1. Modal logic Modal notions are pervasive in the meaning of a wide range of expressions from grammatical categories, such as tenses, to the lexical semantics of particular words, such as modal adverbials (probably, necessarily) and modal auxiliaries (must, may, can). The best known modalities are the alethic 1 modalities necessary and possible. Other modalities include temporal, de-ontic, epis...

Combining non-classical or`sub-classical' logics is not easy, but it is very interesting. In this paper, we combine nonclassical logics of negation and possibility in the presence of conjunction and disjunction, and then we combine the resulting systems with intuitionistic logic. We will nd that Kracht's results on the undecidability o f classical modal logics generalise to a non-classical sett...

In this paper we consider two logics: temporal logic of common knowledge and temporal logic of common belief. These logics involve the discrete time linear temporal logic operators “next” and “until”. In addition the first logic contains an indexed set of unary modal operators “agent i knows”, the second one contains an indexed set of unary modal operators “agent i believes”. Also the first log...

It has been recognised that the expressivity of description logics benefits from the introduction of non-standard modal operators beyond existential and number restrictions. Such operators support notions such as uncertainty, defaults, agency, obligation, or evidence, whose semantics often lies outside the realm of relational structures. Coalgebraic hybrid logic serves as a unified setting for ...

In this paper we discuss two hybrid languages , L(∀) and L(↓), and provide them with complete axiomatizations. Both languages combine features of modal and classical logic. Like modal languages, they contain modal operators and have a Kripke semantics. Unlike modal languages, in these systems it is possible to ‘label’ states by using ∀ and ↓ to bind special state variables . This paper explores...

We enrich propositional modal logic with operators ◇ (n ∈ N) which are interpreted on Kripke structures as “there are more than n accessible worlds for which ...”, thus obtaining a basic graded modal logic GrK. We show how some familiar concepts (such as subframes, p-morphisms, disjoint unions and filtrations) and techniques from modal model theory can be used to obtain results about expressive...

Weighted composition operators appear in the study of dynamical systems and also in characterizing isometries of some classes of Banach spaces. One of the most important generalizations of weighted composition operators, are generalized weighted composition operators which in special cases of their inducing functions give different types of well-known operators like: weighted composition operat...

This paper presents an interval-based positional logic and proves its completeness. The proposed logic combines positional operators, deened by time intervals, with modal operators used to express the subinterval relationship. Moreover, the logic can be easily extended either by including more predicates for absolute temporal references or by adding other operators for relative and periodical t...

In this paper we generalize the Apostoli-Brown strategy developed in 1] to show the completeness of a descending chain of weak aggregative modal logics with multi-ary modal operators. The logics presented here are generalization of the weak aggregative unary modal logics developed by Jennings and Schotch in the 80's.

In the paper we introduce logical calculi for representation of propositions with modal operators indexed by fuzzy values. There calculi are called Heyting-valued modal logics. We introduce the concept of a Heyting-valued Kripke model and consider a semantics of Heyting-valued modal logics at the class of Heyting-valued Kripke models.