Bulletin of the Section of Logic

Ulrich (2005) showed that most of the known axiomatisations of the classical equivalence calculus (EC) are D-incomplete, that is, they are not complete with the condensed detachment rule (D) as the primary rule of the proof procedure. He proved that the axiomatisation \(\{EEpEqrErEqp, EEEpppp\}\) by Wajsberg (1937) is D-complete and pointed out a number of D-complete single axioms, including one organic single axiom. In this paper we present new single axioms for EC with the condensed detachment and the reversed condensed detachment rules that form D-complete bases and are organic.

Marcin Czakon

D-complete Single Axioms for the Equivalential Calculus with the rules D and R

D和R规则下等值演算的D-完备单公理

In this manuscript, we have presented the concept of \(\mathcal{L}\)-weakly 1-absorbing prime ideals and \(\mathcal{L}\)-weakly 1-absorbing prime filters within an ADL. Mainly, we illustrate the connections between \(\mathcal{L}\)-weakly prime ideals (filters) and \(\mathcal{L}\)-weakly 1-absorbing prime ideals (filters), as well as between \(\mathcal{L}\)-weakly 1-absorbing prime ideals (filters) and \(\mathcal{L}\)-weakly 2-absorbing ideals (filters). Lastly, we have shown that both the image and inverse image of \(\mathcal{L}\)-weakly 1-absorbing prime ideals (filters) result in \(\mathcal{L}\)-weakly 1-absorbing prime ideals (filters).

Natnael Teshale Amare

\(\mathcal{L}\)−weakly 1−Absorbing Prime Ideals and Filters

\(\mathcal{L}\)−弱1−吸收素理想与滤子

When humans reason, they are able to revise their beliefs in light of new information and abandon obsolete conclusions. Logicians argued, that in some cases, such reasonings appear to be non-monotonic. Thus, many different, seemingly non-monotonic systems were created to formally model such cases. The purpose of this article is to re-examine the definition of non-monotonicity and its implementation in non-monotonic logics and in examples of everyday human reasoning. We will argue that many non-monotonic logics employ some weakened versions of the definitions of non-monotonicity, since in-between different steps of reasoning they either: a) allow previously accepted premises to be removed, or b) change the rules of inference. Of the two strategies, the second one seems downright absurd, since changing the rules of a given logic is a mere replacement of that logic with the rules of another. As a consequence we obtain two logics, whereas the definition of a non-monotonic logic is supposed to define one. The definition of non-monotonicity does not permit either of these cases, which means that such logics are monotonic.

Piotr Łukowski

Konrad Rudnicki

Exploring the Definition of Non-Monotonicity – Logical and Psychological Considerations

探索非单调性的定义——逻辑与心理学的考量

When it comes to making decisions in vague problems, rough is one of the best tools to help analyzers. So based on rough and hoop concepts, two kinds of approximations (Lower and Upper) for filters in hoops are defined, and then some properties of them are investigated by us. We prove that these approximations- lower and upper- are interior and closure operators, respectively. Also after defining a hyper operation in hoops, we show that by using this hyper operation, set of all rough filters is monoid. For more study, we define the implicative operation on the set of all rough filters and prove that this set with implication and intersection is made a hoop.

Rajab Ali Borzooei

Elham Babaei

Constructing a Hoop Using Rough Filters

用粗糙滤波器构建环

Let \(2&lt;n&lt;\omega\). Then \({\sf CA}_n\) denotes the class of cylindric algebras of dimension \(n\), \({\sf RCA}_n\) denotes the class of representable \(\sf CA_n\)s, \({\sf CRCA}_n\) denotes the class of completely representable \({\sf CA}_n\)s, and \({\sf Nr}_n{\sf CA}_{\omega}(\subseteq {\sf CA}_n\)) denotes the class of \(n\)-neat reducts of \({\sf CA}_{\omega}\)s. The elementary closure of the class \({\sf CRCA}_n\)s (\(\mathbf{K_n}\)) and the non-elementary class \({\sf At}({\sf Nr}_n{\sf CA}_{\omega})\) are characterized using two-player zero-sum games, where \({\sf At}\) is the operator of forming atom structures. It is shown that \(\mathbf{K_n}\) is not finitely axiomatizable and that it coincides with the class of atomic algebras in the elementary closure of \(\mathbf{S_c}{\sf Nr}_n{\sf CA}_{\omega}\) where \(\mathbf{S_c}\) is the operation of forming complete subalgebras. For any class \(\mathbf{L}\) such that \({\sf At}{\sf Nr}_n{\sf CA}_{\omega}\subseteq \mathbf{L}\subseteq {\sf At}\mathbf{K_n}\), it is proved that \({\bf SP}\mathfrak{Cm}\mathbf{L}={\sf RCA}_n\), where \({\sf Cm}\) is the dual operator to \(\sf At\); that of forming complex algebras. It is also shown that any class \(\mathbf{K}\) between \({\sf CRCA}_n\cap \mathbf{S_d}{\sf Nr}_n{\sf CA}_{\omega}\) and \(\mathbf{S_c}{\sf Nr}_n{\sf CA}_{n+3}\) is not first order definable, where \(\mathbf{S_d}\) is the operation of forming dense subalgebras, and that for any \(2&lt;n&lt;m\), any \(l\geq n+3\) any any class \(\mathbf{K}\) (such that \({\sf At}({\sf Nr}_n{\sf CA}_{m})\cap {\sf CRCA}_n\subseteq \mathbf{K}\subseteq {\sf At}\mathbf{S_c}{\sf Nr}_n{\sf CA}_{l}\), \(\mathbf{K}\) is not not first order definable either.

Tarek Sayed Ahmed

Complete Representations and Neat Embeddings

完全表示与整洁嵌入

The paper will study extensions of t-normal logics S0.5o and S0.5 using some axioms of normal logics. We will prove determination theorems for these extensions by appropriate Kripke-style models. It will allow us to obtain the determinations of the logics K45, KB4 (= KB5), KD45 and S5 without using modal rules.

Andrzej Pietruszczak

Some additional axioms for t-normal logics. Defining K45, KB4, KD45 and S5 without using modal rules

一些用于t-范数逻辑的附加公理。在不使用模态规则的情况下定义K45、KB4、KD45和S5

In this paper, we study (open) filters and deductive systems of self-distributive weak Heyting algebras (SDWH-algebras) and obtain some results which determine the relationship between them. We show that the variety of SDWH-algebras is not weakly regular and every open filter is the kernel of at least one congruence relation. Then it presents necessary and sufficient conditions for the existence of a one to one correspondence between open filters and congruence relations.

ISSN	0138-0680, 2449-836X
h-index	16

涉及主题	计算机科学数学哲学程序设计语言纯数学离散数学人工智能语言学认识论域代数上的医学理论计算机科学口腔正畸科牙石（牙科）牙科描述逻辑物理多模态逻辑化学材料科学几何学数学分析中间逻辑
出版信息	出版商: Department of Logic, University of Lodz，出版周期: ，期刊类型: journal，开源期刊: 是
基本数据	创刊年份: 1996，原创研究文献占比: 0.00%，自引率:N.A.， Gold OA占比: 0.00%
平均审稿周期	网友分享经验：8 Weeks

Bulletin of the Section of Logic

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D-complete Single Axioms for the Equivalential Calculus with the rules D and R

\(\mathcal{L}\)−weakly 1−Absorbing Prime Ideals and Filters

Exploring the Definition of Non-Monotonicity – Logical and Psychological Considerations

Constructing a Hoop Using Rough Filters

Complete Representations and Neat Embeddings

\(\mathcal{L}\)−weakly 1−Absorbing Prime Ideals and Filters

D-complete Single Axioms for the Equivalential Calculus with the rules D and R

Exploring the Definition of Non-Monotonicity – Logical and Psychological Considerations

Some additional axioms for t-normal logics. Defining K45, KB4, KD45 and S5 without using modal rules

Open Filters and Congruence Relations on Self-Distributive Weak Heyting Algebras