### Table 4. Shows OWL statements and there representation in a logic program

"... In PAGE 12: ... This is achieved by working with the complete rule set, containing rules for every OWLP Lite statement no matter if they are used in the ontology or not. Table4 shows some of the required facts for comparision with the Direct approach (see Table 1). Table 5 gives a nearly complete summary of the required rules and facts of our Meta Mapping approach.... ..."

### Table 1: Complexity of model checking for default logic

1999

"... In PAGE 4: ... The above property and Theorem 6 also imply p 2- completeness of model checking for prerequisite-free dis- junctive default theories. In Table1 we summarize the complexity results de- scribed in this section. Each column of the table corre- sponds to a di erent condition on the conclusion part of default rules.... In PAGE 6: ... From the computational viewpoint, it turns out that Liberatore and Schaerf apos;s notion of model checking is harder than the one presented in this paper. In fact, comparing Table1 with the results reported in [Liber- atore and Schaerf, 1998], it can be seen that our for- mulation of model checking is computationally easier in almost all the cases examined, with the exception of nor- mal and supernormal default theories, for which the com- plexity of the two versions of model checking is the same. 6 Conclusions In this paper we have studied the complexity of model checking in several nonmonotonic logics.... ..."

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### Table 1: Comparison of techniques for the induction of recursive logic programs

1999

"... In PAGE 11: ...iques are overviewed in Section 3.3. Finally, in Section 3.4, we point out cross-fertilisation opportunities and identify directions for future work. The comparison chart ( Table1 ) at the end of this section will be helpful towards this aim, and it may be a good idea for the reader to briefly study it right now. Techniques that are somehow related to some others, or representative thereof, and techniques that are somehow more sophisticated and powerful (in an absolute, application-independent sense) than others will obviously get more coverage here than those that are completely different from all others, or that feature highly specialised (sub-)machinery that is impossible to explain in the allotted space, or whose power is quite limited.... In PAGE 28: ...3.4 Summary We now summarise our overview by means of a chart (see Table1 ). The top five lines name classification criteria, whereas the bottom sixteen lines name actual comparison criteria and features, so that the techniques may be meas- ured up to each other.... In PAGE 35: ... The two approaches can thus be considered complementary, rather than rivals, and the ultimate decision of which one to use should lie with the specifier, not with the research community. So then, what is our statement on the future of the inductive synthesis of recursive programs applied towards pro- gramming assistance? We believe such techniques can be (made) viable, provided more research is done on over- coming the obstacles listed above, provided more realistic programming scenarios are aimed at, and provided the future work directions and cross-fertilisation opportunities of Table1 are pursued. We believe that some categories of programmers would use such techniques, provided it improves their productivity or increases the class of pro- grams they can write by themselves.... ..."

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### Table 1. Description logic ALC

1997

"... In PAGE 2: ... We use the notation of DLs, focusing on the well-known DL ALC, corresponding to the standard PDL with atomic programs only. Table1 summarizes the syntax and the semantics of ALC and the corresponding PDL. In addition, weusethetwo nonmonotonic modal operators: a minimal knowledge operator K and a default assumption operator A.... ..."

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### Table 2: Inference Rules of Many Sorted Monadic Equational Logic

1991

"... In PAGE 7: ...omplex assertions, e.g. formulas of rst order logic, then they should be interpreted by subobjects; in particular equality = : A should be interpreted by the diagonal [[A]]. The formal consequence relation on the set of equations is generated by the inference rules for equivalences ((re ), (simm) and (trans)), congruence and substitutivity (see Table2 ). This formal consequence relation is sound and complete w.... In PAGE 12: ...7 Given a signature for the programming language, let be the signature for the metalanguage with the same base types and a function p: 1 ! T 2 for each command p: 1 * 2 in . The translation from programs over to terms over is de ned by induction on raw programs: x [x]T (let x1(e1 in e2) (letT x1(e1 in e2 ) p(e1) (letT x(e1 in p(x)) [e] [e ]T (e) (letT x(e in x) The inference rules for deriving equivalence and existence assertions of the simple programming language can be partitioned as follows: general rules (see Table 6) for terms denoting computations, but with variables ranging over values; these rules replace those of Table2 for many sorted monadic equational logic rules capturing the properties of type- and term-constructors (see Table 7) after interpretation of the programming language; these rules replace the additional rules for the metalanguage given in Table 4.... ..."

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### Table 1: The logic CGL.

"... In PAGE 3: ... AXIOMS AND COMPLETENESS We now present an axiomatic system for the language Lc, and prove its soundness and completeness with respect to the class of all coalitional games without transferable payoff. Table1 summarizes the axioms and rules of our logic CGL. For- mally, CGL is the set of all Lc-formulas derivable under turnstileleft.... ..."

### Table 1: The logic CGL.

"... In PAGE 3: ... AXIOMS AND COMPLETENESS We now present an axiomatic system for the language Lc, and prove its soundness and completeness with respect to the class of all coalitional games without transferable payoff. Table1 summarizes the axioms and rules of our logic CGL. For- mally, CGL is the set of all Lc-formulas derivable under turnstileleft.... ..."

### Table 1: The logic CGL.

"... In PAGE 3: ... AXIOMS AND COMPLETENESS We now present an axiomatic system for the language Lc, and prove its soundness and completeness with respect to the class of all coalitional games without transferable payoff. Table1 summarizes the axioms and rules of our logic CGL. For- mally, CGL is the set of all Lc-formulas derivable under turnstileleft.... ..."

### Table 2: BAT Results with Manually Optimized Ordering

2002

"... In PAGE 9: ... After enough effort, we were able to find a good ordering that allows symbolic simulation to run. Table2 shows the results. In this sequence of experiments, we were able to complete the assertion check without using any constant logic values to simplify the assertion.... In PAGE 9: ... In this sequence of experiments, we were able to complete the assertion check without using any constant logic values to simplify the assertion. By comparing the results in Table 1 and in Table2 , we observe that variable ordering sig- nificantly impacts the performance of symbolic simulation. For the OBDD sizes, we show two types of data: the total number of OBDD nodes at the end of symbolic simulation (to- tal OBDD nodes), and the maximum number of OBDD nodes during the symbolic simulation (max OBDD nodes).... ..."

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