Knowing whether a proposition is true means knowing that it is true or knowing that it is false. In this paper, we study logics with a modal operator Kw for knowing whether but without a modal operator K for knowing that. This logic is not a normal modal logic, because we do not have Kw(φ → ψ) → (Kwφ → Kwψ). Knowing whether logic cannot define many common frame properties, and its expressive po...

Modal fuzzy logics is a research topic that has attracted increasing attention in the last years. Several papers have been published treating different aspects, see for instance [6] for a modal expansion of Lukasiewicz logic, [3, 4, 2] for modal expansions of Gödel fuzzy logic, [1] for modal logics over finite residuated lattices, and more recently [7] for a modal expansion of Product fuzzy log...

Introduction and logical background Multimodal logics are an appropriate framework to represent agents, actions, time, knowledge... (see [8J, [9], [14], [18], [25] for some of its uses). For example Knowledge may be represented by means of the modal operator [K] and Time by [T]; and [K]p may be read as "p is known" and [T]p as "p will be true tomorrow". A typical modal formula is [K][T]p meanin...

Allegories are enriched categories generalizing a category of sets and binary relations. In this paper, we extend a new, recently-introduced conceptual data model based on allegories by adding support for modal operators and developing a modal interpretation of the model in any allegory satisfying certain additional (but natural) axioms. The possibility of using different allegories allows us t...

We give sound and complete analytic tableau systems for the propositional bimodal logics KB, KB C , KB 5, and KB 5C . These logics have two universal modal operators K and B , where K stands for knowing and B stands for believing. The logic KB is a combination of the modal logic S5 (for K ) and KD45 (for B ) with the interaction axioms I : Kφ → Bφ and C : Bφ → K Bφ. The logics KB C , KB 5, KB 5...

Proper epistemic knowledge bases (PEKBs) are syntactic knowledge bases that use multi-agent epistemic logic to represent nested multi-agent knowledge and belief. PEKBs have certain syntactic restrictions that lead to desirable computational properties; primarily, a PEKB is a conjunction of modal literals, and therefore contains no disjunction. Sound entailment can be checked in polynomial time,...

1. I n t r o d u c t i o n Graded normal logics ( G N L s ) are the extensions of modal normal logics to a language with graded modalities. The interpretation in usual Kripke models of a formula <>hA (n < w), whose main operator is a graded possibility, is there are more than n accessible worlds where A is true. When graded modalities were introduced (in [7], independently rediscovering a forme...

The concept of knowledge can be modelled in epistemic modal logic and, if modelled by using a standard modal operator, it is subject to the problem of logical omniscience. The classical solution to this problem is to distinguish between implicit and explicit knowledge and to construe the knowledge operator as capturing the concept of implicit knowledge. In addition, since a proposition is said ...

The main goal of this paper is to establish a nonmonotonic epistemic logic EB with two modalities – provability and belief – capable of expressing and comparing a variety of known semantics for extended logic programs, and clarify their meaning. In particular we present here, for the first time, embeddings into epistemic logic of logic programs extended with a second kind of negation under the ...