Supporting Open and Supporting Open and Closed World Reasoning - PowerPoint PPT Presentation

Supporting Open and Supporting Open and Closed World Reasoning Closed World Reasoning in the Semantic Web in the Semantic Web C. V. Damá ásio, A. Analyti, sio, A. Analyti, C. V. Dam G. Antoniou, G. Wagner G. Antoniou, G. Wagner

Overview Overview � Motivation Motivation � � Open and Closed World Reasoning Open and Closed World Reasoning � � Building blocks Building blocks � � Knowledge in the Semantic Web Knowledge in the Semantic Web � � Composing modules together Composing modules together � � Transformational Semantics Transformational Semantics � � Conclusions Conclusions �

Motivation Motivation � Merging knowledge in the Semantic Web is one Merging knowledge in the Semantic Web is one � fundamental unsolved problem unsolved problem fundamental � The need of combining closed and open world The need of combining closed and open world � reasoning is desirable desirable reasoning is � The adopted mechanisms should be The adopted mechanisms should be modular modular � � The solution should be The solution should be independent independent of the of the � semantics adopted semantics adopted � Use of Use of nonmonotonic nonmonotonic reasoning in the Semantic reasoning in the Semantic � Web should be carefully controlled controlled Web should be carefully

Approach Approach � Open and closed world assumptions can be Open and closed world assumptions can be already combined already combined in in � extended logic programming! extended logic programming! It is required two forms two forms of negation: of negation: It is required � � � strong or explicit strong or explicit � as failure weak, default or as failure � weak, default or � � The two forms of negation are available in The two forms of negation are available in � � Well Well- -founded semantics with explicit negation (WFSX) founded semantics with explicit negation (WFSX) � � Answer Set Semantics (AS) Answer Set Semantics (AS) � � The proposed solution uses the The proposed solution uses the same same program transformation program transformation � for both semantics for both semantics � The user should have an easy The user should have an easy syntactic mechanisms syntactic mechanisms to specify to specify � the use of nonmonotonic nonmonotonic reasoning constructs reasoning constructs the use of

Open and Closed World Open and Closed World reasoning reasoning � Open World Reasoning Open World Reasoning � � Founded on First Order Logic Founded on First Order Logic � � Adopted in Description Logics, OWL and SWRL Adopted in Description Logics, OWL and SWRL � � Appropriate for the Semantic Web Appropriate for the Semantic Web � � Sometimes too conservative Sometimes too conservative � � Closed World Reasoning Closed World Reasoning � � Founded on Nonmonotonic Logics Founded on Nonmonotonic Logics � � Adopted in Logic Programming and WRL Adopted in Logic Programming and WRL � � Appropriate for ( Appropriate for (Deducitive Deducitive) Databases ) Databases � � Sometimes too brave Sometimes too brave �

Example Example � Consider the following list of facts Consider the following list of facts � % All current EU countries % All current EU countries CountryEU(Austria) ) … … CountryEU(UK CountryEU(UK) ) CountryEU(Austria % Some non EU countries (not all… …) ) % Some non EU countries (not all ┐ CountryEU(China ┐ CountryEU(China) ) ┐ CountryEU(Djibuti ┐ CountryEU(Djibuti) )

A little geography… … A little geography � Is Austria a EU country ? Is Austria a EU country ? � � YES YES, because it appears the fact , because it appears the fact CountryEU(Austria CountryEU(Austria) in the ) in the � knowledge base knowledge base � Is China a EU country ? Is China a EU country ? � ┐ CountryEU(China � NO, because it is expressed that NO, because it is expressed that ┐ CountryEU(China) ) � � Is Montenegro a EU country ? Is Montenegro a EU country ? � � NO NO, because it is not listed there and the list is complete , because it is not listed there and the list is complete � (CLOSED WORLD REASONING) (CLOSED WORLD REASONING) � DON DON’ ’T KNOW T KNOW, since it is not listed then it might be or not , since it is not listed then it might be or not � (OPEN WORLD REASONING) (OPEN WORLD REASONING)

The help of extended LP The help of extended LP � Closed world reasoning: Closed world reasoning: � ┐ CountryEU(?C ┐ CountryEU(?C) ) ← ← ~ ~ CountryEU(?C CountryEU(?C) ) � Open world reasoning: Open world reasoning: � ┐ CountryEU(?C ┐ CountryEU(?C) ) ← ← ~ ~ CountryEU(?C CountryEU(?C) ) ~ ┐ ┐ CountryEU(?C CountryEU(?C) ) ← ← ~ CountryEU(?C) ) CountryEU(?C

A syntactic detour A syntactic detour � Rule bases are sets of rules of the form Rule bases are sets of rules of the form � � L L 0 ← L L 1 , … …, L , L m , ~ ~ L L m+1 , … …, , ~ ~ L L n 0 ← 1 , m , m+1 , � n � Each L Each L i (0 ≤ ≤ i i ≤ ≤ n) is an objective literal, i.e. n) is an objective literal, i.e. i (0 � � An atom An atom A(t A(t), or ), or � � The strong negation of an atom The strong negation of an atom ┐ ┐ A(t A(t) ) � � The symbol The symbol ~ ~ represents represents nonmonotonic nonmonotonic weak negation, and weak negation, and � cannot occur in the head cannot occur in the head ┐ represents monotonic strong negation, and can � The symbol The symbol ┐ represents monotonic strong negation, and can � occur in the head and in the body of rules occur in the head and in the body of rules � The discussion is restricted to the DATALOG case, i.e. no The discussion is restricted to the DATALOG case, i.e. no � function symbols in the language function symbols in the language

Putting weak negation on the Putting weak negation on the leash leash � The following predicate types are proposed The following predicate types are proposed � � Definite or objective predicates Definite or objective predicates � � Open predicates Open predicates � � Closed predicates Closed predicates � � Normal or unrestricted predicates Normal or unrestricted predicates � � Definite, open and closed predicates are limited Definite, open and closed predicates are limited � to be defined by rules without without weak negation weak negation to be defined by rules � Normal predicates can use the full language Normal predicates can use the full language �

Definite Predicates Definite Predicates � Similar to Similar to Definite Logic Programming, but Definite Logic Programming, but � allowing for explicit negation in the head and allowing for explicit negation in the head and body of rules body of rules � There can exist information gaps: predicates are There can exist information gaps: predicates are � partial partial � Reasoning is purely monotonic Reasoning is purely monotonic � � Reasoning is polynomial on the size of the Reasoning is polynomial on the size of the � ground rule base and can be readily ground rule base and can be readily implemented in Prolog implemented in Prolog

Open Predicates Open Predicates � Rules are like in the previous case, but additionally it is Rules are like in the previous case, but additionally it is � added the following pair of rules for each open added the following pair of rules for each open predicate A A with with arity arity n n predicate � ┐ ┐ A(?x A(?x 1 ,… …,? ,?x x n ) ← ← ~ ~ A(?x A(?x 1 ,… …,? ,?x x n ) 1 , n ) 1 , n ) � ~ ┐ ┐ A(?x � A(?x A(?x 1 ,… …,? ,?x x n ) ← ← ~ A(?x 1 ,… …,? ,?x x n ) 1 , n ) 1 , n ) � � Reasoning is monotonic Reasoning is monotonic � � Reasoning is polynomial for WFSX and co Reasoning is polynomial for WFSX and co- -NP NP � complete for AS complete for AS � Can be implemented with XSB or any answer set Can be implemented with XSB or any answer set � programming system like DLV, Smodels Smodels, etc. , etc. programming system like DLV,

Closed Predicates Closed Predicates � Rules are like in the previous case, but it is Rules are like in the previous case, but it is � added only one only one of the following pair of rules for of the following pair of rules for added closed predicate A A with with arity arity n n closed predicate � ┐ ┐ A(?x A(?x 1 ,… …,? ,?x x n ) ← ← ~ ~ A(?x A(?x 1 ,… …,? ,?x x n ) 1 , n ) 1 , n ) � ~ ┐ ┐ A(?x � A(?x A(?x 1 ,… …,? ,?x x n ) ← ← ~ A(?x 1 ,… …,? ,?x x n ) 1 , n ) 1 , n ) � � Reasoning is Reasoning is nonmonotonic nonmonotonic � � Conclusions obtained by objective predicates are Conclusions obtained by objective predicates are � also obtained by closed ones (common safe also obtained by closed ones (common safe knowledge) knowledge)

Normal Predicates Normal Predicates � Full syntax of extended logic programming Full syntax of extended logic programming � � Nonmonotonic Nonmonotonic � � No guarantees No guarantees… … � � Sometimes it is required Sometimes it is required �