Modal logic is used by game theorists in the form of epistemic modal logic, where the operator is interpreted as a knowledge operator. This is useful because it allows the knowledge of players in games to be formalized and included in models of games. Then outcomes can be characterized by this knowledge, leading to theorems of the form “in games of type x, if all players have knowledge y, then ...

Propositional μ-calculus is an extension of the propositional modal logic with the least fixpoint operator. In the paper introducing the logic Kozen posed a question about completeness of the axiomatisation which is a small extension of the axiomatisation of the modal system K. It is shown that this axiomatisation is complete.

In this paper, we generalize the set-theoretic translation method for polymodal logic introduced in 11] to extended modal logics. Instead of devising an ad-hoc translation for each logic, deening a new set-theoretic function symbol for each new modal operator, we develop a general framework within which a number of extended modal logics can be dealt with. More precisely, we extend the basic set...

In this paper we present completeness results of several fuzzy logics trying to capture different notions of necessity (in the sense of Possibility theory) for Gödel logic formulas. In a first attempt, based on different characterizations of necessity measures on fuzzy sets, a group of logics, with Kripke style semantics, are built over a restricted language, indeed a two level language compose...

Di erent interval modal logics have been proposed for reasoning about the temporal behaviour of digital systems. Some of them are purely propositional and only enable the speci cation of qualitative time requirements. Others, such as ITL and the duration calculus, are rst order logics which support the expression of quantitative, real-time requirements. These two logics have in common the prese...

Let T be an arithmetical theory. We introduce a unary modal operator T to be interpreted arithmetically as the unary interpretability predicate over T. We present complete axiomatizations of the (unary) interpretability principles underlying two important classes of theories. We also prove some basic modal results about these new axiomatizations.

We present a novel multi-modal evidence fusion method for highlevel feature (HLF) detection in videos. The uni-modal features, such as color histogram, transcript texts, etc, tend to capture different aspects of HLFs and hence share complementariness and redundancy in modeling the contents of such HLFs. We argue that such inter-relation are key to effective multi-modal fusion. Here, we formulat...

We introduce a modal language L which is obtained from standard modal logic by adding the diierence 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 F O 2 of rst-order logic but speaks less succinctly about relational structures: if the number of relations ...

We present a terminating tableau system for the modal logic K∗. K∗ extends the basic modal logic K with a reflexive transitive closure operator for relations and is a proper fragment of propositional dynamic logic. We investigate two different approaches to achieve termination, namely chain-based blocking and pattern-based blocking. Pattern based-blocking has not been applied to a modal logic w...