We introduce relativized modal algebra homomorphisms and show that the category of modal algebras and relativized modal algebra homomorphisms is dually equivalent to the category of modal spaces and partial continuous p-morphisms, thus extending the standard duality between the category of modal algebras and modal algebra homomorphisms and the category of modal spaces and continuous p-morphisms...

In the context of the study of modality in interaction with time, the phenomenon whereby a modalized proposition entails its non-modal counterpart has been known as an ‘actuality entailment’ since Bhatt (1999). The question that actuality entailments raise is how modal statements can be distinguished from their non-modal counterparts and how modal contributes meaning. The main idea that the pap...

Autonomous modal parameter estimations may involve sorting a large number of possible solutions to develop one consistent estimate of the modal parameters (frequency, damping, mode shape, and modal scaling). Once the final, consistent estimate of modal parameters is established, this estimate can be compared to related solutions from the larger set of solutions to develop statistical attributes...

Modal vectors frequently have small amounts of contamination or distortion from random errors or bias errors, particularly when compared to results from modeling where normal modal vectors are the common result since damping is not included in the model. In order to understand, and possibly eliminate the contamination, tools are needed to evaluate the contamination. While the traditional modal ...

within a language whose only modal operators are the box and the diamond; other modal idioms cannot be expressed within such a language at all. Nonetheless, quantified modal logic has enjoyed considerable success in uncovering and explaining ambiguities in modal sentences and fallacies in modal reasoning. A prime example of this success is the now standard analysis of the distinction between mo...

This paper presents the Fourier and wavelet characterization of vibratio...

In this thesis, we investigate the modal logic of forcing and the modal logic of grounds of generic multiverses. Hamkins and Löwe showed that the ZFC-provable modal principles of forcing, as well as of grounds, are exactly the theorems of the modal logic S4.2 (see [16],[17]). We prove that the modal logic of forcing of any generic multiverse is also exactly S4.2 by showing that any model of ZFC...

Modal logic has a good claim to being the logic of choice for describing the reactive behaviour of systems modeled as coalgebras. Logics with modal operators obtained from so-called predicate liftings have been shown to be invariant under behavioral equivalence. Expressivity results stating that, conversely, logically indistinguishable states are behaviorally equivalent depend on the existence ...

A modal analogue of Lindstrr om's characterization of rst-order logic is proved. Basic modal logics are characterized as the only modal logics that have a notion of nite rank, or, equivalently, as the strongest modal logic whose formulas are preserved under ultra-products over !. Also, basic modal logic is the strongest classical logic whose formulas are preserved under bisimulations and ultra-...