PSPACE Reasoning for Graded Modal Logics
TLDR
A PSPACE algorithm that decides satisfiability of the graded modal lo gic Gr(KR), a natural extension of propositional modal logic KR by counting expressions, is presented, which is the first known algorithm which meets the lower bound for the complexity of the problem.Abstract:
We present a PSPACE algorithm that decides satisfiability of the graded modal lo gic Gr(KR)—a natural extension of propositional modal logic KR by counting expressions—which plays an important role in the area of knowledge representation The algorithm employs a tableaux approach and is the first known algorithm which meets the lower bound for the complexity of the problem Thus, we exactly fix the complexity of the problem and refute a EXPTIME-hardness conjecture We extend the results to the logic Gr(K R 1 \ ), which augments Gr(KR) with inverse relations and intersection of accessibility relations This establishes a kind of “theoretical benchma rk” that all algorithmic approaches can be measured againstread more
Citations
More filters
Posted Content
Complexity Results and Practical Algorithms for Logics in Knowledge Representation
TL;DR: A number of novel complexity results and practical algorithms for expressive DLs that provide different forms of counting quantifiers are established and it is shown that, in many cases, adding local counting in the form of qualifying number restrictions to DLs does not increase the complexity of the inference problems, even if binary coding of numbers in the input is assumed.
Journal ArticleDOI
ε-connections of abstract description systems
TL;DR: This paper proposes a new combination method which is computationally robust in the sense that the combination of decidable formalisms is again decidable, and which, nonetheless, allows non-trivial interactions between the combined components.
Journal ArticleDOI
The complexity of reasoning with cardinality restrictions and nominals in expressive description logics
TL;DR: This work reduces the complexity of reasoning with cardinality restrictions to reasoning with the (in general weaker) terminological formalism of general axioms for ALCQ extended with nominals, and shows that pure concept satisfiability for A LCQI with Nominals is NExpTime-complete.
Journal ArticleDOI
Decidability of SHIQ with complex role inclusion axioms
Ian Horrocks,Ulrike Sattler +1 more
TL;DR: A tableau algorithm is presented for this DL extended with role inclusion axioms (RIAs) of the form Ro S ⊆ P and its implementation is reported on, which behaves well in practise and provides important additional functionality in a medical terminology application.
Book ChapterDOI
Complexity of reasoning
TL;DR: This work presents lower bounds on the computational complexity of satisfiability and subsumption in several Description Logics, and considers both reasoning with simple concept expressions and reasoning with an underlying TBox.
References
More filters
Journal ArticleDOI
Relationships between nondeterministic and deterministic tape complexities
TL;DR: The amount of storage needed to simulate a nondeterministic tape bounded Turingmachine on a deterministic Turing machine is investigated and a specific set is produced, namely the set of all codings of threadable mazes, such that, if there is any set which distinguishes nondeter microscopic complexity classes from deterministic tape complexity classes, then this is one such set.
Journal ArticleDOI
Attributive concept descriptions with complements
TL;DR: It is shown that deciding coherence and subsumption of such descriptions are PSPACE-complete problems that can be decided with linear space.
Journal ArticleDOI
A guide to completeness and complexity for modal logics of knowledge and belief
Joseph Y. Halpern,Yoram Moses +1 more
TL;DR: It is shown that while the problem of deciding satisfiability of an S5 formula with one agent is NP-complete, the problem for many agents is PSPACE-complete and the problem becomes complete for exponential time once a common knowledge operator is added to the language.
Journal ArticleDOI
The Computational Complexity of Provability in Systems of Modal Propositional Logic
TL;DR: The computational complexity of the provability problem in systems of modal propositional logic is investigated and it is found that every problem computable in polynomial space is reducible to the provable problem in any modal system between K and S4.
Book ChapterDOI
Practical Reasoning for Expressive Description Logics
TL;DR: An algorithm is presented that decides satisfiability of the DL ACC extended with transitive eind inverse roles, role hierarchies, and quaJifying number restrictions, and early experiments indicate that this algorithm is well-suited for implementation.