I. Horrocks, P.F. Patel-Schneider, and R. Sebastiani. An Analysis of Empirical Testing for Modal Decision Procedures. Logic J. of the IGPL, 8(3):293--323, 2000.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....checking there is large and rapidly expanding body of experimental knowledge; see, e.g. 7] In contrast, empirical aspects of modal satisfiability checking have only recently drawn the attention of researchers. We now have a number of test sets, some of which have been evaluated extensively [4, 10, 8, 13, 12]. In addition, we also have a clear set of guidelines for performing empirical testing in the setting of modal logic [10, 12] Currently, there are three main test methodologies for modal satisfiability solvers, one based on hand crafted formulas, the other two based on randomly generating ....

....satisfiability checking have only recently drawn the attention of researchers. We now have a number of test sets, some of which have been evaluated extensively [4, 10, 8, 13, 12] In addition, we also have a clear set of guidelines for performing empirical testing in the setting of modal logic [10, 12]. Currently, there are three main test methodologies for modal satisfiability solvers, one based on hand crafted formulas, the other two based on randomly generating problems. To understand on what kinds of problems a particular prover does or does not do well, it helps to work with test formulas ....

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I. Horrocks, P.F. Patel-Schneider, and R. Sebastiani. An Analysis of Empirical Testing for Modal Decision Procedures. Logic Journal of the IGPL, 8(3):293--323, 2000.

....advantages and disadvantages with respect to the tableau approach. On the one hand we can translate many systems into the same background language and hence explore di erent, and also combined, systems without the need to modify the prover. But empirical tests show that the price to pay is high [28, 5]. The undecidability of the full background language shows up in degraded performance on the modal fragments, and rst order provers can hardly emulate their tableau based competitors. Given the simplicity of propositional resolution, it is natural to wonder why direct resolution methods for ....

....to polynomially simulate PSPACE tableaux. The rst author and Juan Heguiabehere are implementing a rst prototype of the resolution method described in this paper. It would be interesting to perform empirical testing on the performance of this resolution prover along the lines of, for example [28], both in comparison with translation based resolution provers and those based on tableaux. Finally, our completeness proof is constructive: if a refutation cannot be found, we can actually de ne a model for the formula or knowledge base. Hence, our methods can also be used for model extraction. ....

I. Horrocks, P. Patel-Schneider, and R. Sebastiani. An analysis of empirical testing for modal decision procedures. In Areces et al. [4], pages 293-324.

....comparison scale (p search simulation) It shown that KEM p search simulates SST while SST cannot p search simulate KEM. 1 Introduction In the last few years several comparisons (competition) for theorem provers for modal logic have been held and experimental research has been carried out (cf. [11, 10]) Despite the potential interest for future possible applications, we believe, that they provided little or no insight on better theoretical architecture for modal theorem provers, since external factors could influence the performance. In this paper two labelled approaches to modal tableaux are ....

Ian Horrocks, Peter F. Patel-Schneider, and Roberto Sebastiani. An analysis of empirical testing for modal decision procedures. Logic Journal of IGPL, 8:293--323, 2000.

....advantages and disadvantages with respect to the tableau approach. On the one hand we can translate many systems into the same background language and hence explore di erent, and also combined, systems without the need to modify the prover. But empirical tests show that the price to pay is high [28, 5]. The undecidability of the full background language shows up in degraded performance on the modal fragments, and rst order provers can hardly emulate their tableau based competitors. Given the simplicity of propositional resolution, it is natural to wonder why direct resolution methods for ....

....simulate PSPACE tableaux. The ideas behind labeled resolution are simple enough so that adapting available provers should not turn to be a very dicult task. It would be interesting to perform empirical testing on the performance of this resolution prover along the lines of, for example [28], both in comparison with translation based resolution provers and those based on tableaux. Finally, our completeness proof is constructive: if a refutation cannot be found, we can actually de ne a model for the formula or knowledge base. Hence, our methods can also be used for model extraction. ....

I. Horrocks, P. Patel-Schneider, and R. Sebastiani. An analysis of empirical testing for modal decision procedures. In Areces et al. [4], pages 293-324.

....checking there is large body of experimental knowledge; see e.g. 25] for a recent showcase. In contrast, empirical aspects of modal satisfiability checking have only recently drawn the attention of researchers. We now have a number of test sets, some of which have been evaluated extensively [6, 31, 26, 35, 34]. In addition, we have a clear set of guidelines for performing empirical testing in the setting of modal logic [31, 34] Below we report on an empirical evaluation of one of the test sets that is currently in use for evaluating modal satisfiability solvers, viz. the random modal QBF test set. ....

....modal satisfiability checking have only recently drawn the attention of researchers. We now have a number of test sets, some of which have been evaluated extensively [6, 31, 26, 35, 34] In addition, we have a clear set of guidelines for performing empirical testing in the setting of modal logic [31, 34]. Below we report on an empirical evaluation of one of the test sets that is currently in use for evaluating modal satisfiability solvers, viz. the random modal QBF test set. The first random generation technique used in testing modal decision procedures, the random 3CNF#m test methodology, was ....

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I. Horrocks, P.F. Patel-Schneider, and R. Sebastiani. An analysis of empirical testing for modal decision procedures. Logic Journal of the IGPL, 8:293--323, 2000.

.... many decidability results for modal or description logics are based on tableau algorithms (see Ladner 1977, Halpern and Moses 1992, Donini et al. 1997, or Horrocks et al. 1999 for examples) and some of the fastest implementations of modal satis ability procedures are based on tableau calculi (Horrocks et al. 2000). Unlike automata algorithms, the averagecase behaviour in practice is so good that nding really hard problems to test these implementations has become a problem in itself. In this paper, we generalise the principles from tableau algorithms for modal logics in order to develop a tableau ....

....the tree model property, the graphs generated by these algorithms are trees, which allows for simpler algorithms and easier implementation and optimisation of these algorithms. Indeed, some of the fastest implementations of modal or description logics satis ability algorithms use tableau calculi (Horrocks et al. 2000). For many modal or description logics, e.g. K or ALC, termination of these algorithms is due to the fact that the modal depth of the formulas appearing at a node strictly decreases with every step from the root of the tree. For other logics, e.g. K4, K with the universal modality, or the ....

Horrocks, I., P. F. Patel-Schneider, and R. Sebastiani. 2000. An Analysis of Empirical Testing for Modal Decision Procedures. Logic Journal of the IGPL 8(3):293-323.

....of deciding, given a formula of the form (2) in which modal operators are applied only to concepts and TBox axioms, but not to roles) whether is satisfiable in a model with constant domains. Tableau based algorithms have been shown to be practical even for logics of rather high complexity [14, 19, 21]. This gives us grounds to believe that, although the satisfiability problem for KALC is known to be NEXPTIMEcomplete [26] by providing a tableau decision algorithm we demonstrate that highly expressive description logics with modal operators have a chance to be implementable. The logic KALC ....

I. Horrocks, P. Patel-Schneider, and R. Sebastiani. An analysis of empirical testing for modal decision procedures. Logic Journal of the IGPL, 8(3):293-- 323, 2000.

....of deciding, given a formula of the form (2) in which modal operators are applied only to concepts and TBox axioms, but not to roles) whether is satis able in a model with constant domains. Tableau based algorithms have been shown to be practical even for logics of rather high complexity [14, 19, 21]. This gives us grounds to believe that, although the satis ability problem for KALC is known to be NEXPTIMEcomplete [26] by providing a tableau decision algorithm we demonstrate that highly expressive description logics with modal operators have a chance to be implementable. The logic KALC with ....

I. Horrocks, P. Patel-Schneider, and R. Sebastiani. An analysis of empirical testing for modal decision procedures. Logic Journal of the IGPL, 8(3):293{ 323, 2000.

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I. Horrocks, P. F. Patel-Schneider, and R. Sebastiani. An Analysis of Empirical Testing for Modal Decision Procedures. Logic Journal of the IGPL, 8(3):293--323, May 2000.

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Ian Horrocks, Peter Patel-Schneider, and Roberto Sebastiani. An analysis of empirical testing for modal decision procedures. Logic Journal of the IGPL, 8(3):293--324, May 2000.

....have concentrated on eliminating top level propositional disjuncts by setting p = 0 [6] However, formulae with propositional literals showing up only at the deepest modal depth are extremely hard to solve for modal depths greater than 1. Moreover, the resulting formule are not very natural [5]. We have devised a new generation methodology for generating modal formulae for K (m) that eliminates or reduces the problems with the previous generation methods. The first new idea of our approach, first suggested in [5] is to eliminate strictly propositional clauses except at the maximum ....

....greater than 1. Moreover, the resulting formule are not very natural [5] We have devised a new generation methodology for generating modal formulae for K (m) that eliminates or reduces the problems with the previous generation methods. The first new idea of our approach, first suggested in [5], is to eliminate strictly propositional clauses except at the maximum modal depth by requiring that the number of propositional literals in each clause be less than 1 away from the average value, while still maintaining the overall ratio. For three disjuncts per clause (C = 3) and propositional ....

Ian Horrocks, Peter F. Patel-Schneider, and Roberto Sebastiani. An analysis of empirical testing for modal decision procedures. Logic Journal of the IGPL, 8(3):293-- 323, 2000.

....[6] SAT [3] and MSPASS [8] have more optimisations and are much faster than the previous generation of modal decision procedures. As with most theorem proving problems, neither computational complexity nor asymptotic complexity is very useful in determining the effectiveness of optimisations [7]. The worst case complexity of the problem, of course, remains unchanged. For many propositional modal logics, this complexity ranges from PSPACE complete to EXPTIME complete. The asymptotic complexity of the systems also generally remains unchanged. The worst case asymptotic complexity for most ....

....namely three disjuncts in a clause, C, and only one kind of modal box, m. Then several values are picked for the number of top level clauses in a formula, L, and for each value for L many (usually about 100) formulae are generated and tested for satisfiability. Based on some preliminary work [7], we have developed a new random generation method that provides benefits over previous methods for generating empirical tests. 1 Our new method fixes and much generalizes the 3CNF2m methodology for randomly generating clausal formulae in modal logics [4, 9, 1] used in many previous empirical ....

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I. Horrocks, P. F. Patel-Schneider, and R. Sebastiani. An Analysis of Empirical Testing for Modal Decision Procedures. Logic Journal of the IGPL, 8(3):293--323, May 2000.

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I. Horrocks, P.F. Patel-Schneider, and R. Sebastiani. An Analysis of Empirical Testing for Modal Decision Procedures. Logic J. of the IGPL, 8(3):293--323, 2000.

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I. Horrocks, P.F. Patel-Schneider, and R. Sebastiani. An analysis of empirical testing for modal decision procedures. Logic Journal of the IGPL, 8:293--323, 2000.

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I. Horrocks, P. Patel-Schneider, and R. Sebastiani. An analysis of empirical testing for modal decision procedures. Logic Journal of the IGPL, 8:293--323, 2000.

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I. Horrocks, P.F. Patel-Schneider, and R. Sebastiani. An analysis of empirical testing for modal decision procedures. Logic Journal of the IGPL, 8:293--323, 2000.

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Horrocks, I., P. F. Patel-Schneider and R. Sebastiani, An analysis of empirical testing for modal decision procedures, Logic Journal of IGPL 8 (2000), pp. 293-- 323.

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I. Horrocks, P.F. Patel-Schneider, and R. Sebastiani. An Analysis of Empirical Testing for Modal Decision Procedures. Logic Journal of the IGPL, 8(3):293--323, 2000.

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I. Horrocks, P.F. Patel-Schneider, and R. Sebastiani. An Analysis of Empirical Testing for Modal Decision Procedures. Logic J. of the IGPL, 8(3):293--323, 2000.

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I. Horrocks, P.F. Patel-Schneider, and R. Sebastiani. An Analysis of Empirical Testing for Modal Decision Procedures. Logic Journal of the IGPL, 8(3):293--323, 2000.

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Horrocks, I., P. Patel-Schneider and R. Sebastiani, An Analysis of Empirical Testing for Modal Decision Procedures, Logic Journal of the IGPL 8 (2000), pp. 293--323.

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I. Horrocks, P.F. Patel-Schneider, and R. Sebastiani. An Analysis of Empirical Testing for Modal Decision Procedures. Logic J. of the IGPL, 8(3):293--323, 2000.

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I. Horrocks, P. Patel-Schneider, and R. Sebastiani. An analysis of empirical testing for modal decision procedures. Logic Journal of the IGPL, 8(3):293--323, 2000.

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I. Horrocks, P.F. Patel-Schneider, and R. Sebastiani. An Analysis of Empirical Testing for Modal Decision Procedures. Logic J. of the IGPL, 8(3):293--323, 2000.

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I. Horrocks, P. Patel-Schneider, and R. Sebastiani. An analysis of empirical testing for modal decision procedures. In Areces et al. [2000c], pages 293-324.

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