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Spatial logics with connectedness predicates

Roman Kontchakov ; Ian Pratt-Hartmann ; Frank Wolter ; Michael Zakharyaschev.

We consider quantifier-free spatial logics, designed for qualitative spatial representation and reasoning in AI, and extend them with the means to represent topological connectedness of regions and restrict the number of their connected components. We investigate the computational complexity of&nbsp;[&hellip;]

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Modal Logics of Topological Relations

Carsten Lutz ; Frank Wolter.

Logical formalisms for reasoning about relations between spatial regions play a fundamental role in geographical information systems, spatial and constraint databases, and spatial reasoning in AI. In analogy with Halpern and Shoham's modal logic of time intervals based on the Allen relations, we&nbsp;[&hellip;]

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The Data Complexity of Description Logic Ontologies

Carsten Lutz ; Frank Wolter.

We analyze the data complexity of ontology-mediated querying where the ontologies are formulated in a description logic (DL) of the ALC family and queries are conjunctive queries, positive existential queries, or acyclic conjunctive queries. Our approach is non-uniform in the sense that we aim to&nbsp;[&hellip;]

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The Data Complexity of Ontology-Mediated Queries with Closed Predicates

Carsten Lutz ; Inanc Seylan ; Frank Wolter.

In the context of ontology-mediated querying with description logics (DLs), we study the data complexity of queries in which selected predicates can be closed (OMQCs). We provide a non-uniform analysis, aiming at a classification of the complexity into tractable and non-tractable for ontologies in&nbsp;[&hellip;]

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