### Logic Framework Extension -- Jos De Roo
### importing http://www.w3.org/2000/10/swap/log

PREFIX log: <http://www.w3.org/2000/10/swap/log#>
PREFIX math: <http://www.w3.org/2000/10/swap/math#>
PREFIX owl: <http://www.w3.org/2002/07/owl#>
PREFIX rdfs: <http://www.w3.org/2000/01/rdf-schema#>
PREFIX rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#>
PREFIX xsd: <http://www.w3.org/2001/XMLSchema#>
PREFIX e: <http://eulersharp.sourceforge.net/2003/03swap/log-rules#>

<> owl:imports <http://www.w3.org/2000/10/swap/log>.

### classes
e:Builtin a rdfs:Class;
    rdfs:comment "class of EYE built-ins".

e:ComplexNumber a rdfs:Class;
    rdfs:comment "class of complex numbers";
    rdfs:subClassOf e:Tuple;
    e:tupleTypes (e:Number e:Number).

e:Component a rdfs:Class;
    rdfs:comment "class of EYE components".

e:Context a rdfs:Class;
    rdfs:comment "class of contexts";
    rdfs:subClassOf rdf:List;
    e:listType rdfs:Resource.

e:Fact a rdfs:Class;
    rdfs:comment "class of facts".

e:Lemma a rdfs:Class;
    rdfs:comment "class of lemmas".

e:Number a rdfs:Class;
    rdfs:comment "class of numbers";
    rdfs:subClassOf rdfs:Literal.

e:Numbers a rdfs:Class;
    rdfs:comment "class of lists of numbers";
    rdfs:subClassOf rdf:List;
    e:listType e:Number.

e:PairOfNumbers a rdfs:Class;
    rdfs:comment "class of pairs of numbers";
    rdfs:subClassOf e:Tuple;
    e:tupleTypes (e:Numbers e:Numbers).

e:Polynomial a rdfs:Class;
    rdfs:comment "class of polynomials";
    rdfs:subClassOf rdf:List;
    e:listType e:ComplexNumber.

e:Recursion a rdfs:Class;
    rdfs:comment "class of recursion numbers";
    rdfs:subClassOf e:Number.

e:Roots a rdfs:Class;
    rdfs:comment "class of roots of polynomials";
    rdfs:subClassOf rdf:List;
    e:listType e:ComplexNumber.

e:Scope a rdfs:Class;
    rdfs:comment "class of (context recursion) pairs where a context is a list of consulted URI's and a recursion is the deductive closure recursion number";
    rdfs:subClassOf e:Tuple;
    e:tupleTypes (e:Context e:Recursion).

e:ScopeOrFormula a rdfs:Class;
    rdfs:comment "e:Scope or log:Formula";
    rdfs:subClassOf e:Tuple;
    e:tupleTypes (e:Context e:Recursion).

e:Tuple a rdfs:Class;
    rdfs:comment "class of n-tuples";
    rdfs:subClassOf rdf:List.

e:TupleTypes a rdfs:Class;
    rdfs:comment "class of lists of types";
    rdfs:subClassOf rdf:List;
    e:listType rdfs:Class.


### constants
e:epsilon a e:Number;
    rdfs:comment "the difference between the float 1.0 and the first larger floating point number".

e:F a rdfs:Resource;
    rdfs:comment "identifier for boolean false".

e:T a rdfs:Resource;
    rdfs:comment "identifier for boolean true".


### properties
e:avg a rdf:Property, e:Builtin;
    rdfs:comment "built-in to calculate the average e.g. (55 66 72 87 56 77 73 69 74 56) e:avg 68.5";
    rdfs:domain e:Numbers;
    rdfs:range e:Number.

e:becomes a rdf:Property, e:Builtin;
    rdfs:comment "built-in to perform RDF linear implication i.e. retracting the subject graph and asserting the object graph";
    rdfs:domain log:Formula;
    rdfs:range log:Formula.

e:before a rdf:Property, e:Builtin;
    rdfs:comment "built-in to call the subject formula before the object formula";
    rdfs:domain log:Formula;
    rdfs:range log:Formula.

e:biconditional a rdf:Property, e:Builtin;
    rdfs:comment "built-in and object is conditional belief of first element of subject list given rest of subject list";
    rdfs:domain rdf:List;
    rdfs:range e:Number.

e:binaryEntropy a rdf:Property, e:Builtin;
    rdfs:comment "built-in to calculate binary entropy e.g. 0.25 e:binaryEntropy 0.8112781244591328";
    rdfs:domain e:Number;
    rdfs:range e:Number.

e:boolean a rdf:Property;
    rdfs:comment "to model a logical proposition";
    rdfs:domain rdfs:Resource;
    rdfs:range [ owl:oneOf (e:F e:T)].

e:calculate a rdf:Property, e:Builtin;
    rdfs:comment """built-in to evaluate arithmetic expressions e.g.
                ("1+1") e:calculate 2 .
                ?X log:equalTo 3. ("sqrt(_width^2+_length^2)" ?X 4) e:calculate 5.0 .
                ("_period-250" "PT5M2S"^^xsd:dayTimeDuration) e:calculate 52.0 .
            the first element of the subject list is the arithmetic expression in which variable names start with an underscore and the rest of the subject list are the variable values
            the supported arithmetic functions are described in http://www.swi-prolog.org/pldoc/man?section=functions""";
    rdfs:domain rdf:List;
    rdfs:range e:Number.

e:call a rdf:Property, e:Builtin;
    rdfs:comment "built-in to call the object formula within the subject scope or formula and to succeed when the call succeeds";
    rdfs:domain e:ScopeOrFormula;
    rdfs:range log:Formula.

e:cartesianProduct a rdf:Property, e:Builtin;
    rdfs:comment "built-in (L1 L2 ... Ln) e:cartesianProduct L, where L is the n-ary cartesian product of the sets L1, L2, ...., Ln";
    rdfs:domain rdf:List;
    rdfs:range rdf:List.

e:clashesWith a rdf:Property;
    rdfs:comment "to say that the graph is XSD-inconsistent or has a datatype clash";
    rdfs:domain rdfs:Literal;
    rdfs:range rdfs:Datatype.

e:closure a rdf:Property, e:Builtin;
    rdfs:comment "builtin to test the deductive closure; is within the subject scope of all asserted N3 formulae and their log:conclusion";
    rdfs:domain rdf:List;
    rdfs:range log:Formula.

e:columns a rdf:Property;
    rdfs:comment "to list the webized relational database collumns";
    rdfs:domain rdfs:Class;
    rdfs:range rdf:List.

e:compoundTerm a rdf:Property, e:Builtin;
    rdfs:comment """built-in to create a compound term e.g. ("date(_Y, _M, _D, 0, 0, 0.0, 0, 'UTC', -)" ?Y ?M ?D) e:compoundTerm ?T.
            the first element of the subject list is the template expression in which variable names start with an underscore and the rest of the subject list are the variable values""";
    rdfs:domain rdf:List;
    rdfs:range rdfs:Resource.

e:conditional a rdf:Property;
    rdfs:comment "object is conditional belief of first element of subject list given rest of subject list";
    rdfs:domain rdf:List;
    rdfs:range e:Number.

e:cov a rdf:Property, e:Builtin;
    rdfs:comment "built-in to calculate the sample covariance e.g. ((55 66 72 87 56 77 73 69 74 56) (1.66 1.78 1.87 1.92 1.66 1.89 1.86 1.79 1.80 1.66)) e:cov 0.992777777777778";
    rdfs:domain e:PairOfNumbers;
    rdfs:range e:Number.

e:csvTuple a rdf:Property, e:Builtin;
    rdfs:comment "to generate CSV output with --strings; columns ending with ID are outputted as Modified Base64 for XML identifiers encoded SHA-1 hash";
    rdfs:domain rdfs:Resource;
    rdfs:range rdf:List.

e:derive a rdf:Property, e:Builtin;
    rdfs:comment """built-in to interpret prolog predicates e.g.
                ("atom_codes" "HOME" (72 79 77 69)) e:derive true.
                ("=.." ?U ("date" 1970 1 1 0 0 0.0 0 "UTC" "-")) e:derive true.
                ("date_time_stamp" ?U 0^math:equalTo) e:derive true.
            the supported prolog predicates are described in http://www.swi-prolog.org/pldoc/man?section=builtin""";
    rdfs:domain rdf:List;
    rdfs:range xsd:boolean.

e:exec a rdf:Property, e:Builtin;
    rdfs:comment "built-in to execute te subject command line string and return the object integer";
    rdfs:domain xsd:string;
    rdfs:range xsd:integer.

e:fail a rdf:Property, e:Builtin;
    rdfs:comment "built-in to call the object formula within the subject scope and to succeed when the call fails";
    rdfs:domain e:Scope;
    rdfs:range log:Formula.

e:finalize a rdf:Property, e:Builtin;
    rdfs:comment "built-in to call object formula exactly once after subject formula is finished: either on failure, deterministic success, commit, or an exception";
    rdfs:domain log:Formula;
    rdfs:range log:Formula.

e:findall a rdf:Property, e:Builtin;
    rdfs:comment """built-in used as ?SCOPE e:findall (?SELECT ?WHERE ?ANSWER).
            within the subject ?SCOPE it unifies ?ANSWER with a list that contains all the instantiations of ?SELECT satisfying the ?WHERE clause
            it is not binding the free variables in ?WHERE""";
    rdfs:domain e:Scope;
    rdfs:range rdf:List.

e:fileString a rdf:Property, e:Builtin;
    rdfs:comment "built-in to read the file contents into a string";
    rdfs:domain xsd:string;
    rdfs:range xsd:string.

e:firstRest a rdf:Property, e:Builtin;
    rdfs:comment "built-in to convert a list into its first rest tuple";
    rdfs:domain rdf:List;
    rdfs:range e:Tuple.

e:format a rdf:Property, e:Builtin;
    rdfs:comment """built-in with the subject a list, whose first member is a format string, and whose remaining members are
            arguments to the format string. The format string is the one used in prolog's format predicate.
            The object is calculated from the subject""";
    rdfs:domain rdf:List;
    rdfs:range rdfs:Literal.

e:graphCopy a rdf:Property, e:Builtin;
    rdfs:comment "built-in to make a bounded copy of the subject graph e.g. {:a :b :c. :d :e :f} e:graphCopy ?GRAPH";
    rdfs:domain log:Formula;
    rdfs:range log:Formula.

e:graphDifference a rdf:Property, e:Builtin;
    rdfs:comment "built-in used for graph difference e.g. ({:a :b :c. :d :e :f} {:d :e :f}) e:graphDifference {:a :b :c}";
    rdfs:domain rdf:List;
    rdfs:range log:Formula.

e:graphIntersection a rdf:Property, e:Builtin;
    rdfs:comment "built-in used for graph intersection e.g. ({:a :b :c. :d :e :f} {:d :e :f}) e:graphIntersection {:d :e :f}";
    rdfs:domain rdf:List;
    rdfs:range log:Formula.

e:graphList a rdf:Property, e:Builtin;
    rdfs:comment "built-in used for graph/list transformation e.g. {:a :b :c. :d :e :f. :g :h :i} e:graphList ({:a :b :c} {:d :e :f} {:g :h :i})";
    rdfs:domain log:Formula;
    rdfs:range rdf:List.

e:graphMember a rdf:Property, e:Builtin;
    rdfs:comment "built-in to get the triples from the subject graph e.g. {:a :b :c. :d :e :f} e:graphMember {:a :b :c}, {:d :e :f}";
    rdfs:domain log:Formula;
    rdfs:range log:Formula.

e:graphPair a rdf:Property, e:Builtin;
    rdfs:comment "built-in used for graph/pair transformation e.g. {:a :b :c. :d :e :f. :g :h :i} e:graphPair ({:a :b :c} {:d :e :f. :g :h :i})";
    rdfs:domain log:Formula;
    rdfs:range rdf:List.

e:hmac-sha a rdf:Property, e:Builtin;
    rdfs:comment "built-in function where the object is a Modified Base64 for XML identifiers encoded HMAC SHA-1 hash of the subject";
    rdfs:domain rdfs:Literal;
    rdfs:range rdfs:Literal.

e:ignore a rdf:Property, e:Builtin;
    rdfs:comment "built-in to call the object formula within the subject scope and to succeed anyway but only once";
    rdfs:domain e:Scope;
    rdfs:range log:Formula.

e:label a rdf:Property, e:Builtin;
    rdfs:comment "built-in to test wether the subject is a blank node or a Skolem IRI and return the relabeled blank node label or the Skolem IRI fragment as object (this is a level breaker)";
    rdfs:domain rdfs:Resource;
    rdfs:range rdfs:Literal.

e:labelvars a rdf:Property, e:Builtin;
    rdfs:comment "built-in to make a bounded copy of the subject";
    rdfs:domain rdfs:Resource;
    rdfs:range rdfs:Resource.

e:length a rdf:Property, e:Builtin;
    rdfs:comment "built-in that calculates the length of the subject list";
    rdfs:domain rdf:List;
    rdfs:range xsd:integer.

e:listType a rdf:Property;
    rdfs:comment "to declare that all the elements of a list have a common type";
    rdfs:domain rdfs:Class;
    rdfs:range rdfs:Class.

e:match a rdf:Property, e:Builtin;
    rdfs:comment "built-in to succeed when the object formula succeeds and to forget the bindings";
    rdfs:domain rdf:Resource;
    rdfs:range log:Formula.

e:max a rdf:Property, e:Builtin;
    rdfs:comment "built-in to get the maximum value e.g. (8 5 6 7 9 4) e:max 9";
    rdfs:domain e:Numbers;
    rdfs:range e:Number.

e:min a rdf:Property, e:Builtin;
    rdfs:comment "built-in to get the minimum value e.g. (8 5 6 7 9 4) e:min 4";
    rdfs:domain e:Numbers;
    rdfs:range e:Number.

e:multisetEqualTo a rdf:Property, e:Builtin;
    rdfs:comment "built-in to succeed when the subject multiset is equal to the object multiset e.g. (1 3 6 6 7 2 3) e:multisetEqualTo (3 3 7 6 6 2 1)";
    rdfs:domain rdf:List;
    rdfs:range rdf:List.

e:multisetNotEqualTo a rdf:Property, e:Builtin;
    rdfs:comment "built-in to succeed when the subject multiset is not equal to the object multiset e.g. (1 3 6 6 7 2 3) e:multisetEqualTo (3 3 7 6 2 1)";
    rdfs:domain rdf:List;
    rdfs:range rdf:List.

e:notLabel a rdf:Property, e:Builtin;
    rdfs:comment "built-in to test wether the subject is not a blank node with label in object (this is a level breaker)";
    rdfs:domain rdfs:Resource;
    rdfs:range rdfs:Literal.

e:numeral a rdf:Property, e:Builtin;
    rdfs:comment """built-in to convert literals to numbers e.g. "2012"^^xsd:long e:numeral 2012""";
    rdfs:domain rdfs:Literal;
    rdfs:range e:Number.

e:optional a rdf:Property, e:Builtin;
    rdfs:comment "built-in to call the object formula within the subject scope and to succeed anyway";
    rdfs:domain e:Scope;
    rdfs:range log:Formula.

e:pcc a rdf:Property, e:Builtin;
    rdfs:comment "built-in to calculate the Pearson correlation coefficient e.g. ((55 66 72 87 56 77 73 69 74 56) (1.66 1.78 1.87 1.92 1.66 1.89 1.86 1.79 1.80 1.66)) e:pcc 0.9569729506311461";
    rdfs:domain e:PairOfNumbers;
    rdfs:range e:Number.

e:prefix a rdf:Property, e:Builtin;
    rdfs:comment "built-in to produce an object literal containing all prefixes";
    rdfs:domain rdfs:Resource;
    rdfs:range rdfs:Literal.

e:propertyChainExtension a rdf:Property, e:Builtin;
    rdfs:comment "built-in to support owl:propertyChainAxiom inferencing i.e. {?p owl:propertyChainAxiom ?x. ?x e:propertyChainExtension (?s ?o)} => {?s ?p ?o}";
    rdfs:domain rdf:List;
    rdfs:range rdf:List.

e:random a rdf:Property, e:Builtin;
    rdfs:comment "object is a random integer i such that 0 =< i < first element of subject list; when the rest of subject list rest is not empty i is reproducible in function of the subject list";
    rdfs:domain rdf:List;
    rdfs:range xsd:integer.

e:relabel a rdf:Property, e:Builtin;
    rdfs:comment "relabel subject with object in the output of the reasoning run";
    rdfs:domain rdfs:Resource;
    rdfs:range rdfs:Resource.

e:reverse a rdf:Property, e:Builtin;
    rdfs:comment "built-in to reverse the subject list into the object list";
    rdfs:domain rdf:List;
    rdfs:range rdf:List.

e:rms a rdf:Property, e:Builtin;
    rdfs:comment "built-in to calculate the root mean square e.g. (55 66 72 87 56 77 73 69 74 56) e:rms 69.2105483289939";
    rdfs:domain e:Numbers;
    rdfs:range e:Number.

e:roc a rdf:Property, e:Builtin;
    rdfs:comment "built-in to simulate ROC curve e.g. strength e:roc (sensitivity aspecificity)";
    rdfs:domain e:Number;
    rdfs:range rdf:List.

e:sha a rdf:Property, e:Builtin;
    rdfs:comment "built-in function where the object is a Modified Base64 for XML identifiers encoded SHA-1 hash of the subject";
    rdfs:domain rdfs:Literal;
    rdfs:range rdfs:Literal.

e:sigmoid a rdf:Property, e:Builtin;
    rdfs:comment "built-in to calculate a sigmoid e.g. -6 e:sigmoid 0.0024726231566347743";
    rdfs:domain rdf:List;
    rdfs:range e:Number.

e:skolem a rdf:Property, e:Builtin;
    rdfs:comment "built-in to generate a Skolem IRI object which is a function of the arguments in the subject list";
    rdfs:domain rdf:List;
    rdfs:range rdfs:Resource.

e:sort a rdf:Property, e:Builtin;
    rdfs:comment "built-in to sort the subject list and remove duplicates";
    rdfs:domain rdf:List;
    rdfs:range rdf:List.

e:std a rdf:Property, e:Builtin;
    rdfs:comment "built-in to calculate the sample standard deviation e.g. (55 66 72 87 56 77 73 69 74 56) e:std 10.426994879744703";
    rdfs:domain e:Numbers;
    rdfs:range e:Number.

e:stringEscape a rdf:Property, e:Builtin;
    rdfs:comment "built-in to escape the subject string";
    rdfs:domain rdfs:Literal;
    rdfs:range rdfs:Literal.

e:stringReverse a rdf:Property, e:Builtin;
    rdfs:comment "built-in to reverse the subject string";
    rdfs:domain rdfs:Literal;
    rdfs:range rdfs:Literal.

e:stringSplit a rdf:Property, e:Builtin;
    rdfs:comment """built-in to split a string into a list of strings according to a string containing separator characters e.g. ("a-b/c-d/e" "-/") e:stringSplit ("a" "b" "c" "d" "e")""";
    rdfs:domain rdf:List;
    rdfs:range rdf:List.

e:subsequence a rdf:Property, e:Builtin;
    rdfs:comment "built-in to succeed if all elements of object list appear in subject list in the same order";
    rdfs:domain rdf:List;
    rdfs:range rdf:List.

e:trace a rdf:Property, e:Builtin;
    rdfs:comment "built-in that outputs the object";
    rdfs:domain rdfs:Resource;
    rdfs:range rdfs:Resource.

e:transaction a rdf:Property, e:Builtin;
    rdfs:comment "used to rewrite P => C. as P => {P e:transaction C}. {P e:transaction C} => C";
    rdfs:domain log:Formula;
    rdfs:range log:Formula.

e:transpose a rdf:Property, e:Builtin;
    rdfs:comment "built-in to transpose the subject matrix e.g. ((0 1) (2 3) (4 5)) e:transpose ((0 2 4) (1 3 5))";
    rdfs:domain rdf:List;
    rdfs:range rdf:List.

e:tripleList a rdf:Property, e:Builtin;
    rdfs:comment "built-in used for triple/list transformation e.g. {:a :b :c} e:tripleList (:a :b :c)";
    rdfs:domain log:Formula;
    rdfs:range rdf:List.

e:tuple a rdf:Property, e:Builtin;
    rdfs:comment "built-in to bind the subject to a unique blank node which is a function of the object tuple";
    rdfs:domain rdfs:Resource;
    rdfs:range rdf:List.

e:tupleTypes a rdf:Property;
    rdfs:comment "to declare the types of all the elements of a tuple";
    rdfs:domain rdfs:Class;
    rdfs:range e:TupleTypes.

e:unique a rdf:Property, e:Builtin;
    rdfs:comment "built-in to succeed when the subject object pair is unique";
    rdfs:domain rdfs:Resource;
    rdfs:range rdfs:Resource.

e:valuation a rdf:Property;
    rdfs:comment "to express (lower upper) valuation of a formula e.g. {:PatientWithNoFlu rdfs:subClassOf :PatientWithFever} e:valuation (0.032 0.048)";
    rdfs:domain log:Formula;
    rdfs:range rdf:List.

e:weight a rdf:Property;
    rdfs:comment "used to express the weight in MLN (Markov Logic Network) inspired descriptions";
    rdfs:domain rdf:List;
    rdfs:range e:Number.

e:whenGround a rdf:Property, e:Builtin;
    rdfs:comment "when the subject is RDF ground the object is called, otherwise this built-in succeeds e.g.?value e:whenGround {?value math:greaterThan 40}";
    rdfs:domain rdfs:Resource;
    rdfs:range rdfs:Resource.

e:wwwFormEncode a rdf:Property, e:Builtin;
    rdfs:comment "built-in bidirectional www form encoder";
    rdfs:domain rdfs:Literal;
    rdfs:range rdfs:Literal.
