AIR Abstract Syntax

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Contents

Notations

we specify the abstract syntax using the extended BNF used in OWL Abstract Syntax.

The abstract syntax is specified here by means of a version of Extended BNF, very similar to the EBNF notation used for XML [XML]. Terminals are quoted; non-terminals are bold and not quoted. Alternatives are either separated by vertical bars (|) or are given in different productions. Components that can occur at most once are enclosed in square brackets ([...]); components that can occur any number of times (including zero) are enclosed in braces ({...}). Whitespace is ignored in the productions here.
list of notations
semantics example notes
terminal term ' term ' (?) quoted string
non-terminal term Term bold but not quoted string
alternative terms term1 | term2 separated by vertical bar
term occurs at most once [ term ] enclosed by square brackets
term occurs any number of times (including zero) { term } enclosed by curly brackets
grouping of terms? ( term1 | term2 )? enclosed by round brackets

AIR 2.0

Abstract Syntax


Policy-document is the start element.

1. Action-container ::= Rule-reference | Assertion.
2. Action-nl-description ::= 'description(' { (Variable | String) blank-space} ')'.
3. Alphanumeric ::= concatenation of alpha-numeric characters
4. Annotation ::= ??
5. Assertion ::= 'assert(' [Action-nl-description] 'statement(' Assertion-stmt {Assertion-stmt} ')' ')'.
6. Assertion-stmt ::= 'Triple(' Subject-wo-blank Property Object-wo-blank ')'.
7. Blank-node ::= '_:' Alphanumeric.
8. Blank-space ::= blank .
9. Condition ::= {Existential-variable-declaration} Condition-stmt {Condition-stmt}.
10. Condition-actions ::= 'if (' [Condition] ')' ['matched-graph(' Graph-variable ')']

('then(' Action-container ')' | 'else(' Action-container ')') {'then(' Action-container ')' | 'else(' Action-container ')'}.

11. Condition-stmt ::= 'Triple(' Subject Property Object ')'.
12. dataLiteral ::= as defined in OWL Abstract Syntax 1
13. Existential-variable-declaration ::= 'forSome(' Variable ')'.
14. Global-variable-declaration ::= {Universal-variable-declaration}.
15. Graph-variable ::= Variable.
16. Hidden-or-ellipsed ::= 'hidden' | 'ellipsed'.
17. Object ::= Object-wo-blank | Blank-node.
18. Object-wo-blank := URIReference | dataLiteral | Variable.
19. Policy ::= 'Policy(' Policy-id {Annotation} Rule-reference { Rule-reference } ')'.
20. Policy-document ::= (Global-variable-declaration | Policy | Rule-def) {Global-variable-declaration | Policy | Rule-def}.
21. Policy-id ::= URIReference.
22. Property ::= URIReference | Variable.
23. Rule-def := 'Rule(' Rule-id [Hidden-or-ellipsed] {Annotation} Condition-actions ')'.
24. Rule-id ::= URIReference.
25. Rule-reference ::= 'rule(' [Action-nl-description] (Rule-id | 'Rule(' {Annotation} Condition-actions ')') ')'.
26. Subject ::= Subject-wo-blank | Blank-node.
27. Subject-wo-blank := URIReference | Variable.
28. Universal-variable-declaration ::= 'forAll(' Variable ')'.
29. URIReference ::= as defined in OWL Abstract Syntax 1
30. Variable ::= URIReference.

Examples

Example 1

Policy 

@forAll :PERSON1, :PERSON2 .

:Policy1 a air:Policy;
   air:rule [     
     air:if { :PERSON1 tamip:Has_Father :PERSON2. };     
     air:then 
        [ air:description (:PERSON1 "has parent" :PERSON2 " because of their has_father relation" );
          air:assertion 
            [ air:statement [ { :PERSON1 air:compliant-with :Demo1_Policy ;
                                         tamip:Has_Parent :PERSON2.} ] ] ].

Policy in Abstract-syntax 

forAll(:PERSON1).
forAll(:PERSON2).
Policy ( 
  Policy1 
  rule ( 
    Rule ( 
      if( Triple(:PERSON1 tamip:Has_Father :PERSON2) ) 
      then ( 
	assert ( 
	  description (:PERSON1 "has parent" :PERSON2 " because of their has_father relation") 
          statement( Triple(:PERSON1 air:compliant-with :Demo1_Policy) 
          	     Triple(:PERSON1 tamip:Has_Parent :PERSON2 ) 
          )  
	) 
      ) 
    )
  ).

Example 2

Policy 

@forAll :PERSON, :CITY, :NY_STATE_ID, :G1 .

Policy1 a air:Policy;
      air:rule :state-residency-rule.

:state-residency-rule a air:Belief-rule;
    air:if { :PERSON tamip:Lives_in_city :CITY .
             :CITY tamip:Has_state :NY . };
    air:then [ air:rule :state-id-check ].   

:state-id-check a air:Hidden-rule;
    rdfs:label "state id check rule";
    air:if { :PERSON tamip:Has_ny_state_id :NY_STATE_ID. };    
    air:then 
       [ air:assert 
           [ air:description ( :PERSON "is a new york state resident" );
             air:statement { :PERSON air:compliant-with :Demo7_Policy1.} ] ].

Policy in Abstract-syntax 

forAll(:PERSON).
forAll(:CITY).
forAll(:NY_STATE_ID).
forAll(:G1).

Policy ( Policy1 rule ( :state-residency-rule ) ).
Rule ( :state-residency-rule 
       if ( Triple (:PERSON tamip:Lives_in_city :CITY) Triple (:CITY tamip:Has_state :NY) ) 
       then ( rule ( :state-id-check ) ) ).
Rule ( :state-id-check 
       'hidden'
       if ( Triple ( :PERSON tamip:Has_ny_state_id :NY_STATE_ID ) ) 
       then ( 
         description ( :PERSON "is a new york state resident" )
         assert ( statement ( Triple (:PERSON air:compliant-with :Demo7_Policy1 ) ) ) ) )

AIR 1.0

Abstract Syntax

  • Policy-Document ::= Global-variable-declaration Rule-container {Rule-container}.
  • Global-variable-declaration ::= {Universal-variable-declaration}.
  • Existential-variable-declaration ::= 'forSome(' Variable ')'.
  • Universal-variable-declaration ::= 'forAll(' Variable ')'.
  • Rule-container ::= Policy | Rule.
  • Policy ::= 'Policy(' PolicyID [Annotation] 'rule(' RuleID | 'Rule(' Rule-content ')' ')' {'rule(' RuleID | 'Rule(' Rule-content ')' ')'}')'.
  • Rule := 'Rule(' RuleID Rule-content ')'.
  • Rule-content := [Annotation] [Hide-justification] Pattern-action.
  • Hide-justification ::= 'true'| 'false'.
  • Pattern-action ::= Action| Pattern Action ['alt(' Action ')'] | Pattern 'alt('Action')').
  • Pattern ::= 'pattern(' N3-Pattern ')' ['matched-graph(' Graph-variable ')'].
  • N3-pattern ::= {Universal-variable-declaration|Existential-variable-declaration} Statement {Statement }.
  • Statement ::= 'Triple(' (Term|Blank) Term (Term|Blank) ')'.
  • Action ::= {'rule(' RuleID | 'Rule(' Rule-content ')' ')'} ['assert(' Asserted-Statement {Asserted-Statement} ')’] [Action-Description] [Justification].
  • Asserted-Statement ::= 'Triple(' Term Term Term ')'.
  • Justification ::= 'justification(' 'rule-id(' RuleID ')' 'antecedent(' Graph-variable ')' ')'.
  • Action-description ::= { (Variable|String) blank-space}.
  • Term ::= URIReference | Variable.
  • PolicyID ::= URIReference.
  • RuleID ::= URIReference.
  • Graph-variable ::= Variable.
  • Variable ::= URIReference.
  • Blank ::= '_:' string ???
  • Annotation ::=??
  • URIReference ::= ??
  • String ::= ??



Retrieved from "http://tw.rpi.edu/proj/tami/AIR_Abstract_Syntax"
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