基于中介逻辑的时序逻辑系统

本文基于中介逻辑建立了一种中介时序逻辑系统ＭＴＬ（Ｍｅｄｉｕｍ Ｔｅｍｐｏｒａｌ Ｌｏｇｉｃ），文中着重讨论了ＭＴＬ的形式系统并给出了它的语义解释，证明了ＭＴＬ系统的可靠性．最后对ＭＴＬ系统和经典时序命题逻辑系统进行对比，指出经典时序命题逻辑系统是ＭＴＬ的子系统     

Logic of agreement: Foundations,semantic system and proof theory

In this paper a multi-valued propositional logic — logic of agreement — in terms of its model theory and inference system is presented. This formal system is the natural consequence of a new way to approach concepts as commonsense knowledge, uncertainty and approximate reasoning — the point of view of agreement. Particularly, it is discussed a possible extension of the Classical Theory of Sets based on the idea that, instead of trying to conceptualize sets as “fuzzy” or “vague” entities, it is more adequate to define membership as the result of a partial agreement among a group of individual agents. Furthermore, it is shown that the concept of agreement provides a framework for the development of a formal and sound explanation for concepts (e.g. fuzzy sets) which lack formal semantics. According to the definition of agreement, an individual agent agrees or not with the fact that an object possesses a certain property. A clear distinction is then established, between an individual agent — to whom deciding whether an element belongs to a set is just a yes or no matter — and a commonsensical agent — the one who interprets the knowledge shared by a certain group of people. Finally, the logic of agreement is presented and discussed. As it is assumed the existence of several individual agents, the semantic system is based on the perspective that each individual agent defines her/his own conceptualization of reality. So the semantics of the logic of agreement can be seen as being similar to a semantics of possible worlds, one for each individual agent. The proof theory is an extension of a natural deduction system, using supported formulas and incorporating only inference rules. Moreover, the soundness and completeness of the logic of agreement are also presented.     

Compositional Meaning in Logic

The Fregean-inspired Principle of Compositionality of Meaning (PoC) for formal languages asserts that the meaning of a compound expression is analysable in terms of the meaning of its constituents, taking into account the mode in which these constituents are combined so as to form the compound expression. From a logical point of view, this amounts to prescribing a constraint—that may or may not be respected—on the internal mechanisms that build and give meaning to a given formal system. Within the domain of formal semantics and of the structure of logical derivations, the PoC is often directly reflected by metaproperties such as truth-functionality and analyticity, characteristic of computationally well-behaved logical systems.     

Logic, language games and ludics

Wittgenstein’s language games can be put into a wider service by virtue of elements they share with some contemporary opinions concerning logic and the semantics of computation. I will give two examples: manifestations of language games and their possible variations in logical studies, and their role in some of the recent developments in computer science. It turns out that the current paradigm of computation that Girard termed Ludics bears a striking resemblance to members of language games. Moreover, the kind of interrelations that are emerging could be scrutinised from the viewpoint of logic that virtually necessitates game-theoretic conceptualisations, demonstrating the fact that the meaning of utterances may, in many situations, be understood as Wittgenstein’s language games of ‘showing or telling what one sees’. This provides motivation for the use of games in relation to logic and formal semantics that some commentators have called for. Many of the ideas can be traced to C.S. Peirce, for whom signs were vehicles of strategic communication. The conclusion about Wittgenstein is that the notions of saying and showing converge in his late philosophy.     

Infinitary S5-Epistemic Logic

It is known that a theory in S5-epistemic logic with several agents may have numerous models. This is because each such model specifies also what an agent knows about infinite intersections of events, while the expressive power of the logic is limited to finite conjunctions of formulas. We show that this asymmetry between syntax and semantics persists also when infinite conjunctions (up to some given cardinality) are permitted in the language. We develop a strengthened S5-axiomatic system for such infinitary logics, and prove a strong completeness theorem for them. Then we show that in every such logic there is always a theory with more than one model.     

网络体系结构建模和性能评价的形式化方法——随机进程代数

随机进程代数是从经典进程代数发展起来 ,用于并发系统的定性和定量分析的形式化方法 ,特别适合在计算机网络和通信协议的建模和性能评价 .首先介绍了 SPA的语法和操作语义 .并以令牌环局域网模型为例来说明其应用 .进一步讨论了 SPA的三种等价关系 ,以期解决模型状态空间爆炸问题 .     

Logic of secrets in collaboration networks

The article proposes Logic of Secrets in Collaboration Networks, a formal logical system for reasoning about a set of secrets established over a fixed configuration of communication channels. The system’s key feature, a multi-channel relation called independence, is a generalization of a two-channel relation known in the literature as nondeducibility. The main result is the completeness of the proposed system with respect to a semantics of secrets.     

Interface of global and local semantics in a self-navigating system based on the concept lattice

If the syntax–semantics interaction is driven by the interface, it also interrupts the interaction on its own right. Because the syntax is verified to be isomorphic to the semantics, the interaction is open to the diagonal argument leading to a contradiction. That is why it is necessary to introduce a particular interface to drive the interface to make the interaction possible despite the contradiction. In this context we propose the system implemented with the syntax–semantics loop by using a concept lattice and a particular weak quantifier. This system is expressed as the self-navigating system which wanders in a two-dimensional space, encounters some landmarks, constructs the relationship among landmarks to which decision making with respect to the move is referred. The syntax of this system is defined as two-dimensional move and the semantics is defined as a concept lattice [B. Ganter, R. Wille, Formal Concept Analysis, Springer, Berlin, 1999] constructed by the binary relation between landmarks and some properties of landmarks, and by Galois connection. To implement the interface driving and interrupting the interaction between syntax and semantics, we divided semantics into local and global concept lattices, and introduce a weak quantifier to connect a local with a global lattice. Because the contradiction results from diagonal argument or using a normal quantifier ∀, the use of a quantifier is restricted dependent on the situation to avoid a contradiction. It is shown that due to the role of a weak quantifier our self-navigating system is both robust and open to the emergent property through simulating studies.     

Separation logic and logics with team semantics

Separation logic is a successful logical system for formal reasoning about programs that mutate their data structures. Team semantics, on the other side, is the basis of modern logics of dependence and independence. Separation logic and team semantics have been introduced with quite different motivations, and are investigated by research communities with rather different backgrounds and objectives. Nevertheless, there are obvious similarities between these formalisms. Both separation logic and logics with team semantics involve the manipulation of second-order objects, such as heaps and teams, by first-order syntax without reference to second-order variables. Moreover, these semantical objects are closely related; it is for instance obvious that a heap can be seen as a team, and the separating conjunction of separation logic is (essentially) the same as the team-semantical disjunction. Based on such similarities, the possible connections between separation logic and team semantics have been raised as a question at several occasions, and lead to informal discussions between these research communities. The objective of this paper is to make this connection precise, and to study its potential but also its obstacles and limitations.     

Some difficulties with abstract and concrete syntax

Abstract syntax is a useful mechanism in defining the semantics of programming languages as it relieves the semantic definition from text handling and syntactic analysis and shows clearly the semantically essential parts of program texts. Abstract syntax is usually required to have a high quality semantic content and so a straightforward forming of abstract syntax from a concrete one may lead to many errors. This paper introduces three error-prone constructs: parentheses that have an uncommon meaning, ambiguous concrete syntax, and empty lists. The first two errors originate in problems with concrete syntax while the last one is due to a weakness of some formalisms for abstract syntax.     

L—Fuzzy命题逻辑系统的语构分层方案

建立一种L－Fuzzy命题逻辑的语构分层构造,引进诸如λ－信息,λ－公理系,λ－语构,λ－证明,λ－定理,λ－语构结论,λ－语构闭包,λ－紧性,,上L－Fuzzy语构闭包,下Fuzzy语构闭包,λ－语构分层和谐,语构分层和谐,强语构分层和谐等新的观念和方法,从而L－Fuzzy命题逻辑语构和语义分层次的程度化的和谐性度量提供了一种方案。     

On the equivalence between logic programming semantics and argumentation semantics

In the current paper, we re-examine the connection between formal argumentation and logic programming from the perspective of semantics. We observe that one particular translation from logic programs to instantiated argumentation (the one described by Wu, Caminada and Gabbay) is able to serve as a basis for describing various equivalences between logic programming semantics and argumentation semantics. In particular, we are able to show equivalence between regular semantics for logic programming and preferred semantics for formal argumentation. We also show that there exist logic programming semantics (L-stable semantics) that cannot be captured by any abstract argumentation semantics.     

Truth versus validity in mathematical proof

In mathematics education, it is often said that mathematical statements are necessarily either true or false. It is also well known that this idea presents a great deal of difficulty for many students. Many authors as well as researchers in psychology and mathematics education emphasize the difference between common sense and mathematical logic. In this paper, we provide both epistemological and didactic arguments to reconsider this point of view, taking into account the distinction made in logic between truth and validity on one hand, and syntax and semantics on the other. In the first part, we provide epistemological arguments showing that a central concern for logicians working with a semantic approach has been finding an appropriate distance between common sense and their formal systems. In the second part, we turn from these epistemological considerations to a didactic analysis. Supported by empirical results, we argue for the relevance of the distinction and the relationship between truth and validity in mathematical proof for mathematics education.     

Some Connections between Topological and Modal Logic

We study modal logics based on neighbourhood semantics using methods and theorems having their origin in topological model theory. We thus obtain general results concerning completeness of modal logics based on neighbourhood semantics as well as the relationship between neighbourhood and Kripke semantics. We also give a new proof for a known interpolation result of modal logic using an interpolation theorem of topological model theory.     

Logic of proofs with substitution

The substitution operation in logic of proofs is axiomatized. For the system constructed, symbolic semantics is introduced and a completeness theorem is proved.     

Dual‐Context Sequent Calculus and Strict Implication

We introduce a dual‐context style sequent calculus which is complete with respectto Kripke semantics where implication is interpreted as strict implication in the modal logic K. The cut‐elimination theorem for this calculus is proved by a variant of Gentzen's method.     

逻辑,语义和计算机科学中的一些基本思想

本文对理论计算机科学，特别是对其在逻辑与语义方面的基本思想作了一个直观易懂的综述，旨在使上述思想为希望在该领域开拓视野之士敞开大门。     

A denotational semantics ofLC2

The aim of this paper is to extend the classical sequent calculusLC to the second order. This task is realized by a semantical approach mixing the correlation spaces semantics ofLC on the one hand, and the analogy with the interpretation of systemF in coherent spaces on the other hand. This relies on the introduction of a new semantical object:noetherian correlation spaces.From the semantics we deduce the syntax of the second order classical sequent calculusLC2.