31 research outputs found
Practical Reasoning for Very Expressive Description Logics
Description Logics (DLs) are a family of knowledge representation formalisms
mainly characterised by constructors to build complex concepts and roles from
atomic ones. Expressive role constructors are important in many applications,
but can be computationally problematical. We present an algorithm that decides
satisfiability of the DL ALC extended with transitive and inverse roles and
functional restrictions with respect to general concept inclusion axioms and
role hierarchies; early experiments indicate that this algorithm is well-suited
for implementation. Additionally, we show that ALC extended with just
transitive and inverse roles is still in PSPACE. We investigate the limits of
decidability for this family of DLs, showing that relaxing the constraints
placed on the kinds of roles used in number restrictions leads to the
undecidability of all inference problems. Finally, we describe a number of
optimisation techniques that are crucial in obtaining implementations of the
decision procedures, which, despite the worst-case complexity of the problem,
exhibit good performance with real-life problems
Consistency in Fuzzy Description Logics over Residuated De Morgan Lattices
Fuzzy description logics can be used to model vague knowledge in application domains. This paper analyses the consistency and satisfiability problems in the description logic SHI with semantics based on a complete residuated De Morgan lattice. The problems are undecidable in the general case, but can be decided by a tableau algorithm when restricted to finite lattices. For some sublogics of SHI, we provide upper complexity bounds that match the complexity of crisp reasoning
Tableau-based decision procedure for the multi-agent epistemic logic with all coalitional operators for common and distributed knowledge
We develop a conceptually clear, intuitive, and feasible decision procedure
for testing satisfiability in the full multi-agent epistemic logic CMAEL(CD)
with operators for common and distributed knowledge for all coalitions of
agents mentioned in the language. To that end, we introduce Hintikka structures
for CMAEL(CD) and prove that satisfiability in such structures is equivalent to
satisfiability in standard models. Using that result, we design an incremental
tableau-building procedure that eventually constructs a satisfying Hintikka
structure for every satisfiable input set of formulae of CMAEL(CD) and closes
for every unsatisfiable input set of formulae.Comment: Substantially extended and corrected version of arXiv:0902.2125. To
appear in: Logic Journal of the IGPL, special issue on Formal Aspects of
Multi-Agent System