J. Log. Comput.最新文献_第6页

Sublattices and Δ-blocks of orthomodular posets 正模偏集的子格和Δ-blocks

J. Log. Comput. Pub Date : 2020-07-28 DOI: 10.1093/logcom/exaa037

I. Chajda, H. Länger

引用次数: 0

Recursive Rules with Aggregation: A Simple Unified Semantics 带聚合的递归规则:一个简单的统一语义

J. Log. Comput. Pub Date : 2020-07-26 DOI: 10.1007/978-3-030-93100-1_11

Yanhong A. Liu, S. Stoller

引用次数: 7

On the different types of collective attacks in abstract argumentation: equivalence results for SETAFs 抽象论证中不同类型的集体攻击:SETAFs的等价结果

J. Log. Comput. Pub Date : 2020-07-23 DOI: 10.1093/logcom/exaa033

W. Dvořák, Anna Rapberger, S. Woltran

{"title":"On the different types of collective attacks in abstract argumentation: equivalence results for SETAFs","authors":"W. Dvořák, Anna Rapberger, S. Woltran","doi":"10.1093/logcom/exaa033","DOIUrl":"https://doi.org/10.1093/logcom/exaa033","url":null,"abstract":"Argumentation frameworks with collective attacks are a prominent extension of Dung’s abstract argumentation frameworks, where an attack can be drawn from a set of arguments to another argument. These frameworks are often abbreviated as SETAFs. Although SETAFs have received increasing interest recently, a thorough study on the actual behavior of collective attacks has not been carried out yet. In particular, the richer attack-structure SETAFs provide, can lead to different forms of redundant attacks, i.e., attacks that are subsumed by attacks involving less arguments. Also the notion of strong equivalence, which is fundamental in nonmonotonic formalisms to characterize equivalent replacements, has not been investigated for SETAFs so far. In this paper, we first provide a classification of different types of collective attacks, and analyze for which semantics they can be proven redundant. We do so for eleven well established abstract argumentation semantics. We then study how strong equivalence between SETAFs can be decided with respect to the considered semantics and also consider variants of strong equivalence. Our results show that removing redundant attacks in a suitable way provides direct means to characterize strong equivalence by syntactical equivalence of so-called kernels, thus generalizing well-known results on strong equivalence between Dung AFs.","PeriodicalId":398763,"journal":{"name":"J. Log. Comput.","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132885115","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4

The generalized orthomodularity property: configurations and pastings 广义正模性:构形与浆糊

J. Log. Comput. Pub Date : 2020-07-23 DOI: 10.1093/logcom/exaa028

I. Chajda, D. Fazio, Antonio Ledda

引用次数: 4

A study of possible-worlds semantics of relevance-sensitive belief revision 关联敏感信念修正的可能世界语义研究

J. Log. Comput. Pub Date : 2020-07-23 DOI: 10.1093/logcom/exaa029

T. Aravanis, P. Peppas, Mary-Anne Williams

引用次数: 3

Hypersequent calculi for non-normal modal and deontic logics: Countermodels and optimal complexity 非正态模态和道义逻辑的超序演算:反模型和最优复杂性

J. Log. Comput. Pub Date : 2020-06-09 DOI: 10.1093/logcom/exaa072

Tiziano Dalmonte, Björn Lellmann, N. Olivetti, Elaine Pimentel

引用次数: 7

Sette's calculus P1 and some hierarchies of paraconsistent systems 塞特演算P1与副相容系统的一些层次

J. Log. Comput. Pub Date : 2020-06-02 DOI: 10.1093/logcom/exaa030

J. Ciuciura

引用次数: 4

The Axiom of Choice in computability theory and Reverse Mathematics with a cameo for the Continuum Hypothesis 可计算理论与逆向数学中的选择公理，兼论连续统假设

J. Log. Comput. Pub Date : 2020-05-30 DOI: 10.1093/logcom/exaa080

D. Normann, Sam Sanders

{"title":"The Axiom of Choice in computability theory and Reverse Mathematics with a cameo for the Continuum Hypothesis","authors":"D. Normann, Sam Sanders","doi":"10.1093/logcom/exaa080","DOIUrl":"https://doi.org/10.1093/logcom/exaa080","url":null,"abstract":"The Axiom of Choice (AC for short) is the most (in)famous axiom of the usual foundations of mathematics, ZFC set theory. The (non-)essential use of AC in mathematics has been well-studied and thoroughly classified. Now, fragments of countable AC not provable in ZF have recently been used in Kohlenbach's higher-order Reverse Mathematics to obtain equivalences between closely related compactness and local-global principles. We continue this study and show that NCC, a weak choice principle provable in ZF and much weaker systems, suffices for many of these results. In light of the intimate connection between Reverse Mathematics and computability theory, we also study realisers for NCC, i.e. functionals that produce the choice functions claimed to exist by the latter from the other data. Our hubris of undertaking the hitherto underdeveloped study of the computational properties of (choice functions from) AC leads to interesting results. For instance, using Kleene's S1-S9 computation schemes, we show that various total realisers for NCC compute Kleene's $exists^3$, a functional that gives rise to full second-order arithmetic, and vice versa. By contrast, partial realisers for NCC should be much weaker, but establishing this conjecture remains elusive. By way of catharsis, we show that the Continuum Hypothesis (CH for short) is equivalent to the existence of a countably based partial realiser for NCC. The latter kind of realiser does not compute Kleene's $exists^3$ and is therefore strictly weaker than a total one.","PeriodicalId":398763,"journal":{"name":"J. Log. Comput.","volume":"81 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122218246","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 10

Locally constant constructive functions and connectedness of intervals 区间的局部常构造函数与连通性

J. Log. Comput. Pub Date : 2020-05-29 DOI: 10.1093/LOGCOM/EXAA038

V. Chernov

引用次数: 3

On embedding Lambek calculus into commutative categorial grammars Lambek微积分嵌入可交换范畴语法的研究

J. Log. Comput. Pub Date : 2020-05-20 DOI: 10.1093/LOGCOM/EXAB065

Sergey Slavnov

{"title":"On embedding Lambek calculus into commutative categorial grammars","authors":"Sergey Slavnov","doi":"10.1093/LOGCOM/EXAB065","DOIUrl":"https://doi.org/10.1093/LOGCOM/EXAB065","url":null,"abstract":"Abstract categorial grammars (ACG), as well as some other, closely related systems, are based on the ordinary, commutative implicational linear logic and linear $lambda$-calculus in contrast to the better known \"noncommutative\" Lambek grammars and their variations. ACG seem attractive in many ways, not the least of which is the simplicity of the underlying logic. Yet it is known that ACG and their relatives behave poorly in modeling many natural language phenomena (such as, for example, coordination) compared to \"noncommutative\" formalisms. Therefore different solutions have been proposed in order to enrich ACG with noncommutative constructions. \u0000Tensor grammars of this work are another example of \"commutative\" grammars, based on the classical, rather than intuitionistic linear logic. They can be seen as a surface representation of ACG in the sense that derivations of ACG translate to derivations of tensor grammars and this translation is isomorphic on the level of string languages. An advantage of this representation, as it seems to us, is that the syntax becomes extremely simple and a direct geometric meaning is transparent. \u0000We address the problem of encoding noncommutative operations in our setting. This turns out possible after enriching the system with new unary operators. The resulting system allows representing both ACG and Lambek grammars as conservative fragments, while the formalism remains, as it seems to us, rather simple and intuitive.","PeriodicalId":398763,"journal":{"name":"J. Log. Comput.","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133481134","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2