The basic modal operator bounded until of Metric Temporal Logic (MTL) comes in several variants. In particular it can be strict (when it does not constrain the current instant) or not, and matching (when it requires its two arguments to eventually hold together) or not. This paper compares the relative expressiveness of the resulting MTL variants over dense time. We prove that the expressivenes...

It is well-known that satisfiability (and hence validity) in the minimal classical modal logic is a PSPACE-complete problem. In this paper we consider the satisfiability and validity problems (here they are not dual, although mutually reducible) for the minimal modal logic over a finite Lukasiewicz chain, and show that they also are PSPACE-complete. This result is also true when adding either t...

Modifier logics are considered as generalizations of "classiea1" modal logics. Thus modifier logics are soeanled multimodal logios. Multimodality means here that the basic logics are modal logics with graded modalities. The interpretation of modal operators is more generan, too. Leibniz's mottvating semantical ideas (see [8]. p. 20-21) givejustification to these generalizations. Semantics of ca...

Processes of timed process algebras may be modelled as timed transition systems and modal and temporal logics can be used to express properties of transition systems. This paper introduces an extension to propositional modal-calculus with an additional modal operator. This quantitative box operator is used to express quantitative properties of timed transition systems. Deenabil-ity of important...

An extension of the concept description language ACC used in KL-ONE-like terminological reasoning is presented. The extension includes multi-modal operators that can either stand for the usual role quantifications or for modalities such as belief, time etc. The modal operators can be used at all levels of the concept terms, and they can be used to modify both concepts and roles. This is an inst...

Every endofunctor B on the category Set can be lifted to a fibred functor on the category (fibred over Set) of equivalence relations and relation-preserving functions. In this paper, the least (fibre-wise) of such liftings, L(B), is characterized for essentially any B. The lifting has all the useful properties of the relation lifting due to Jacobs, without the usual assumption of weak pullback ...

Many languages allow for ”fake” uses of their past tense marker: the marker can occur in certain contexts without conveying temporal pastness. Instead it appears to bear a modal meaning. Iatridou [2000] has coined this phenomenon Fake Tense. Fake Tense is particularly common to conditional construction. This paper proposes to explain Fake Tense in English conditional sentences as a certain kind...

Granular reasoning proposed by Murai et al. is a mechanism for reasoning using granular computing, and the concept of “focus” has been proposed as a key concept of granular reasoning. On the other hand, the authors have proposed another concept of granularity, called “visibility”. In this paper, we try to capture the concepts of visibility and focus as modalities of modal logics by introducing ...

We define the notion of a model of higher-order modal logic in an arbitrary elementary topos E . In contrast to the wellknown interpretation of (non-modal) higher-order logic, the type of propositions is not interpreted by the subobject classifier ΩE , but rather by a suitable complete Heyting algebra H . The canonical map relating H and ΩE both serves to interpret equality and provides a modal...

in terms of de dicto necessity, necessity conceived as a property of propositions or sentences. The heart of Plantinga's theory is his scheme for the reduction of de re modal sentences to equivalent de dicto ones. The idea is to provide an equivalent sentence containing no modal operators within the scope of a quantifier for every sentence asserting that some thing is necessarily or essentially...