泛逻辑学中UB代数系统的(∈,∈∨q)-fuzzy滤子

何华灿教授给出了理想状态下的泛逻辑学的形式演绎系统β,并证明了该系统的可靠性。并且提出了理想状态下的泛逻辑学对应的代数系统-UB代数,并讨论了它们的性质。在以上这些结果的基础上,引入UB代数的(∈,∈∨q)-fuzzy滤子和(∈,∈∨q)-fuzzy关联滤子的概念,获得了它们的若干等价刻画,证明了(∈,∈∨q)-fuzzy关联滤子的扩张定理。     

The logic of Peirce algebras

Peirce algebras combine sets, relations and various operations linking the two in a unifying setting. This paper offers a modal perspective on Peirce algebras. Using modal logic a characterization of the full Peirce algebras is given, as well as a finite axiomatization of their equational theory that uses so-called unorthodox derivation rules. In addition, the expressive power of Peirce algebras is analyzed through their connection with first-order logic, and the fragment of first-order logic corresponding to Peirce algebras is described in terms of bisimulations.     

An Algebraic Approach to Propositional Fuzzy Logic

We investigate the variety corresponding to a logic (introduced in Esteva and Godo, 1998, and called there), which is the combination of ukasiewicz Logic and Product Logic, and in which Gödel Logic is interpretable. We present an alternative (and slightly simpler) axiomatization of such variety. We also investigate the variety, called the variety of algebras, corresponding to the logic obtained from by the adding of a constant and of a defining axiom for one half. We also connect algebras with structures, called f-semifields, arising from the theory of lattice-ordered rings, and prove that every algebra can be regarded as a structure whose domain is the interval [0, 1] of an f-semifield , and whose operations are the truncations of the operations of to [0, 1]. We prove that such a structure is uniquely determined by up to isomorphism, and we establish an equivalence between the category of algebras and that of f-semifields.     

-Resolution principle based on lattice-valued propositional logic LP(X)

In the present paper, resolution-based automated reasoning theory in an L-type fuzzy logic is focused. Concretely, the -resolution principle, which is based on lattice-valued propositional logic LP(X) with truth-value in a logical algebra – lattice implication algebra, is investigated. Finally, an -resolution principle that can be used to judge if a lattice-valued logical formula in LP(X) is always false at a truth-valued level (i.e., -false), is established, and the theorems of both soundness and completeness of this -resolution principle are also proved. This will become the theoretical foundation for automated reasoning based on lattice-valued logical LP(X).     

基于格值命题逻辑系统LP(X)的多元α-归结原理的注记

进一步深入研究了基于格蕴涵代数的格值命题逻辑系统LP(X)的多元α-归结原理的基本理论,给出了基于LP(X)的多元α-归结演绎中参与多元α-归结的广义文字个数随着归结演绎的推进而动态变化的基本原则;对基于LP(X)的多元α-归结原理的有效性进行了一定分析,这为建立基于LP(X)的多元α-归结方法以及构造多元α-归结算法奠定了理论基础.     

基于格值一阶逻辑LF（X）的多元α-归结原理的注记

进一步深入研究了基于格蕴涵代数的格值一阶逻辑系统 LF(X )的多元α-归结原理的基本理论,给出了在基于 LF(X )的多元α-归结演绎中参与多元α-归结的广义文字个数随着归结演绎的推进而动态变化的基本原则。对基于 LF(X )的多元α-归结原理的有效性进行了一定分析;这为建立基于 LF(X )的多元α-归结方法以及构造多元α-归结算法建立了理论基础。     

A note on functions associated with Gödel formulas

We give a characterization of functions associated with formulas of Gödel logic, following what has been done by McNaughton for Lukasiewicz logic.     

Geometry of Interaction V: Logic in the hyperfinite factor

Geometry of Interaction is a transcendental syntax developed in the framework of operator algebras. This fifth installment of the program takes place inside a von Neumann algebra, the hyperfinite factor. It provides a built-in interpretation of cut-elimination as well as an explanation for light, i.e., complexity sensitive, logics.     

WBR0-代数的∧-半格表示及其实例

对WBR0-代数进行了再研究。给出WBR0-代数的一种∧-半格结构表示的简化形式,并根据这一简化形式构造了一个非BR0-代数的WBR0-代数的实例,进一步说明了WBR0-代数提出的合理性。     

分层格值命题逻辑系统中几类推理规则的讨论

在基于格值逻辑的不确定性推理的研究中,推理规则的选取是其重要研究内容之一。基于分层格值命题逻辑系统,提出了几类既包含有语义又含有语法的推理规则,且这些推理规则具备协调水平的特性;同时也证明了这几类推理规则在一定程度上有闭性。     

Algebras of Relations and Relevance Logic

We prove that algebras of binary relations whose similaritytype includes intersection, composition, converse negation andthe identity constant form a non-finitely axiomatizable quasivarietyand that the equational theory is not finitely based. We applythis result to the problem of the completeness of relevant logicwith respect to binary relations.     

On the axiomatizability of priority II

This paper contributes to the study of the equational theory of the priority operator of Baeten, Bergstra and Klop in the setting of the process algebra BCCSP. It is shown that, in the presence of at least two actions, the collection of process equations over BCCSP with the priority operator that are valid modulo bisimilarity, irrespective of the chosen priority order over actions, is not finitely based. This holds true even if one restricts oneself to the collection of valid process equations that do not contain occurrences of process variables.     

Free poset algebras and combinatorics of cones

In Free poset Boolean algebra F(P ), uniqueness of normal form of non-zero elements is proved and the notion of support of a non-zero element is, therefore, well defined. An Inclusion–Exclusion-like formula is given by defining, for each non-zero element x, using support of x ∈F(P ) in a very natural way.      

Weak pseudo-Wajsberg and weak pseudo-MV algebras

 We introduce and study a generalization of pseudo-Wajsberg and pseudo-MV algebras. The weakening of the axioms leads to the existence of two lattice structures, and of two multiplicative monoid structures. Some categorical equivalences are established.     

N-可分效应代数

引入了N-可分效应代数的定义,证明了N-可分效应代数是区间效应代数且N-可分效应代数可嵌入到可分效应代数中.     

Complete and ready simulation semantics are not finitely based over BCCSP, even with a singleton alphabet

This note shows that the complete and the ready simulation preorders do not have a finite inequational basis over the language BCCSP when the set of actions is a singleton. Moreover, the equivalences induced by those preorders do not have a finite (in)equational axiomatization either. These results are in contrast with a claim of finite axiomatizability for those semantics in the literature, which was based on the erroneous assumption that they coincide with complete trace semantics in the presence of a singleton set of actions.     

Theorems on the structure of finite dimensional estimation algebras

In this paper we proved several theorems concerning the structure of finite dimensional estimation algebras. In particular, under proper technical assumptions, we proved the following: (1) The observation of a filtering system must be linear if the estimation algebra is finite dimensional. (2) All elements of a finite dimensional estimation algebra belong to a special class of polynomial differential operators. (3) All finite dimensional estimation algebras are solvable.     

Cartesian product of compressible effect algebras

In the paper, we prove that is compatible with p}, the set of commutant of p, and , the projection commutant of a, are all normal sub-effect algebras of a compressible effect algebra E, and is a direct retraction on E} is a normal sub-effect algebra of an effect algebra E. Moreover, we answer an open question in Gudder’s (Rep Math Phys 54:93–114, 2004), Compressible effect algebras, Rep Math Phys, by showing that the cartesian product of an infinite number of E _i is a compressible effect algebra if and only if each E _i is a compressible effect algebra. This work was supported by the SF of Education Department of Shaanxi Province (Grant No. 07JK267), P. R. China.     

Decidable and undecidable logics with a binary modality

We give an overview of decidability results for modal logics having a binary modality. We put an emphasis on the demonstration of proof-techniques, and hope that this will also help in finding the borderlines between decidable and undecidable fragments of usual first-order logic.Research supported by the Hungarian National Foundation for Scientific Research grants no. T16448, F17452, T7255. Research of the first author is also supported by a grant of Logic Graduate School of Eötvös Loránd University Budapest