动力学视角下的选言量子逻辑

正常形式与可表示函数在莫伊西逻辑中的研究

Normal forms and representable functions in Moisil logic

本文通过析取范式定理研究了标准n-模糊卢卡谢夫斯基-莫伊西代数中可表示函数的特性，并探讨了其在自由代数结构确定中的应用。

统一模糊逻辑和量子逻辑的代数逻辑体系

Algebraic hierarchy of logics unifying fuzzy logic and quantum logic

本文对一般逻辑的基本概念作了一个简短的综述。特别是，一个新的严格定义的模糊否定作为一个操作上的格，使其成为一个模糊逻辑。根据这一定义，模糊否定满足弱双重否定条件，要求双重否定是可扩张的;反义词条件，等价于析取的德摩根法则，从而排除了否定与格运算的相容性;从这个角度来看，最一般的逻辑是模糊逻辑，包含作为特例的次协调（量子）逻辑、量子逻辑、直觉主义逻辑和布尔逻辑，每一种逻辑都有自己的代数限制。新的例子的非矛盾逻辑违反合取德摩根法则，一个典型的非正交模模糊逻辑及其显式格表示。

Quantum decoherence: a logical perspective

The so-called classical limit of quantum mechanics is generally studied in terms of the decoherence of the state operator that characterizes a system. This is not the only possible approach to decoherence. In previous works we have presented the possibility of studying the classical limit in terms of the decoherence of relevant observables of the system. On the basis of this approach, in this paper we introduce the classical limit from a logical perspective, by studying the way in which the logical structure of quantum properties corresponding to relevant observables acquires Boolean character…

从 Łukasiewicz 逻辑视角看热带化，并兼论拓扑斯理论观点

Tropicalization through the lens of Łukasiewicz logic, with a topos theoretic perspective

本文以幂等半域和 MV-代数为桥梁，借助范畴与拓扑斯理论刻画热带几何同 Łukasiewicz 多值逻辑之间的结构等价与深层联系。

Neighborhood Contingency Logic: A New Perspective

In this paper, we propose a new neighborhood semantics for contingency logic, by introducing a simple property in standard neighborhood models. This simplifies the neighborhood semantics given in (Fan and van Ditmarsch, 2015), but does not change the set of valid formulas. Under this perspective, among various notions of bisimulation and respective Hennessy-Milner Theorems, we show that $c$-bisimulation is equivalent to nbh-$Δ$-bisimulation in the literature, which guides us to understand the essence of the latter notion. This perspective also provides various frame definability and axiomatiza…

Probability Logic: A Model Theoretic Perspective

In this paper (propositional) probability logic ($PL$) is investigated from model theoretic point of view. First of all, the ultraproduct construction is adapted for $σ$-additive probability models, and subsequently when this class of models is considered it is shown that the compactness property holds with respect to a fragment of $PL$ called basic probability logic ($BPL$). On the other hand, when dealing with finitely-additive probability models, one may extend the compactness property for a larger fragment of probability logic, namely positive probability logic ($PPL$). We finally prove th…

On Three-Valued Modal Logics: from a Four-Valued Perspective

This paper aims at providing a comprehensive solution to the archaic open problem: how to define semantics of three-valued modal logic with vivid intuitive picture, convincing philosophical justification as well as versatile practical usage. Based on an existing line of work concerned with investigating three-valued logic out of innovative angles of view, we adopt a detour approach to interpret three-valued logic from a four-valued perspective, which results in the invention of an universal and systematic methodology for developing, explaining as well as utilizing three-valued modal logic. We …

Novosibirsk algebra and logic in the mid 1960s: A personal perspective

Being asked to write about Asan D. Taimanov, I had a little problem. I knew Taimanov. I liked and respected him, and so I wanted to write something. But I didn't know him well. I didn't live in the Novosibirsk Akademgorodok where he lived and worked; I just visited Novosibirsk a number of times. So I decided to widen the topic and write about my own Novosibirsk experience, including interactions with Taimanov.