Abstract
Object-relational combinations are reviewed with a focus on the integrated Positional-Slotted, Object-Applicative (PSOA) RuleML. PSOA RuleML permits a predicate application (atom) to be without or with an Object IDentifier (OID) – typed by the predicate as its class – and, orthogonally, the predicate’s arguments to be positional, slotted, or combined. This enables six uses of atoms, which are systematically developed employing examples in presentation syntaxes derived from RuleML/POSL and RIF-BLD, and visualized in Scratch Grailog. These atoms, asserted as facts, are retrieved by object-relational look-in queries. On top of such facts, PSOA rules and their inferential querying are explored, e.g. permitting F-logic-like frames derived from relational joins. A use case of bidirectional SQL-PSOA-SPARQL transformation (schema/ontology mapping) is shown. Objectification and the presentation plus (XML-)serialization syntaxes of PSOA RuleML are described. The first-order model-theoretic semantics is formalized, blending (OID-over-)slot distribution, as in RIF, with integrated psoa terms, as in RuleML. The PSOATransRun implementation is surveyed, translating PSOA RuleML to TPTP (PSOA2TPTP) or Prolog (PSOA2Prolog).
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Notes
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With ‘object-centered’ rather than ‘object-oriented’ atoms we refer to atoms that have a typed OID described by slots and/or positional arguments. Object-Oriented Programming (OOP) usually only employs descriptive slots but not positional arguments; on the other hand, OOP allows the re-assignment of slot fillers (instance variables) while object-centered modeling – as its declarative core – only allows the refinement of non-ground slot fillers and – in PSOA RuleML – positional arguments.
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We use the upper-cased “PSOA” as a qualifier for the language and the lower-cased “psoa” for its terms.
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The usual “stick figures” for directed graphs – connecting pairs of nodes with arrows – are generalized to “skewer figures” for directed hypergraphs – each (bendable) skewer holding arbitrarily many nodes together in a totally ordered fashion.
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A labelnode can be used as a label (relation) or as a node (argument).
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In the following, “hyperarc” will be used as an abbreviation for “directed hyperarc”.
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The POsitional-SLotted language started integrating positional and slotted syntaxes: http://ruleml.org/submission/ruleml-shortation.html.
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This is partly due to the RIF-like Presentation syntax used here being somewhat simplified w.r.t. the one used by PSOA RuleML tools: in particular, the “_” prefix is omitted from local constants, except for system-generated ones.
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For the infrequent case of n = 0, not needed in this paper, hyperarcs (‘connecting’ one labelnode) degenerate to an outgoing arrow head attached to the relation labelnode or branch line.
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Such merging of tuples – and (later) slots – centered on the same OID is called ‘centralization’. It constructs one object-identified psoa term from a given set of equally identified psoa terms. Centralization will be assumed when illustrating the proof-theoretic semantics in Sects. 3 and 4. It is the inverse of tupribution – and slotribution – to be introduced in Sect. 7. Harvesting the set of all psoa terms with a fixed OID from a distributed network – e.g. published on the Web – can use techniques analogous to finding all RDF triples having a fixed resource as their subject (cf. http://www.w3.org/wiki/TaskForces/CommunityProjects/LinkingOpenData/SemanticWebSearchEngines). This is a non-trivial task, since such OIDs and resources normally are not dereferenceable locators themselves but occur within documents at other locators (although, ideally, those documents have filename extensions like .ruleml and .rdf, respectively).
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In RIF called “named-argument terms” [2].
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The figure’s representation of dimension = 2 indicates that this betweenness is relative to a 2D plane (rather than, say, to a 3D sphere).
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As usual in Logic Programming, a non-ground query is understood to have existential quantification for all free variables. For basic LP terminology and notions see [13].
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Betweenness with dimension = 2 for geographical entities assumes some projection of the globe to a 2D coordinate system.
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Earlier (flat and nested) positional versions have been used to explain XML-to-XML transformation (http://www.cs.unb.ca/~boley/cs6795swt/cs6795swt-XML.pdf). Later, a similar use case was employed to demonstrate SPINMap for RDF-to-RDF transformation [15].
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Alternatively, given column headings like Name, Street, and Town, the input conversion for PSOA could skip the relationship addressRel("Seminaris" "Wikingerufer 7" "14195 Berlin"), but generate a pairship addressRel(name->"Seminaris" street->"Wikingerufer 7" town->"14195 Berlin"), already closer to the level of frames and SPARQL.
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The “lift” and “drop” terminology for conversions at the input and output interfaces has been introduced in http://yosemiteproject.org, and is related to the “lifting” and “lowering” terminology of http://www.w3.org/TR/sawsdl/#schemaMapping.
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For an example-based introduction to the basic tags of Deliberation RuleML see http://ruleml.org/papers/Primer.
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TPTP-FOF is also targeted by http://wiki.ruleml.org/index.php/TPTP_RuleML.
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Acknowledgements
Many thanks go to Gen Zou for helpful discussions on multiple drafts of this paper and for spearheading the PSOATransRun implementation. I want to thank Tara Athan, Sadnan Al Manir, Alexandre Riazanov, and Robert Kirby for reviewing earlier partial versions. I extend my thanks to Michael Genesereth, Sudhir Agarwal, Abhijeet Mohapatra, and Eric Kao for comments on a PSOA RuleML presentation in the Computational Logic Seminar, and to Michael Genesereth and the entire Stanford Logic Group for hosting my research stay. My thankfulness goes to Richard Waldinger for comments at various occasions, and for hosting my recent SRI visits. The 11th Reasoning Web Summer School (RW 2015) reviewer and organizers are thanked for early feedback and for running this event. NSERC is thanked for its support through Discovery Grants.
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Boley, H. (2015). PSOA RuleML: Integrated Object-Relational Data and Rules. In: Faber, W., Paschke, A. (eds) Reasoning Web. Web Logic Rules. Reasoning Web 2015. Lecture Notes in Computer Science(), vol 9203. Springer, Cham. https://doi.org/10.1007/978-3-319-21768-0_5
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