Modal operator

About: Modal operator is a research topic. Over the lifetime, 1151 publications have been published within this topic receiving 22865 citations. The topic is also known as: modal connective.

A temporal logic for Markov chains

Abstract: Most models of agents and multi-agent systems include information about possible states of the system (that defines relations between states and their external characteristics), and information about relationships between states. Qualitative models of this kind assign no numerical measures to these relationships. At the same time, quantitative models assume that the relationships are measurable, and provide numerical information about the degrees of relations. In this paper, we explore the analogies between some qualitative and quantitative models of agents/processes, especially those between transition systems and Markovian models.Typical analysis of Markovian models of processes refers only to the expected utility that can be obtained by the process. On the other hand, modal logic offers a systematic method of describing phenomena by combining various modal operators. Here, we try to exploit linguistic features, offered by propositional modal logic, for analysis of Markov chains and Markov decision processes. To this end, we propose Markov temporal logic - a multi-valued logic that extends the branching time logic CTL*.

A definition of secure dependencies using the logic of security

Abstract: In the context of the modal logic of security, confidentiality is defined by the formula K/sub B/ phi to R/sub B/ phi that could be read 'If B knows phi then B should have the permission to know phi '. The authors propose a new semantics for the R/sub B/ modal operator, such that the definition of security would allow a certain number of dependencies (called secure dependencies) between objects of the system. They formally compare this definition of security with non-interference, non-deducibility and generalized non-interference, especially with respect to assumptions on the systems as non-determinism and input-totalness. >

Algebraic semantics for quasi-classical modal logics

Abstract: A well-known result, going back to the twenties, states that, under some reasonable assumptions, any logic can be characterized as the set of formulas satisfied by a matrix 〈 , F 〉, where is an algebra of the appropriate type, and F a subset of the domain of , called the set of designated elements. In particular, every quasi-classical modal logic—a set of modal formulas, containing the smallest classical modal logic E , which is closed under the inference rules of substitution and modus ponens—is characterized by such a matrix, where now is a modal algebra, and F is a filter of . If the modal logic is in fact normal, then we can do away with the filter; we can study normal modal logics in the setting of varieties of modal algebras. This point of view was adopted already quite explicitly in McKinsey and Tarski [8]. The observation that the lattice of normal modal logics is dually isomorphic to the lattice of subvarieties of a variety of modal algebras paved the road for an algebraic study of normal modal logics. The algebraic approach made available some general results from Universal Algebra, notably those obtained by Jonsson [6], and thereby was able to contribute new insights in the realm of normal modal logics [2], [3], [4], [10]. The requirement that a modal logic be normal is rather a severe one, however, and many of the systems which have been considered in the literature do not meet it. For instance, of the five celebrated modal systems, S1–S5, introduced by Lewis, S4 and S5 are the only normal ones, while only SI fails to be quasi-classical. The purpose of this paper is to generalize the algebraic approach so as to be applicable not just to normal modal logics, but to quasi-classical modal logics in general.

A Van Benthem/Rosen theorem for coalgebraic predicate logic

Abstract: Coalgebraic modal logic serves as a unifying framework to study a wide range of modal logics beyond the relational realm, including probabilistic and graded logics as well as conditional logics and logics based on neighbourhoods and games. Coalgebraic predicate logic (CPL), a generalization of a neighbourhood-based first-order logic introduced by Chang, has been identified as a natural first-order extension of coalgebraic modal logic, which in particular coincides with the standard first-order correspondence language when instantiated to Kripke-style relational modal operators. Here, we generalize to the CPL setting the classical van Benthem/Rosen theorem stating that both over arbitrary and over finite models, modal logic is precisely the bisimulation-invariant fragment of first-order logic. As instances of this generic result, we obtain corresponding characterizations for, e.g. conditional logic, neighbourhood logic (i.e. classical modal logic) and monotone modal logic.

Die Modalpartikeln ja, doch und schon : Zu ihrer Syntax, Semantik und Pragmatik

Abstract: The aim of this thesis is to show how modal particles can be integrated into a modular description of language where grammar and pragmatics are seen as two independent but interacting modules. The modular approach is chosen because of the problems connected with a functional approach. On the syntactic level, it is assumed that modal particles are XPs. The fact that modal particles cannot occur alone in the initial field of a clause has, presumably, semantic-pragmatic reasons. It is also argued that the many positions possible for modal particles in a clause can be accounted for by assuming that they are generated in one special position in the (theoretical) syntactic structure, namely as adjuncts to the highest VP, and that other constituents may move past them for information structural reasons that have to do with the interaction of the grammatical focus-background structure and the pragmatic theme-rheme structure. In the light of the differences between the various occurrences of the words ja, doch and schon, modal particles are regarded as a category of their own, separated from categories such as adverbs, focus particles and sentence equivalents. On the semantic level, it is shown that the modular approach makes it possible to minimalistically assume one semantic form per modal particle, irrespective of stress. In the case of the modal particles ja, doch and schon, it is argued that they are non-referential and non-attitudinal. It is suggested that, in view of their common feature, ‘affirmative1, they be analysed as expressions of facticity. They are represented by an operator in a duality group based on the operator FAKT. The meaning is compositionally integrated into the meaning of a clause at the level of semantic form, where it takes scope over the proposition [e INST p]. It interacts with other modal particles and sentence adverbials, the order of which shows the scope relations. Finally, on the pragmatic level, it is maintained that there is no inherent connection between modal particles and the focus-background structure or the theme-rheme structure. Moreover, modal particles do not even seem to be included in the theme-rheme structure. However, they take part in the focus-background structure and may be focussed themselves. The functions of modal particles are derived from their meaning in interaction with the illocutionary force or the sentence mood, the Principle of Relevance, and stress. The functions thus derived are a strengthening or a weakening effect on assertions, the triggering of implicatures, and the indication of the type of relation between the utterance concerned and the context.