In this paper, we consider the influence of trust on the assimilation of acquired information into an agent’s belief. By use of modal logic, we semantically and axiomatically characterize the relationship among belief, information acquisition and trust. The belief and information acquisition operators are respectively represented by KD45 and KD normal modalities, whereas trust is denoted by a m...

In a range of contexts, one comes across processes resembling inference, but where input propositions are not in general included among outputs, and the operation is not in any way reversible. Examples arise in contexts of conditional obligations, goals, ideals, preferences, actions, and beliefs. Our purpose is to develop a theory of such input/output operations. Four are singled out: simplemin...

We propose a new version of formula size game for modal logic. The game characterizes the equivalence of pointed Kripke-models up to formulas of given numbers of modal operators and binary connectives. Our game is similar to the well-known Adler-Immerman game. However, due to a crucial difference in the definition of positions of the game, its winning condition is simpler, and the second player...

In this paper, we construct a new concept description language intended for representing dynamic and intensional knowledge. The most important feature distinguishing this language from its predecessors in the literature is that it allows applications of modal operators to all kinds of syntactic terms: concepts, roles and formulas. Moreover, the language may contain both local (i.e., state-depen...

We develop an algebraic frame for the simultaneous treatment of actual and possible properties of quantum systems. We show that, in spite of the fact that the language is enriched with the addition of a modal operator to the orthomodular structure, contextuality remains a central feature of quantum systems.

Recent work within the eld of Categorial Grammar has seen the development of approaches that allow diierent modes of logical behaviour to be displayed within a single system, something corresponding to making available diiering modes of linguistic description. Earlier attempts to achieve this goal have employed modal operators called structural modalities, whose use presents a number of problem...

This paper is an exploration in the light of modal logic of Dunn’s ideas about two treatments of negation in non-classical logics: perp and star. We take negation as an impossibility modal operator and choose the base positive logic to be distributive lattice logic (DLL). It turns out that, if we add one De Morgan law and contraposition to DLL (call this system K−), then we can prove a natural ...

In the context of the modal logic of security, conden-tiality is dened by the formula K B ' ! R B ' that could be read \ If B knows ' then B should have the permission to know '". We propose a new semantics for the R B modal operator, such that the denition of security would allow a certain number of dependencies (called secure dependencies) between objects of the system. We formally compare th...

We study prefixed tableaux for first-order multi-modal logic, providing proofs for soundness and completeness theorems, a Herbrand theorem on deductions describing the use of Herbrand or Skolem terms in place of parameters in proofs, and a lifting theorem describing the use of variables and constraints to describe instantiation. The general development applies uniformly across a range of regime...

We propose a general and uniform modal framework for the Event Calculus (EC) and its skeptical and credolous variants. The resulting temporal formalism, called the Generalized Modal Event Calculus (GMEC), extends considerably the expressive power of EC when information about the ordering of events is incomplete. It provides means of inquiring about the evolution of the maximal validity interval...