An Abstract Tableau Calculus for the Description Logic SHOI Using UnrestrictedBlocking and Rewriting

Abstract This paper presents an abstract tableau calculus for the description logic SHOI. SHOI is the extension of ALC with singleton concepts, role inverse, transitive roles and role inclusion axioms. The presented tableau calculus is inspired by a recently introduced tableau synthesis framework. Termination is achieved by a variation of the unrestricted blocking mechanism that immediately rewrites terms with respect to the conjectured equalities. This approach leads to reduced search space for decision procedures based on the calculus. We also discuss restrictions of the application of the blocking rule by means of additional side conditions and/or additional premises.

On the uniform one-dimensional fragment

The uniform one-dimensional fragment of first-order logic, U1, is a recently introduced formalism that extends two-variable logic in a natural way to contexts with relations of all arities. We survey properties of U1 and investigate its relationship to description logics designed to accommodate higher arity relations, with particular attention given to DLR_reg. We also define a description logic version of a variant of U1 and prove a range of new results concerning the expressivity of U1 and related logics

Deciding regular grammar logics with converse through first-order logic

We provide a simple translation of the satisfiability problem for regular grammar logics with converse into GF2, which is the intersection of the guarded fragment and the 2-variable fragment of first-order logic. This translation is theoretically interesting because it translates modal logics with certain frame conditions into first-order logic, without explicitly expressing the frame conditions. A consequence of the translation is that the general satisfiability problem for regular grammar logics with converse is in EXPTIME. This extends a previous result of the first author for grammar logics without converse. Using the same method, we show how some other modal logics can be naturally translated into GF2, including nominal tense logics and intuitionistic logic. In our view, the results in this paper show that the natural first-order fragment corresponding to regular grammar logics is simply GF2 without extra machinery such as fixed point-operators.Comment: 34 page

Fuzzy Description Logics with General Concept Inclusions

Description logics (DLs) are used to represent knowledge of an application domain and provide standard reasoning services to infer consequences of this knowledge. However, classical DLs are not suited to represent vagueness in the description of the knowledge. We consider a combination of DLs and Fuzzy Logics to address this task. In particular, we consider the t-norm-based semantics for fuzzy DLs introduced by Hájek in 2005. Since then, many tableau algorithms have been developed for reasoning in fuzzy DLs. Another popular approach is to reduce fuzzy ontologies to classical ones and use existing highly optimized classical reasoners to deal with them. However, a systematic study of the computational complexity of the different reasoning problems is so far missing from the literature on fuzzy DLs. Recently, some of the developed tableau algorithms have been shown to be incorrect in the presence of general concept inclusion axioms (GCIs). In some fuzzy DLs, reasoning with GCIs has even turned out to be undecidable. This work provides a rigorous analysis of the boundary between decidable and undecidable reasoning problems in t-norm-based fuzzy DLs, in particular for GCIs. Existing undecidability proofs are extended to cover large classes of fuzzy DLs, and decidability is shown for most of the remaining logics considered here. Additionally, the computational complexity of reasoning in fuzzy DLs with semantics based on finite lattices is analyzed. For most decidability results, tight complexity bounds can be derived

Satisfiability of CTL* with constraints

We show that satisfiability for CTL* with equality-, order-, and modulo-constraints over Z is decidable. Previously, decidability was only known for certain fragments of CTL*, e.g., the existential and positive fragments and EF.Comment: To appear at Concur 201

Reasoning for the description logic ALC with link keys

Data interlinking is a critical task for widening and enhancing linked open data. One way to tackle data interlinking is to use link keys, which generalise keys to the case of two RDF datasets described using different ontologies. Link keys specify pairs of properties to compare for finding same-as links between instances of two classes of two different datasets. Hence, they can be used for finding links. Link keys can also be considered as logical axioms just like keys, ontologies and ontology alignments. We introduce the logic ALC+LK extending the description logic ALC with link keys. It may be used to reason and infer entailed link keys that may be more useful for a particular data interlinking task. We show that link key entailment can be reduced to consistency checking without introducing the negation of link keys. For deciding the consistency of an ALC+LK ontology, we introduce a new tableau-based algorithm. Contrary to the classical ones, the completion rules concerning link keys apply to pairs of individuals not directly related. We show that this algorithm is sound, complete and always terminates