scholarly journals Fusions of Description Logics and Abstract Description Systems

2002 ◽  
Vol 16 ◽  
pp. 1-58 ◽  
Author(s):  
F. Baader ◽  
C. Lutz ◽  
H. Sturm ◽  
F. Wolter
Keyword(s):  
Large Class ◽  
Description Logics ◽  
General Setting ◽  
Modal Logics ◽  
Common Generalization ◽  
Abstract Description ◽  
Normal Modal Logics ◽  
Combining Logics

Fusions are a simple way of combining logics. For normal modal logics, fusions have been investigated in detail. In particular, it is known that, under certain conditions, decidability transfers from the component logics to their fusion. Though description logics are closely related to modal logics, they are not necessarily normal. In addition, ABox reasoning in description logics is not covered by the results from modal logics. In this paper, we extend the decidability transfer results from normal modal logics to a large class of description logics. To cover different description logics in a uniform way, we introduce abstract description systems, which can be seen as a common generalization of description and modal logics, and show the transfer results in this general setting.

Modal sequents for normal modal logics

1993 ◽  
Vol 39 (1) ◽  
pp. 231-240 ◽  
Author(s):  
Claudio Cerrato
Keyword(s):  
Modal Logics ◽  
Normal Modal Logics

scholarly journals Simplified Kripke-Style Semantics for Some Normal Modal Logics

Studia Logica ◽  
2019 ◽  
Vol 108 (3) ◽  
pp. 451-476 ◽  
Author(s):  
Andrzej Pietruszczak ◽  
Mateusz Klonowski ◽  
Yaroslav Petrukhin
Keyword(s):  
Modal Logics ◽  
Normal Modal Logics

On a class of random motions of point processes involving interaction

1978 ◽  
Vol 10 (3) ◽  
pp. 613-632 ◽  
Author(s):  
Harry M. Pierson
Keyword(s):  
Large Class ◽  
Uniform Distribution ◽  
Point Process ◽  
Stationary Point ◽  
Point Processes ◽  
General Setting ◽  
Invariant Distributions ◽  
Stationary Point Process ◽  
Random Motions ◽  
Interval Lengths

Starting with a stationary point process on the line with points one unit apart, simultaneously replace each point by a point located uniformly between the original point and its right-hand neighbor. Iterating this transformation, we obtain convergence to a limiting point process, which we are able to identify. The example of the uniform distribution is for purposes of illustration only; in fact, convergence is obtained for almost any distribution on [0, 1]. In the more general setting, we prove the limiting distribution is invariant under the above transformation, and that for each such transformation, a large class of initial processes leads to the same invariant distribution. We also examine the covariance of the limiting sequence of interval lengths. Finally, we identify those invariant distributions with independent interval lengths, and the transformations from which they arise.

Normal monomodal logics can simulate all others

1999 ◽  
Vol 64 (1) ◽  
pp. 99-138 ◽  
Author(s):  
Marcus Kracht ◽  
Frank Wolter
Keyword(s):  
Modal Logic ◽  
Modal Logics ◽  
Normal Modal Logics

AbstractThis paper shows that non-normal modal logics can be simulated by certain polymodal normal logics and that polymodal normal logics can be simulated by monomodal (normal) logics. Many properties of logics are shown to be reflected and preserved by such simulations. As a consequence many old and new results in modal logic can be derived in a straightforward way, sheding new light on the power of normal monomodal logic.

scholarly journals Logics with Impossibility as the Negation and Regular Extensions of the Deontic Logic D2

2017 ◽  
Vol 46 (3/4) ◽  
Author(s):  
Krystyna Mruczek-Nasieniewska ◽  
Marek Nasieniewski
Keyword(s):  
Intuitionistic Logic ◽  
Deontic Logic ◽  
Modus Ponens ◽  
Modal Logics ◽  
Point Of View ◽  
Modal Operator ◽  
Modal Interpretation ◽  
Semantical Point ◽  
The Right ◽  
Normal Modal Logics

In [1] J.-Y. Bèziau formulated a logic called Z. Bèziau’s idea was generalized independently in [6] and [7]. A family of logics to which Z belongs is denoted in [7] by K. In particular; it has been shown in [6] and [7] that there is a correspondence between normal modal logics and logics from the class K. Similar; but only partial results has been obtained also for regular logics (see [8] and [9]). In (Došen; [2]) a logic N has been investigated in the language with negation; implication; conjunction and disjunction by axioms of positive intuitionistic logic; the right-to-left part of the second de Morgan law; and the rules of modus ponens and contraposition. From the semantical point of view the negation used by Došen is the modal operator of impossibility. It is known this operator is a characteristic of the modal interpretation of intuitionistic negation (see [3; p. 300]). In the present paper we consider an extension of N denoted by N+. We will prove that every extension of N+ that is closed under the same rules as N+; corresponds to a regular logic being an extension of the regular deontic logic D21 (see [4] and [13]). The proved correspondence allows to obtain from soundnesscompleteness result for any given regular logic containing D2, similar adequacy theorem for the respective extension of the logic N+.

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