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.

Half-order modal logic: how to prove real-time properties

Abstract: We introduce a novel extension of propositional modal logic that is interpreted over Kripke structures in which a value is associated with every possible woxld. These values are, however, not treated as full first-order objects; they can be accessed only by a very restricted form of quantification: the “freeze” quantifier binds a variable to the value of the current world. We present a complete proof system for this (“hulf_o4er”) modal logic. As a special case, we obtain the real-time temporal logic TPTL of [AH89]: the models are restricted to infinite sequences of states, whose values are monotonically increasing natural numbers. The ordering relation between states is interpreted as temporal precedence, while the value associated with a state is interpreted as its “real” time. We extend our proof system to be complete for TPTL, and demonstrate how it can be used to derive real-time properties.

A logic to reason about likelihood

Abstract: We present a logic LL which uses a modal operator L to help capture the notion of likely. Despite the fact that no use is made of numbers, LL can capture many of the properties of likelihood in an intuitively appealing way. Using standard techniques of modal logic, we give a complete axiomatization for LL and show that satisfiability of LL formulas can be decided in exponential time. We discuss how the logic might be used in areas where decision making is crucial, such as management and medical diagnosis, and conclude by using LL to give a formal proof of correctness of a protocol for exchanging secrets.

Combinations of Modal Logics

Abstract: There is increasing use of combinations of modal logics in both foundational and applied research areas. This article provides an introduction to both the principles of such combinations and to the variety of techniques that have been developed for them. In addition, the article outlines many key research problems yet to be tackled within this callenging area of work.

A Logical View of Secure Dependencies

Abstract: In the context of the modal logic of security, confidentiality is defined by the formula KBφ→RBφ that could be read “If B knows φ then B should have the permission to know φ”. We propose a new semantics for the RB modal operator, such that the definition of security would allow a certain number of dependencies (called secure dependencies) between objects of the system. We formally compare this new definition of security with non-interference, non-deducibility and generalized non-interference, especially with respect to assumptions of non-determinism and input-totalness.

Modal Logic and the Two-Variable Fragment

Abstract: We introduce a modal language L which is obtained from standard modal logic by adding the difference operator and modal operators interpreted by boolean combinations and the converse of accessibility relations. It is proved that L has the same expressive power as the two-variable fragment FO^2 of first-order logic but speaks less succinctly about relational structures: if the number of relations is bounded, then L-satisfiability is ExpTime-complete but FO^2 satisfiability is NExpTime-complete. We indicate that the relation between L and FO^2 provides a general framework for comparing modal and temporal languages with first-order languages.