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... UΠ . Π is consistent if it has an answer set. Π entails a ground literal a, Π |= a, if a belongs to every answer set of Π. For convenience in notation, we will make use of choice atoms as defined in =-=[20]-=- that can occur in a rule wherever a literal can. Answer sets of logic programs can be computed using answer set solvers (e.g., Clasp [12], dlv [8]). 2.2 Object-Oriented Knowledge Bases We will now re...

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... • Taxonomic Knowledge: This group of facts encodes the class hierarchy, the relation hierarchy, individual constants and their class membership. It contains ASP-atoms of the following form: class(c) =-=(2)-=- individual(i) (3) subclass of(c1, c2) (4) disjoint(c1, c2) (5) instance of(i, c) (6) relation(r) (7) range(r, c) (8) domain(r, c) (9) subrelation of(r1, r2) (10) compose(r1, r2, r3) (11) inverse(r1, ...

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...d from the set of all rules of Π by deleting (i) each rule that has a naf-literal not a in its body with a ∈ S, and (ii) all naf-literals in the bodies of the remaining rules. S is an answer set of Π =-=[13]-=- if it satisfies the following conditions: (i) If Π does not contain any naf-literal then S is the minimal set of ground literals satisfying all rules in Π; and (ii) If Π contains some naf-literal the...

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...e in notation, we will make use of choice atoms as defined in [20] that can occur in a rule wherever a literal can. Answer sets of logic programs can be computed using answer set solvers (e.g., Clasp =-=[12]-=-, dlv [8]). 2.2 Object-Oriented Knowledge Bases We will now review the notion of an OOKB [6]. We note that an OOKB could be viewed as a logic program with function symbols and the language of OOKBs co...

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...B5. 2.3 KB Bio 101: An OOKB Usage and Some Key Characteristics The KB Bio 101 is an instance of OOKB and is available in ASP format6. The KB is based on an upper ontology called the Component Library =-=[3]-=-. The biologists used a knowledge authoring system called AURA to represent knowledge from a biology textbook. As an example, in Figure 1, we show an example AURA graph. The white node labeled as Euka...

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...es such as 3 http://www.projecthalo.com/ 4 http://www.aaaivideos.org/2012/inquire_intelligent_textbook/ ar X iv :1 31 2. 61 38 v1s[ cs .A I]s20sD ecs20 13 82 V.K. Chaudhri et al . FDNC [11], Datalog± =-=[5]-=-, and ASPfs [1] in its support for function symbols. It differs from these previous LP languages as well as from the DL systems in that the functions can be used to specify graph-structured objects wh...

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...he KB Bio 101 cannot be expressed in commonly available decidable DLs because it contains graph structured descriptions. Efficient reasoning with graph structures is an area of active recent research =-=[15, 16]-=-, and since there exists an export of KB Bio 101 for DL systems also [7], it provides an ideal usecase to explore the relative effectiveness of DL reasoners vs ASP solvers on a common problem. • The r...

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...ng (LP) languages such as 3 http://www.projecthalo.com/ 4 http://www.aaaivideos.org/2012/inquire_intelligent_textbook/ ar X iv :1 31 2. 61 38 v1s[ cs .A I]s20sD ecs20 13 82 V.K. Chaudhri et al . FDNC =-=[11]-=-, Datalog± [5], and ASPfs [1] in its support for function symbols. It differs from these previous LP languages as well as from the DL systems in that the functions can be used to specify graph-structu...

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...part is a relationship between those individuals. It is required that if f (or g) appears in (13) or (14), then the OOKB also contains the following rule instance of(f(X), cf ) ← instance of(X, c) or =-=(15)-=- instance of(g(X), cg) ← instance of(X, c) (16) which specify the class of which f(X) (resp. g(X)) is a member. For example, if f(X) represents a nucleus individual, then cf will be the class Nucleus....

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...tp://www.projecthalo.com/ 4 http://www.aaaivideos.org/2012/inquire_intelligent_textbook/ ar X iv :1 31 2. 61 38 v1s[ cs .A I]s20sD ecs20 13 82 V.K. Chaudhri et al . FDNC [11], Datalog± [5], and ASPfs =-=[1]-=- in its support for function symbols. It differs from these previous LP languages as well as from the DL systems in that the functions can be used to specify graph-structured objects which cannot be d...

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...owledge encoded in KB Bio 101. These queries were developed by extensive analysis of the questions from an exam, the questions at the back of the book, and the questions that are educationally useful =-=[4, 18]-=-. We divide these queries into four groups. The first type of queries which includes the first two queries asks about facts and relatiolnships. The second type of queries asks about the taxonomic info...

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...owledge encoded in KB Bio 101. These queries were developed by extensive analysis of the questions from an exam, the questions at the back of the book, and the questions that are educationally useful =-=[4, 18]-=-. We divide these queries into four groups. The first type of queries which includes the first two queries asks about facts and relatiolnships. The second type of queries asks about the taxonomic info...

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...vidual constants and their class membership. It contains ASP-atoms of the following form: class(c) (2) individual(i) (3) subclass of(c1, c2) (4) disjoint(c1, c2) (5) instance of(i, c) (6) relation(r) =-=(7)-=- range(r, c) (8) domain(r, c) (9) subrelation of(r1, r2) (10) compose(r1, r2, r3) (11) inverse(r1, r2) (12) The predicate names are self-explanatory. • Descriptive statements: Relationships between in...

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...questions. The third type is about the differences and similarities between individuals from different classes. This type of query has been traditionally studied as an example of analogical reasoning =-=[10]-=-. The fourth type of queries that includes the last two questions query for relationships between concepts and are unique to our work. • what is a eukaryotic cell? • what process provides raw material...

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...scriptive rule Table 1. Statistics on KB Bio 101 3 Queries in OOKBs We will now describe the queries given an OOKB, say KB(D). These queries play a central role in the educational application Inquire =-=[17]-=- which employs the knowledge encoded in KB Bio 101. These queries were developed by extensive analysis of the questions from an exam, the questions at the back of the book, and the questions that are ...

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... the relation values of individuals (rules (25)—(27)), in/equality between terms (rules (28)—(40)), and enforcing constraints (rules (42)—(47)). subclass of(C,B) ← subclass of(C,A), subclass of(A,B). =-=(21)-=- instance of(X,C) ← instance of(X,D), subclass of(D,C). (22) disjoint(C,D) ← disjoint(D,C). (23) ¬instance of(X,C) ← instance of(X,D), disjoint(D,C). (24) value(U,X,Z) ← compose(S, T, U), value(S,X, Y...