Allowing the student to have some control over the diagnosis inspecting and changing the model the system has made of him is a feasible approach in student modelling which tracks the dynamics of student behaviour and provides for reflective learning. We present an approach for maintaining the student model in interactive diagnosis where a computer and a student discuss about the student's knowl...

In this paper, we investigate the Lukasiewicz’s 4-valued modal logic based on the Aristotele’s modal syllogistic. We present a new interpretation of the set of algebraic truth values by introducing the truth and knowledge orderings similar to those in Belnap’s 4-valued bilattice but by replacing the original Belnap’s negation with the lattice pseudo-complement instead. Based on it, we develop a...

We investigate a modal logic of probability with a unary modal operator expressing that a proposition is more probable than its negation. Such an operator is not closed under conjunction, and its modal logic is therefore non-normal. Within this framework we study the relation of probability with other modal concepts: belief and action. We focus on the evolution of belief, and propose an integra...

In this paper we study paraconsistent negation as a modal operator, considering the fact that the classical negation of necessity has a paraconsistent behavior. We examine this operator on the one hand in the modal logic S5 and on the other hand in some new four-valued modal logics.  2004 Published by Elsevier B.V.

We define an interpretation of modal languages with polyadic operators in modal languages that use monadic operators (diamonds) only. We also define a simulation operator which associates a logic Λ in the diamond language with each logic Λ in the language with polyadic modal connectives. We prove that this simulation operator transfers several useful properties of modal logics, such as finite/r...

Harold Hodes in [1] introduces an extension of rst-order modal logic featuring a backtracking operator, and provides a possible worlds semantics, according to which the operator is a kind of device for ‘world travel’; he does not provide a proof theory. In this paper, I provide a natural deduction system for modal logic featuring this operator, and argue that the system can be motivated in ter...

The goal of the current study is to suggest a novel paradigm of epistemic modal operator originated from the disjunction. Our main data is Korean disjunction operator nka which forms a non-factual question. Examining how the modal effect in question is induced by nka, I propose that the prerequisite of nka brings about non-homogenous nonveridical (i.e. modal) spaces partitioned in equipoised ep...

Epistemic modal operators give rise to something very like, but also very unlike, Moore’s paradox. I set out the puzzling phenomena, explain why a standard relational semantics for these operators cannot handle them, and recommend an alternative semantics. A pragmatics appropriate to the semantics is developed and interactions between the semantics, the pragmatics, and the definition of consequ...

The weak epistemic modal operators might, possible, likely, and probable display embedding behaviors and scope interactions that are interestingly different from their logically stronger counterparts must and certain. I present two problematic sets of facts about these operators which have not received much attention in the literature. The first is that weak epistemic modals embed freely under ...

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.