A social network service is a platform to build social relations among people sharing similar interests and activities. The underlying structure of a social networks service is the social graph, where nodes represent users and the arcs represent the users’ social links and other kind of connections. One important concern in social networks is privacy: what others are (not) allowed to know about...

This thesis presents efficient parallel algorithms for checking temporal logic formulas over finite paths and trees. We show that LTL path checking is in AC(logDCFL) and CTL tree checking is in AC(logDCFL). For LTL with pasttime and bounded modalities, which is an exponentially more succinct logic, we show that the path checking problem remains in AC(logDCFL). Our results provide a foundation f...

My concern [...] will be with the contrast between different lessons that different philosophers think should be learned from the story Kripke told. The account of the phenomena, and of the apparatus used to describe them, that I want to defend (and to attribute to Kripke) can be seen as a variation on, and development of, the skeptical lesson about a priori knowledge and truth taught by Quine....

By studying the accessibility relations in logics of knowledge and belief, we reveal that almost all prominent nonmonotonic reasoning semantics can be characterized in terms of standard Kripke structures by altering the accessibility relation. This result not just extends the expressive power of the Kripke structure but also clearly demonstrates that the nonmonotonic reasoning is a reasoning ab...

Halpern and Vardi have proposed the notion of reenement of S5 n Kripke models in order to solve multi-agent problems in which knowledge evolves. We argue that there are some problems with their proposal and attempt to solve them by moving from Kripke models to their corresponding trees. We deene reenement of a tree with a formula, show some properties of the notion, and illustrate with the mudd...

We present a version of separation logic for modular reasoning about concurrent programs with dynamically allocated storable locks and dynamic thread creation. The assertions of the program logic are modelled by a Kripke model over a recursively defined set of worlds and the program logic is proved sound through a Kripke relation to the standard operational semantics. This constitutes an elegan...

In this paper, we introduce a class of substructural logics, called normal substructural logics, which includes not only relevant logic, BCK logic, linear logic and the Lambek calculus but also weak logics with strict implication, and de ne Kripkestyle semantics (Kripke frames and models) for normal substructural logics. Then we show a correspondence between axioms and properties on frames, and...

It has been said that modal logic consists of three main disciplines: duality theory, completeness theory and correspondence theory; and that they are the pillars on which this edifice called modal logic rests. This seems to be true if one looks at the history of modal logic, for all three disciplines have been explicitly defined around the same time, namely in the mid-seventies. While it is ce...

We introduce a class of neighbourhood frames for graded modal logic using an operation from Kripke to frames. This is shown be first-order definable but not modally definable. also obtain new definition bisimulation by modifying the monotonic bisimulation.

Graded modal logic (GML) was originally presented by Kit Fine (1972) to make the modal analogue to counting quantifiers explicit. A graded modal formula ♦k is true at a state w in a Kripke model if there are at least k successor states of w where φ is true. One open problem in GML is to show a Goldblatt-Thomason theorem for it. See M. De Rijke’s notes (2000). Recently, Katsuhiko Sano and Minghu...