We examine a certain modal consequence relation, and define the notion of validity of a modal sequent on a frame. We demonstrate that it is possible to define classes of frames. not definable by modal formulas, by modal sequents. Through the use of modal algebras and general frames, we obtain a characterization of modal sequent-definable classes of frames which are also first-order definable, a...

In this paper, we investigate the Lukasiewicz’s 4-valued modal logic based on the Aristotele’s modal syllogistic. We present a new interpretation of the set of algebraic truth values by introducing the truth and knowledge orderings similar to those in Belnap’s 4-valued bilattice but by replacing the original Belnap’s negation with the lattice pseudo-complement instead. Based on it, we develop a...

In this paper, newly defined level operators and modal-like operators over extensional generalized intuitionistic fuzzy sets (GIFSB) are proposed. Some of the basic properties of the new operators are discussed.

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...

Bisimulation quantifiers are a natural extension of modal logics. They preserve the bisimulation invariance of modal logic, while allowing monadic second-order expressivity. Unfortunately, it is not the case that extension by bisimulation quantifiers always preserves the decidability of a modal logic. Here we examine a general class of modal logics for which decidability is preserved under exte...

Nominalizations describing events and tropes have a received considerable interest in the semantic (and philosophical) literature. By contrast, nominalizations of modal predicates and the modal objects they describe have received little, if any, attention in the literature so far. This paper is a case study of nominalizations of the sort need and possibility as well as permission, obligation, i...

We set up a generic framework for proving completeness results for variants of the modal mucalculus, using tools from coalgebraic modal logic. We illustrate the method by proving two new completeness results: for the graded mu-calculus (which is equivalent to monadic second-order logic on the class of unranked tree models), and for the monotone modal mu-calculus. Besides these main applications...

Recent work with autonomous modal parameter estimation has shown great promise in the quality of the modal parameter estimation results when compared to results from experienced user interaction using traditional methods. Current research with the Common Statistical Subspace Autonomous Mode Identification (CSSAMI) procedure involves the integration of multiple modal parameter estimation algorit...