Modal Operators Research Articles

MODAL RESTRICTION SEMIGROUPS: TOWARDS AN ALGEBRA OF FUNCTIONS

Restriction semigroups model algebras of partial maps under composition and domain. Here we consider restriction semigroups for which the usual Boolean operations on domains are modeled. Such algebras are capable of modeling the usual modal operators considered in dynamic logic. Indeed adding a natural functional variant of union to the signature gives a deterministic version of the modal semirings of Möller and Struth, but also a monoidal version of the classical restriction categories of Cockett and Manes. Other operations modeled are intersection and (in the finite case) functional iteration. In each case, axiomatizations of the concrete functional examples are given, leading to algebraic models of partial maps incorporating all the domain-related and set-theoretic operations previously considered. Our algebras furnish natural algebraic semantics for the logics of deterministic computer programs, leading to new results for some variants of propositional dynamic logic.

Two-sorted Point-Interval Temporal Logics

There are two natural and well-studied approaches to temporal ontology and reasoning: point-based and interval-based. Usually, interval-based temporal reasoning deals with points as particular, duration-less intervals. Here we develop explicitly two-sorted point-interval temporal logical framework whereby time instants (points) and time periods (intervals) are considered on a par, and the perspective can shift between them within the formal discourse. We focus on fragments involving only modal operators that correspond to the inter-sort relations between points and intervals. We analyze their expressiveness, comparative to interval-based logics, and the complexity of their satisfiability problems. In particular, we identify some previously not studied and potentially interesting interval logics.

A logic of agent organizations

Organization concepts and models are increasingly being adopted for the design and specification of multi-agent systems. Agent organizations can be seen as mechanisms of social order, created to achieve global (or organizational) objectives by more or less autonomous agents. In order to develop a theory on the relation between organizational structures, organizational objectives and the actions of agents fulfilling roles in the organization a theoretical framework is needed to describe organizational structures and actions of (groups of) agents. Current logical formalisms focus on specific aspects of organizations (e.g. power, delegation, agent actions, or normative issues) but a framework that integrates and relates different aspects is missing. Given the amount of aspects involved and the subsequent complexity of a formalism encompassing them all, it is difficult to realize. In this paper, a first step is taken to solve this problem. We present a generic formal model that enables to specify and relate the main concepts of an organization (including, activity, structure, environment and others) so that organizations can be analyzed at a high level of abstraction. However, for some aspects we use a simplified model in order to avoid the complexity of combining many different types of (modal) operators.

Prefixed tableaus and nested sequents

Nested sequent systems for modal logics are a relatively recent development, within the general area known as deep reasoning. The idea of deep reasoning is to create systems within which one operates at lower levels in formulas than just those involving the main connective or operator. Prefixed tableaus go back to 1972, and are modal tableau systems with extra machinery to represent accessibility in a purely syntactic way. We show that modal nested sequents and prefixed modal tableaus are notational variants of each other, roughly in the same way that Gentzen sequent calculi and tableaus are notational variants. This immediately gives rise to new modal nested sequent systems which may be of independent interest. We discuss some of these, including those for some justification logics that include standard modal operators.

The Genesis of Hi-Worlds: Towards a Principle-Based Possible World Semantics

A Leibnizian semantics proposed by Becker in 1952 for the modal operators has recently been reviewed in Copeland’s paper The Genesis of Possible World Semantics (Copeland in J Philos Logic 31:99–137, 2002), with a remark that “neither the binary relation nor the idea of proving completeness was present in Becker’s work”. In light of Frege’s celebrated Sense-Determines-Reference principle, we find, however, that it is Becker’s semantics, rather than Kripke’s semantics, that has captured the true spirit of Frege’s semantic program. Furthermore, for Kripke’s possible world semantics to fit in Frege’s framework of senses, worlds and referents, it will have to be thoroughly reformulated. By introducing the notion of a hi-world into the picture, we manage to keep the key ingredients of Becker’s semantics intact, while at the same time solve a fatal problem that used to shadow Becker’s original semantics—it had not been able to make sense of inhomogeneous modality. The resulting generalized Beckerian semantics provides, in effect, a Beckerian analysis of the Kripkean possible worlds. It reveals the subtle hierarchical internal structure of a Kripkean world that has not been discovered before.

Aristotle's Megarian Manoeuvres

Towards the end of Theta.4 of the Metaphysics, Aristotle appears to endorse the obviously invalid modal principle that the truth of A will entail the truth of B if the possibility of A entails the possibility of B. I attempt to show how Aristotle's endorsement of the principle can be seen to arise from his accepting a non-standard interpretation of the modal operators and I indicate how the principle and its interpretation are of independent interest, quite apart from their role in understanding Aristotle.

PHYSARUM SPATIAL LOGIC

Plasmodium of Physarum polycephalum is a large single cell capable for distributed sensing, information processing, decentralized decision-making and collective action. In the paper, we interpret basic features of the plasmodium foraging behavior in terms of process calculus and spatial logic and show that this behavior could be regarded as one of the natural implementations of spatial logic without modal operators.

Two-Dimensional Description Logics for Context-Based Semantic Interoperability

Description Logics (DLs) provide a clear and broadly accepted paradigm for modeling and reasoning about terminological knowledge. However, it has been often noted, that although DLs are well-suited for representing a single, global viewpoint on an application domain, they offer no formal grounding for dealing with knowledge pertaining to multiple heterogeneous viewpoints — a scenario ever more often approached in practical applications, e.g. concerned with reasoning over distributed knowledge sources on the Semantic Web. In this paper, we study a natural extension of DLs, in the style of two-dimensional modal logics, which supports declarative modeling of viewpoints as contexts, in the sense of McCarthy, and their semantic interoperability. The formalism is based on two-dimensional semantics, where one dimension represents a usual object domain and the other a (possibly infinite) domain of viewpoints, addressed by additional modal operators and a metalanguage, on the syntactic level. We systematically introduce a number of expressive fragments of the proposed logic, study their computational complexity and connections to related formalisms.

Cut Elimination and Realization for Epistemic Logics with Justification

Epistemic logics with justification, S4LP and S4LPN, are combinations of the modal epistemic logic S4 and the Logic of Proofs LP, with some connecting principles. These logics together with the modal knowledge operator F (F is known), contain infinitely many operators of the form t :F (t is a justification for F), where t is a term. Regarding the Realization Theorem of S4, LP is the justification counterpart of S4, in the sense that, every theorem of S4 can be transformed into a theorem of LP (by replacing all occurrences of by suitable terms), and vise versa. In this article, we first introduce a new cut-free sequent calculus LPLG for LP, and then extend it to obtain a cut-free sequent calculus for S4LP and a cut-free hypersequent calculus for S4LPN. All cut elimination theorems are proved syntactically. Moreover, these sequent systems enjoy a weak subformula property. Then, we show that theorems of S4LP can be realized in LP and theorems of S4LPN can be realized in JS5 (the justification counterpart of modal logic S5). Consequently, we prove that S4LP and S4LPN are conservative extensions of LP.

PSPACE Tableau Algorithms for Acyclic Modalized $\boldsymbol{\mathcal{ALC}}$

We study \(\mathcal{ALCK}_m\) and \(\mathcal{ALCS}4_m\), which extend the description logic \(\mathcal{ALC}\) by adding modal operators of the basic multi-modal logics Km and S4m. We develop a sound and complete tableau algorithm \(\Lambda_\mathcal{K}\) for answering \(\mathcal{ALCK}_m\) queries w.r.t. an \(\mathcal{ALCK}_m\) knowledge base with an acyclic TBox. Defining tableau expansion rules in the presence of acyclic definitions by considering only the concept names on the left-hand side of TBox definitions or their negations, allows us to give a PSPACE implementation for \(\Lambda_\mathcal{K}\). We then consider answering \(\mathcal{ALCS}4_m\) queries w.r.t. an \(\mathcal{ALCS}4_m\) knowledge base (with an acyclic TBox) in which the epistemic operators correspond to those of classical multi-modal logic S4m. The expansion rules in the tableau algorithm ΛS4 are designed to syntactically incorporate the epistemic properties. Blocking is corporated into the tableau expansion rules to ensure termination. We also provide a PSPACE implementation for ΛS4. In light of the fact that the satisfiability problem for \(\mathcal{ALCK}_m\) with general TBox and no epistemic properties (i.e., \(\mathbf{K}_{\mathcal{ALC}}\)) is NEXPTIME-complete, we conclude that both \(\mathcal{ALCK}_m\) and \(\mathcal{ALCS}4_m\) offer computationally manageable and practically useful fragments of \(\mathbf{K}_{\mathcal{ALC}}\).

Computing Distances between Probabilistic Automata

We present relaxed notions of simulation and bisimulation on Probabilistic Automata (PA), that allow some error epsilon. When epsilon is zero we retrieve the usual notions of bisimulation and simulation on PAs. We give logical characterisations of these notions by choosing suitable logics which differ from the elementary ones, L with negation and L without negation, by the modal operator. Using flow networks, we show how to compute the relations in PTIME. This allows the definition of an efficiently computable non-discounted distance between the states of a PA. A natural modification of this distance is introduced, to obtain a discounted distance, which weakens the influence of long term transitions. We compare our notions of distance to others previously defined and illustrate our approach on various examples. We also show that our distance is not expansive with respect to process algebra operators. Although L without negation is a suitable logic to characterise epsilon-(bi)simulation on deterministic PAs, it is not for general PAs; interestingly, we prove that it does characterise weaker notions, called a priori epsilon-(bi)simulation, which we prove to be NP-difficult to decide.

Logics for information systems and their dynamic extensions

The article proposes logics for information systems , which provide information about a set of objects regarding a set of attributes. Both “ complete ” and “ incomplete ” information systems are dealt with. The language of these logics contains modal operators, and constants corresponding to attributes and attribute values. Sound and complete deductive systems for these logics are presented, and the problem of decidability is addressed. Furthermore, notions of information and information update are defined, and dynamic extensions of the above logics are presented to accommodate these notions. A set of reduction axioms enables us to obtain a complete axiomatization of the dynamic logics.

Da ética do dever-ser a ética do diálogo

Este artigo tem o objetivo de demonstrar a aparente contradição do pensamento hegeliano. A tentativa de Hegel é unir a substância de Espinosa com o “Eu” de Kant, ou seja, necessidade e contingência. Como sabemos este projeto é inacabado, e um operador modal, ou seja, um dever-ser cósmico mais fraco que o dever-ser kantiano perpassando todo o sistema, não resolve esta questão. Refletir sobre esta problemática nos conduz ao conceito de ética do diálogo em Gadamer sendo possível nos levar em direção a uma estrutura ética intersubjetiva. Portanto, deve-se postular tal questão "ab initio” para justificar o caminho da presente argumentação, que ao reconhecer essa dimensão de encontro do humano, defende o diálogo hermenêutico como cerne dessa estrutura ética. Em Gadamer existe um convite para um reconhecimento do que esta em jogo: o diálogo. No horizonte da perspectiva hermenêutica, o diálogo constitui-se em uma práxis, uma postura fundamentalmente ética.

Time-Dependent Cryptographic Protocol Logic and Its Formal Semantics

PDF HTML阅读 XML下载 导出引用 引用提醒 时间相关密码协议逻辑及其形式化语义 DOI: 10.3724/SP.J.1001.2011.03732 作者: 作者单位: 作者简介: 通讯作者: 中图分类号: 基金项目: 国家自然科学基金(60873260, 60903210); 国家高技术研究发展计划(863)(2009AA01Z414); 国家重点基础研究发展计划(973)(2007CB311202); 江苏省自然科学基金(BK2008090) Time-Dependent Cryptographic Protocol Logic and Its Formal Semantics Author: Affiliation: Fund Project: 摘要 | 图/表 | 访问统计 | 参考文献 | 相似文献 | 引证文献 | 资源附件 | 文章评论 摘要:在密码协议中,主体的认知与信仰状态是随时间推移而不断变化的.为了在协议分析中体现这种动态性,提出一种时间相关密码协议逻辑.该逻辑基于谓词模态逻辑,通过在谓词及模态词中引入时间参数以体现时间因素,使得逻辑可表达各个主体在协议不同时间点的行为、知识及信仰.给出该逻辑的形式化语义,在避免逻辑语言二义性的同时保证了逻辑的可靠性.该语义基于Kripke 结构,将可能世界建立在主体局部世界与时间局部世界的基础上,使得任一可能世界能够反映协议的一个可能的全过程.该逻辑为密码协议,特别是时间相关密码协议提供了灵活的分析方法,增强了基于逻辑方法的协议分析能力. Abstract:In cryptographic protocols, the agent’s epistemic and doxastic states are changeable over time. To model these dynamics, a time-dependent cryptographic protocol logic is proposed. Our logic is based on the predicate modal logic and the time factor can be expressed in it by invoking a time variable as a parameter of predicates and modal operators. This makes it possible to model every agent’s actions, knowledges and beliefs at different time points. We also give the formal semantics of our logic to avoid the ambiguity of its language and make the logic sound. The semantics is based on the kripke structure and the possible world in it is built both on the local world of agent and the specific world of time. This makes every possible world can give a global view of each point of the protocol. Our logic provides a flexible method for analyzing the cryptographic protocols, especially the time-dependent cryptographic protocols, and increases the power of the logical method for analyzing protocols. 参考文献 相似文献 引证文献

Conceptual modeling in full computation-tree logic with sequence modal operator

In this paper, we propose a method for modeling concepts in full computation-tree logic with sequence modal operators. An extended full computation-tree logic, CTLS*, is introduced as a Kripke semantics with a sequence modal operator. This logic can appropriately represent hierarchical tree structures in cases where sequence modal operators in CTLS* are applied to tree structures. We prove a theorem for embedding CTLS* into CTL*. The validity, satisfiability, and model-checking problems of CTLS* are shown to be decidable. An illustrative example of biological taxonomy is presented using CTLS* formulas. © 2011 Wiley Periodicals, Inc. (This paper is an extended version of Kamide and Kaneiwa.)

Algebraic models of deviant modal operators based on de Morgan and Kleene lattices

An algebraic model of a kind of modal extension of de Morgan logic is described under the name MDS5 algebra. The main properties of this algebra can be summarized as follows: (1) it is based on a de Morgan lattice, rather than a Boolean algebra; (2) a modal necessity operator that satisfies the axioms N, K, T, and 5 (and as a consequence also B and 4) of modal logic is introduced; it allows one to introduce a modal possibility by the usual combination of necessity operation and de Morgan negation; (3) the necessity operator satisfies a distributivity principle over joins. The latter property cannot be meaningfully added to the standard Boolean algebraic models of S5 modal logic, since in this Boolean context both modalities collapse in the identity mapping. The consistency of this algebraic model is proved, showing that usual fuzzy set theory on a universe U can be equipped with a MDS5 structure that satisfies all the above points (1)–(3), without the trivialization of the modalities to the identity mapping. Further, the relationship between this new algebra and Heyting-Wajsberg algebras is investigated. Finally, the question of the role of these deviant modalities, as opposed to the usual non-distributive ones, in the scope of knowledge representation and approximation spaces is discussed.

Complex-coupled photonic crystal THz lasers with independent loss and refractive index modulation

Compared to near infra-red photonic crystal (PhC) band-edge lasers, achieving vertical emission with quantum cascade (QC) material operating in the THz range needs dedicated engineering because the TM polarized emission of QCLs favors in-plane emitting schemes and the currently used double plasmon waveguide, prevents vertical light extraction. We present an approach with independent refractive index and extraction losses modulation. The extraction losses are obtained with small extracting holes located at appropriate positions. The modal operation of the PhC is shown to critically depend on the external losses introduced. Very high surface emission power for optimum loss extractor design is achieved.

Reasoning About Permitted Announcements

We formalize what it means to have permission to say something. We adapt the dynamic logic of permission by van der Meyden (J Log Comput 6(3):465–479, 1996) to the case where atomic actions are public truthful announcements. We also add a notion of obligation. Our logic is an extension of the logic of public announcements introduced by Plaza (1989) with dynamic modal operators for permission and for obligation. We axiomatize the logic and show that it is decidable.

Ell Secure Information System Using Modal Logic Technique

In this paper, the authors propose a formal logic technique to protect information systems. As the widespread use of computer systems grows, the security of the information stored in such systems has become more important. As a security mechanism, authorization or access control ensures that all accesses to the system resources occur exclusively according to the access polices and rules specified by the system security agent. Authorization specification has been widely studied and a variety of approaches have been investigated. The authors propose a formal language with modal logic to specify the system security policies. The authors also provide the reasoning in response to system access requests, especially in situations where the security agent’s knowledge base is incomplete. The semantics of this language is provided by translating it into epistemic logic program in which knowledge related modal operators are employed to represent agents’ knowledge in reasoning. The authors demonstrate how this approach handles the situation where the security agent’s knowledge on access decision is incomplete. The proposed mechanism effectively prevents unauthorized and malicious access to information systems.

The γ-admissibility of Relevant Modal Logics II — The Method using Metavaluations

The γ/em>-admissibility is one of the most important problems in the realm of relevant logics. To prove the γ-admissibility, either the method of normal models or the method using metavaluations may be employed. The γ-admissibility of a wide class of relevant modal logics has been discussed in Part I based on a former method, but the γ-admissibility based on metavaluations has not hitherto been fully considered. Sahlqvist axioms are well known as a means of expressing generalized forms of formulas with modal operators. This paper shows that γ is admissible for relevant modal logics with restricted Sahlqvist axioms in terms of the method using metavaluations.