We propose a modal logic programming language called MProlog, which is as expressive as the general modal Horn fragment. We give a fixpoint semantics and an SLD-resolution calculus for MProlog in all of the basic serial modal logics KD , T , KDB , B , KD4, S4, KD5, KD45, and S5. For an MProlog program P and for L being one of the mentioned logics, we define an operator TL,P , which has the leas...

The purpose of this article is modal analysis of ionic polymer metal composite beams, then briefing the system to the unique parameters to help in up modeling of the actuator. In this paper at first using of Mathematical analysis and Closed form transfer function of cantilever beam dynamic response to the forces of different inputs (intensive and continuous) is calculated and for different type...

We generalize the traditional concept of temporal optical interferometry to any degree of freedom of a coherent optical field. By identifying the structure of a unitary optical transformation that we designate the generalized phase operator, we enable optical interferometry to be carried out in any modal basis describing a degree of freedom. The structure of the generalized phase operator is th...

A new logic, sequence-indexed linear-time temporal logic (SLTL), is obtained semantically from the standard linear-time temporal logic LTL by adding a sequence modal operator which represents a sequence of symbols. By the sequence modal operator of SLTL, we can appropriately express “sequential information” in temporal reasoning. A Gentzen-type sequent calculus for SLTL is introduced, and the c...

In [8], P. Hájek and V. Švejdar determined normal forms for the system ILF, and showed that we can eliminate the modal operator ¤ from IL–formulas. The normal form for the closed fragment of the interpretability logic IL is an open problem (see [13]). We prove that in some cases we can eliminate the modal operator ¤. We give an example where it is impossible to eliminate ¤. AMS subject classifi...

In [1] the authors considered finitely-valued modal logics with Kripke style semantics where both propositions and the accessibility relation are valued over a finite residuated lattice. Unfortunately, the necessity operator does not satisfy in general the normality axiom (K). In this paper we focus on the case of finite chains, and we consider a different approach based on introducing a multim...

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 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. ?

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...