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1.
When rewriting is used to generate convergent and complete rewrite systems in order to answer the validity problem for some
theories, all the rewriting theories rely on a same set of notions, properties, and methods. Rewriting techniques have been
used mainly to answer the validity problem of equational theories, that is, to compute congruences. Recently, however, they
have been extended in order to be applied to other algebraic structures such as preorders and orders. In this paper, we investigate
an abstract form of rewriting, by following the paradigm of logical-system independency. To achieve this purpose, we provide a few simple conditions (or axioms) under which rewriting (and then the set of classical
properties and methods) can be modeled, understood, studied, proven, and generalized. This enables us to extend rewriting
techniques to other algebraic structures than congruences and preorders such as congruences closed under monotonicity and
modus ponens. We introduce convergent rewrite systems that enable one to describe deduction procedures for their corresponding
theory, and we propose a Knuth-Bendix–style completion procedure in this abstract framework. 相似文献
2.
移动进程演算中的开互模拟 总被引:1,自引:0,他引:1
该文就移动进程演算中的弱开同余关系进行了研究。文中考虑了一种简单的非确定性移动进程演算模型,证明了Milner的三条tau规则在有等名测试算子时不足以将强开同余关系的完全公理化系统提升到同余关系的完全公理化系统,文中提出了第四条tau规则,处理了在前缀操作下的等名测试算子,并证明了强开同余关系的完全公理化系统加上四条tau规则可得到弱开同余关系的完全公理化系统。该文的结论否定了关于Milner的三条tau规则足以将π-演算中的强同余关系的完全公理化系统提升到弱同余关系的完全公理化系统的猜想。 相似文献
3.
数据依赖在数据库设计中起着十分重要的作用.自Codd提出函数依赖(FDs)、Fagin引入多值依赖(MVDs)后,近几年来人们又根据设计中的需要引入多种新的依赖,如在工程数据库设计中所引进的传递闭包依赖(CDs)等.对这些依赖一般是按其是否具有完备的公理系统而划分为两大类,因为完备性公理系统往往具有有效的判定算法为先决条件.本文对CDs和FDs的k元完备公理系统存在问题进行了研究,证明了CDs和FDs不具有共同的k元完备公理系统这一结论. 相似文献
4.
Hierarchies of modal and temporal logics with reference pointers 总被引:1,自引:1,他引:0
Valentin Goranko 《Journal of Logic, Language and Information》1996,5(1):1-24
We introduce and study hierarchies of extensions of the propositional modal and temporal languages with pairs of new syntactic devices: point of reference-reference pointer which enable semantic references to be made within a formula. We propose three different but equivalent semantics for the extended languages, discuss and compare their expressiveness. The languages with reference pointers are shown to have great expressive power (especially when their frugal syntax is taken into account), perspicuous semantics, and simple deductive systems. For instance, Kamp's and Stavi's temporal operators, as well as nominals (names, clock variables), are definable in them. Universal validity in these languages is proved undecidable. The basic modal and temporal logics with reference pointers are uniformly axiomatized and a strong completeness theorem is proved for them and extended to some classes of their extensions. 相似文献
5.
数学原始概念的新选择 总被引:5,自引:4,他引:1
温邦彦 《重庆理工大学学报(自然科学版)》2008,22(5):135-144
选择元素作为数学的原始概念.元素满足基本、统一、独立、确定、分明的5条公设.元素可构成序列和集合.集合满足5条生成新公理:空起查后继、后继能加列、终结才确集、后继可永存、理想设穷竭.给出了无限集合的新定义:元素在现实中永有后继而且在理想中一个不漏的集合.用无限序列来反映无穷的进程,用无限集合来反映无穷的终结,强调两者不能混淆.还给出了5条自然数序集的生成新公理:下界0存在,正向1次序,素量n标准、后继w无限,上界∞存在.与皮亚诺公理相比,反映了数的度量性和无穷设终结.将数学哲学的研究和数学基础的建构紧密结合,力求3组公设公理的逻辑关系清楚,形式简明优美,语言通俗易懂. 相似文献
6.
该文研究非对称χ^≠-演算的基同余.文中引入一组L-互模拟关系,并确定基互模拟就是由L-互模拟定义导出的12个互异的互模拟关系中的最小关系,给出了某些L-互模拟的开模拟性质,利用开模拟性质引入开基互模拟概念,并证明开基互模拟与基互模拟是一致的,构造了基于基同余的可靠和完备的等式系统,最后给出了基同余的完备性定理. 相似文献
7.
8.
The skew Boolean propositional calculus () is a generalization of the classical propositional calculus that arises naturally in the study of certain well-known deductive
systems. In this article, we consider a candidate presentation of and prove it constitutes a Hilbert-style axiomatization. The problem reduces to establishing that the logic presented by
the candidate axiomatization is algebraizable in the sense of Blok and Pigozzi. In turn, this process is equivalent to verifying
four particular formulas are derivable from the candidate presentation. Automated deduction methods played a central role
in proving these four theorems. In particular, our approach relied heavily on the method of proof sketches. 相似文献
9.
Klaus Schild 《Autonomous Agents and Multi-Agent Systems》2000,3(3):259-283
The behavior of an agent is mainly governed by the specific way in which it handles the rational balance between information and deliberation. Rao and Georgeff's BDI theory is most popular among the formalisms capturing this very balance. This formalism has been proposed as a language for specifying agents in an abstract manner or, alternatively, for verifying various properties of agents implemented in some other programming language. In mainstream computer science, there are formalisms designed for a purpose similar to the BDI theory; not specifically aiming at agents, but at concurrency in general. These formalisms are known as logics of concurrent programs. In this paper these two frameworks are compared with each other for the first time. The result shows that the basic BDI theory, BDICTL*, can be captured within a standard logic of concurrency. The logic which is relevant here is Kozen's propositional -calculus. -calculus turns out to be even strictly stronger in expressive power than BDICTL* while enjoying a computational complexity which is not higher than that of BDCTL*'s small fragment CTL. This correspondence puts us in a position to provide the first axiomatization of Rao and Georgeff's full theory. Immediate consequences for the computational complexity of BDI theory are also explored, both for theorem proving and model checking. 相似文献
10.
Qingliang CHEN Kaile SU Abdul SATTAR Xiangyu LUO Aixiang CHEN 《Frontiers of Computer Science》2016,10(2):233-245
Coalition logic (CL) enables us to model the strategic abilities and specify what a group of agents can achieve whatever the other agents do. However, some rational mental attitudes of the agents are beyond the scope of CL such as the prestigious beliefs, desires and intentions (BDI) which is an interesting and useful epistemic notion and has spawned substantial amount of studies in multi-agent systems. In this paper, we introduce a first-order coalition BDI (FCBDI) logic for multi-agent systems, which provides a semantic glue that allows the formal embedding and interaction of BDI, coalition and temporal operators in a first-order language. We further introduce a semantic model based on the interpreted system model and present an axiomatic system that is proved sound and complete with respect to the semantics. Finally, it is shown that the computational complexity of its model checking in finite structures is PSPACE-complete. 相似文献