Analyzing the AIR Language: A Semantic Web (Production) Rule Language

Notes

AIR was developed as an extension to N3Logic

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AIR rules are encoded in N3, which extends the expressiveness of RDF with (i) the ability to use graphs as literal values, (ii) universal or existential quantification of variables in a graph and (iii) built-in functions and operators represented as RDF properties.

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AIR is designed to provide detailed explanations

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AIR permits natural language descriptions to be added

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Since justifications can potentially reveal sensi- tive information from the knowledge base or expose bias in the rules, AIR also provides ways to customize explanations, e.g. hiding actions of certain rules.

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AIR rules have unique IDs (IRIs)

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AIR rules can be nested

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objectively checked for patterns

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SCR is important for a Web rule languages because information on the Web is often assumed to be incomplete, and its correctness is subject to the trustworthiness of the source.

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N3Logic supports monotonic negation, and AIR supports non-monotonic negation

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Rule Interchange Format (RIF) [14] has two major dialects – the Framework for Logic Dialects (FLD) and the Production Rule Dialect (PRD).

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AIR is neither more nor less expressive than BLD. Unlike BLD, function symbols are not supported in AIR, whereas AIR supports negation.

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AIR is as expressive as SWRL, and also supports negation.

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Other than AIR, of the systems men- tioned above, only Jena supports (partially) nesting of rules.

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SILK also supports SCR.

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In contrast, the explanations for conclusions in AIR are gen- erated by the reasoner itself

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AIR’s focus on explanation generation for Web reasoning makes it unique.

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Other distinguishing features include AIR’s ability to treat AIR rules as part of linked data

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ability to match patterns against remote triple stores.

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While AIR has a production rule syntax, it is limited to assertions of facts, and addition of rules.

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Therefore, we can define its declarative semantics

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Not only is the notion of nesting of rules absent from Jess, AIR’s negation is different from NAF.

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The reasoner computes the closure, AIR-closure, for given facts, in N3, with respect to given AIR-program.

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The closure contains the initial facts and all the facts that can be deduced from it using the given rules.

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The condition is specified as a graph pattern

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pattern matched against N3 graphs.

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actions can be annotated with natural language description through the air:description property

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The existentially quantified variables may be declared within the condition.

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The universally quantified variables are declared outside of the rule.

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When the nested rule is activated, an instance of the rule with known variable bindings substituted is created.

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Traditionally, rule languages have been designed assuming that all rules will apply on all input data. However, this is not desirable for a web rule language

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AIR supports SCR. The matching of a condition pattern can be scoped

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2.2 AIR Reasoning (The Procedural Semantics)

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The AIR reasoner employs a RETE [6] based forward-chaining approach

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Positively Stratified Negatively Hierarchical Logic Programs

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An LP P is PSNHLP if there is an assignment of ordinal levels to predicates such that whenever a predicate appears in the body (negatively or positively) of a negative rule, the predicate in the head of that rule is of strictly higher level, and whenever a predicate appears in the body of a positive rule, the predicate in the head has at least that level.

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Declarative Semantics

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The declarative semantics of AIR-program can be defined in terms of a seman- tically equivalent PSNHLP.

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AIR and Logic Programming

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AIR rules have different semantics from the LP rules

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The nesting of rules impacts the order in which the rules are fired, and they may be nested properly to get the desired semantics.

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PLPs can be losslessly rewritten into AIR

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OWL 2 RL inference rules are all positive, and therefore they can be encoded in AIR

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PSNHLPs can be losslessly rewritten into AIR.

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AIR does not support well-founded negation and is less expressive than other rule systems

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ability to construct explanations, declaratively manipulate them, and its support for scoped contextualized reasoning (SCR) make it sufficiently unique and useful

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nesting can also be leveraged to order rules and therefore encode fairly expressive LPs

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