Cartesian Product in Description Logics
نویسنده
چکیده
We extend two description logics by introducing cartesian product (CP) of concepts and roles. In SROIQ , we show how CP axioms can be reduced using other language constructs. We present a polynomial algorithm for subsumption checking in EL++ with CP axioms. We prove that the introduction of CP does not increase the complexity of reasoning tasks in both SROIQ and EL++ .
منابع مشابه
Axiomatizing the lexicographic products of modal logics with linear temporal logic
Given modal logics 1, 2, their lexicographic product 1 ⇤ 2 is a new logic whose frames are the Cartesian products of a 1-frame and a 2-frame, but with the new accessibility relations reminiscent of a lexicographic ordering. This article considers the lexicographic products of several modal logics with linear temporal logic (LTL) based on “next” and “always in the future”. We provide axiomatizat...
متن کاملThe reliability Wiener number of cartesian product graphs
Reliability Wiener number is a modification of the original Wiener number in which probabilities are assigned to edges yielding a natural model in which there are some (or all) bonds in the molecule that are not static. Various probabilities naturally allow modelling different types of chemical bonds because chemical bonds are of different types and it is well-known that under certain condition...
متن کاملA A Cookbook for Temporal Conceptual Data Modelling with Description Logics
We design temporal description logics suitable for reasoning about temporal conceptual data models and investigate their computational complexity. Our formalisms are based on DL-Lite logics with three types of concept inclusions (ranging from atomic concept inclusions and disjointness to the full Booleans), as well as cardinality constraints and role inclusions. The logics are interpreted over ...
متن کاملThe Merrifield-Simmons indices and Hosoya indices of some classes of cartesian graph product
The Merrifield-Simmons index of a graph is defined as the total number of the independent sets of the graph and the Hosoya index of a graph is defined as the total number of the matchings of the graph. In this paper, we give formula for Merrifield-Simmons and Hosoya indices of some classes of cartesian product of two graphs K{_2}×H, where H is a path graph P{_n}, cyclic graph C{_n}, or star gra...
متن کاملLogic of subtyping
We introduce new modal logical calculi that describe subtyping properties of Cartesian product and disjoint union type constructors as well as mutually-recursive types defined using those type constructors. Basic Logic of Subtyping S extends classical propositional logic by two new binary modalities ⊗ and ⊕. An interpretation of S is a function that maps standard connectives into set-theoretica...
متن کامل