Inspired by Hintikka’s treatment of question embedding verbs in [8] and the variations of noncontingency operator, we propose a logic with strong noncontingency operator N as the only primitive modality. A proposition is strongly noncontingent, if no matter whether it is true or false, it does it necessarily; otherwise, it is weakly contingent. This logic is not a normal modal logic, since N(φ ...

Using only a simple transition relation one cannot model commands that may or may not terminate in a given state. In a more general approach commands are relations enriched with termination vectors. We reconstruct this model in modal Kleene algebra. This links the recursive definition of the do od loop with a combination of the Kleene star and a convergence operator. Moreover, the standard wp o...

We reanalyze the proton decay in the minimal SU(5) SUGRA GUT model. Unlike previous analyses, we take into account a Higgsino dressing diagram of dimension 5 operator with right-handed matter fields (RRRR operator). It is shown that this diagram gives a dominant contribution for p → Kντ over that from LLLL operator, and decay rate of this mode can be comparable with that of p → Kνμ which is dom...

We reanalyze the proton decay in the minimal SU(5) SUGRA GUT model. Unlike previous analyses, we take into account a Higgsino dressing diagram of dimension 5 operator with right-handed matter fields (RRRR operator). It is shown that this diagram gives a dominant contribution for p → Kντ over that from LLLL operator, and decay rate of this mode can be comparable with that of p → Kνμ which is dom...

We consider some modal languages with a modal operator D whose semantics is based on the relation of inequality. Basic logical properties such as definability, expressive power and completeness are studied. Also, some connections with a number of other recent proposals to extend the standard modal language are pointed at. ?

The behavior of the disjunctive operator, defined by Balas, Ceria and Cornuéjols, in the context of the “antiblocker duality diagram” associated with the stable set polytope,QSTAB(G), of a graph and its complement, was first studied byAguilera, Escalante and Nasini. The authors prove the commutativity of this diagram in any number of iterations of the disjunctive operator. One of the main conse...

In this paper we present refinement modal logic. A refinement is like a bisimulation, except that from the three relational requirements only ‘atoms’ and ‘back’ need to be satisfied. Our logic contains a new operator ∀ in additional to the standard modalities 2 for each agent. The operator ∀ acts as a quantifier over the set of all refinements of a given model. We call it the refinement operato...

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...