入直觉模糊理想和直觉模糊素(Boolean/关联/超/固执)理想的概念并考察它们的特征性质和相互关系.证明了对MTL代数的非常值直觉模糊理想A而言,如下各条件是等价的:(ⅰ)A是直觉模糊Boolean理想和直觉模糊素理想;(ⅱ)A是直觉模糊关联理想和直觉模糊素理想;(ⅲ)A是直觉模糊超理想;(ⅳ)A是直觉模糊固执理想.

EQ-代数上M-算子研究

EQ-代数是高阶模糊逻辑所对应的一类重要逻辑代数,将其作为模糊逻辑理论的主要研究领域,对推动人工智能的发展有重要意义。文中主要在EQ-代数上引入Multiplier算子(M-算子)、单M-算子、幂等M-算子等算子的概念,并研究其相关性质,得到了M-算子的复合依然是M-算子,并给出了保序M-算子的等价刻画,证明了在n元好的EQ-代数上,至少可以定义n个互异的M-算子;其次,讨论了M-算子与一些特殊映射(闭包算子、同态映射、幂等映射、恒等映射)之间的关系,给出了M-算子是恒等映射的等价刻画;最后,研究了EQ-代数E上关于M-算子f的不动点集(即Fixf(E))的相关性质,得到在给定条件下,M-算子的不动点集可以构成EQ-代数。