A miracle happens In one hand we have a class of marvelously complex theories in predicate logic theories with su cient coding potential like PA Peano Arithmetic or ZF Zermelo Fraenkel Set Theory In the other we have certain modal propositional theories of striking simplicity We translate the modal operators of the modal theories to certain speci c xed de ned predicates of the predicate logical...

In recent years a wide variety of intensional modal-like logics with the propositional operators determined by relations play an important role in a number of application areas such as spatial reasoning, cognitive agent technologies, knowledge-based systems, etc. Many of these applications require much more involved logical systems than the ordinary modal logics can offer. In one direction, one...

Epistemic modal operators give rise to something very like, but also very unlike, Moore’s paradox. I set out the puzzling phenomena, explain why a standard relational semantics for these operators cannot handle them, and recommend an alternative semantics. A pragmatics appropriate to the semantics is developed and interactions between the semantics, the pragmatics, and the definition of consequ...

In this paper several systems of modal logic based on four-valued matrices are presented. We start with pure modal logics, i.e. modal logics with modal operators as the only operators, using the Polish framework of structural consequence relation. We show that with a four-valued matrix we can define modal operators which have the same behavior as in pure S5 (S5 with only modal operators). We th...

It is well known that modal satisfiability is PSPACEcomplete [Lad77]. However, the complexity may decrease if we restrict the set of propositional operators used. Note that there exist an infinite number of propositional operators, since a propositional operator is simply a Boolean function. We completely classify the complexity of modal satisfiability for every finite set of propositional oper...

The theory of rough sets is an extension of set theory with two additional unary set-theoretic operators deened based on a binary relation on the universe. These two operators are related to the modal operators in modal logics. By exploring the relationship between rough sets and modal logics, this paper proposes and examines a number of extended rough set models. By the properties satissed by ...

In this paper, we study modal operator F α,β in intuitionistic fuzzy subgroup of a group and derive some results. 1. Introduction The idea of intuitionistic fuzzy sets (IFSs) was given by [1, 2] to generalize the notion of fuzzy sets (FSs). Intuitionistic fuzzy modal operator was defined by Atanassov in [3]. The modal operators have been known to be important tools for IFSs where the operators ...

Modal Logic is traditionally concerned with the intensional operators \possibly" and \necessary", whose intuitive correspondence with the standard quantiiers \there ex-ists" and \for all" comes out clearly in the usual Kripke semantics. This observation underlies the well-known translation from modal logic into the rst-order language over possible worlds models 12, 13]. In this way, modal forma...