Modal Logic is traditionally concerned with the intensional operators “possibly” and “necessary”, whose intuitive correspondence with the standard quantifiers “there exists” and “for all” comes out clearly in the usual Kripke semantics. This observation underlies the well-known translation from propositional modal logic with operators ♦ and , possibly indexed, into the first-order language over...

Sometimes it is needed in approximate reasoning to deal simultaneously with both fuzziness of propositions and modalities, for instance one may try to assign a degree of truth to propositions like “John is possibly tall”or “John is necessarily tall”, where “John is tall”is presented as a fuzzy proposition. Fuzzy logic should be a suitable tool to model not only vagueness but also other kinds of...

The paper considers the set ML1 of rst-order polymodal formulas the modal operators in which can be applied to subformulas of at most one free variable. Using the mosaic technique, we prove a general satissability criterion for formulas in ML1 which reduces the modal satissability to the classical one. The criterion is then used to single out a number of new, in a sense optimal, decidable fragm...

We introduce the modal system BT which is a multi-modal language designed to talk about trust and belief of two agents. The belief operators are based on modal system KS. This gives the main difference with already known system BA introduced by Churn-Jung Liau [2] and also carries its own intuitive meaning. As a main result we prove that BT is sound and complete with respect to the given semant...

The paper considers the set ML1 of rst-order polymodal formulas the modal operators in which can be applied to subformulas of at most one free variable. Using the mosaic technique, we prove a general satissability criterion for formulas in ML1 which reduces the modal satissability to the classical one. The criterion is then used to single out a number of new, in a sense optimal, decidable fragm...

The system description presents the conception and a prototypical implementation of a multi-context system, used for computing and implementing temporal modalities within given data without the use of modal operators. Instead, an external constraint based rule system is used for computing the corresponding temporal relations, making use of the way a multi-context system works for transporting t...

The BDI model of agency is a well studied concept in Formal Logic for Rational Agents, mainly through the BDICTL [7] and KARO [7] logical frameworks. The former is based on the Branching Time Logic CTL [3], whereas the latter in based on Dynamic Logic [4]. Both have advantages and disadvantages, but the union of some properties of both frameworks provide, in our opinion, all the formal tools th...

for the first time in the history of logic, abd al razzaq al-jili (d. 570/1174), in the treatise al-lame fi al-shakl al-rabe, dealt with the modal syllogisms of the fourth figure. previous to him, dinha, the priest, and ibn salah al-hamadani had discussed the non-modal moods of the fourth figure. jili’s treatise deals only with simple modalities and ignores the complex ones. his pupil, fakhr al...

This paper is a survey and systematic presentation of decidability and complexity issues for modal and non-modal two-variable logics. A classical result due to Mortimer says that the two-variable fragment of rst-order logic, denoted FO 2 , has the nite model property and is therefore decidable for satissability. One of the reasons for the signiicance of this result is that many propositional mo...

Context-sensitivity has been for long a subject of study in linguistics, logic and computer science. Recently the problem of representing and reasoning with contextual knowledge has been brought up in the research on the Semantic Web. In this paper we introduce a conservative extension to Description Logic, the formalism underlying Web Ontology Languages, supporting representation of ontologies...