Pawe#l Cholewinski, V. Wiktor Marek, Artur Mikitiuk, and Miros#law Truszczynski. Computing with Default Logic. Artificial Intelligence, 112(2--3):105--147, 1999.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....examples, we have studied two kinds of problems on graphs : the Hamilton cycle problem and the 3 coloring problem. We used the three kinds of graphs (ladder, board and simplex) presented in gure 4. Both problems have been generated and encoded in a logic program by means of system TheoryBase [3] and we refer to the ladder graph lad 4 board graph board 4 simplex graph sim 4 Fig. 3. Graphs for experimental studies di erent problems by the following conventions : ham lad N is an hamiltonian cycle problem on a ladder graph with 2N vertices, ham sim N is an hamiltonian cycle problem on a ....

P. Cholewiski, V. Marek, A. Mikitiuk, and M. Truszczyski. Computing with default logic. Articial Intelligence, 112:105146, 1999.

....predicate not p. The covering tests, that are necessary to determine which examples are not yet generalized and also to determine exceptions to a default, require either extension calculus or query answering in Reiter s default logic. For both tasks, operational systems exist (for instance DeRes [4], GADEL [19] XRay [20] and they could be integrated in a whole system for default theory learning. Example 1. The initial theory W concerns a set of people and a set of dishes . W = hb(1) hb(45) hb(46) hb(50) hb(51) hb(55) v(46) ....

P. Cholewiski, V. Marek, A. Mikitiuk, and M. Truszczyski. Computing with default logic. Articial Intelligence, 112:105146, 1999.

....default theory is 2 complete [5] The di erence in performances between human and arti cial approaches relies on the fact that human reasoning can avoid many veri cations while default logic builds a set of coherent conclusions and discards some kind of inconsistencies. Previous works [11, 2] have already investigated this computational aspect of default logic and even if some systems have good performances on certain classes of default theories, there is no e cient system for general extension calculus. Due to this computational complexity, a deterministic method based on the whole ....

....in Sicstus Prolog 3.8. 3 (we have also implemented ACO LS but due to a lack of space we only point out here some of our results) Diversi cation : Table 1 refers to the in uence of the Hamming distance for the problem ham 6 2 that encodes, with 45 defaults, a Hamiltonian cycle problem as in [2]. hd s ani at ati anis ats 6 50 124:0 481:0 3:9 48:1 194:1 8 57 116:2 355:5 3:1 52:1 164:3 10 73 108:9 263:3 2:4 75:8 185:7 12 57 139:7 227:5 1:6 93:6 156:7 14 27 173:0 183:1 1:1 98:9 108:7 Table 1. In uence of Hamming distance Tests have been done by 30 runs per Hamming distance hd with ....

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P. Cholewiski, V. Marek, A. Mikitiuk, and M. Truszczyski. Computing with default logic. Articial Intelligence, 112:105146, 1999.

....and proper entailment can be similarly polynomially reduced to one resp. two calls of a SAT procedure, which may be processed in parallel. As for the other semantics, theorem provers for logics with complexity up to 2 are needed as host for efficient translations. For example, DLV [78] DeRes [23], or a disjunctive extension of smodels [75] which all provide this expressiveness, might be used, as well as theorem provers based on quantified Boolean formulas [20, 83, 32] However, efficient transformations of the problems to these logics remain to be designed. In the case of problems with ....

.... only prototype implementations handling small examples have been developed so far, see [12] Notice that in related areas such as nonmonotonic reasoning, knowledge about complexity results proved extremely useful for developing efficient implementations of reasoning systems such as DeReS [23], smodels [75] and DLV [78] Secondly, our work contributes on a refinement of the tractability intractability frontier of default reasoning from conditional knowledge bases, by establishing new tractable cases. In particular, we have introduced q Horn (resp. ff Horn) conditional knowledge ....

P. Cholewinski, V. W. Marek, A. Mikitiuk, and M. Truszczynski. Computing with default logic. Artificial Intelligence, 112(2--3):105--147, 1999.

.... 2 complete decision problem in analogy to brave reasoning with stationary extensions. The results of this paper enable implementing brave reasoning with stationary and regular extensions. In addition to an inference engine for brave reasoning with Reiter s extensions (such as the system DeReS [2]) we need a program that computes the translation Tr ST2 (hD; T i) for a default theory hD; T i given as input. 7 Conclusions and Future Work In this paper, we have analyzed the possibilities of reducing stationary default logic (i.e. default theories under stationary extensions) to Reiter s ....

....if nested logic programs [15] are taken into consideration. Moreover, the properties of stationary and regular extensions and the translation function Tr ST2 enable implementing brave reasoning with stationary and regular extensions simply by using existing implementations of DL (such as DeReS [2]) By the theorems presented, the stationary default logic (STDL) is strictly less expressive than default logic (DL) but strictly more expressive than classical propositional logic (CL) Moreover, STDL is incomparable with the other representatives of the classes of EPH: NDL (normal DL) PDL ....

P. Cholewiski, V.W. Marek, A. Mikitiuk, and M. Truszczyski. Computing with default logic. Articial Intelligence, 112:105146, 1999.

....proper entailment can be similarly polynomially reduced to one resp. two calls of a SAT procedure, which may be processed in parallel. As for the other semantics, theorem provers for logics with complexity up to P 2 are needed as host for efficient translations. For example, DLV [78] DeRes [23], or a disjunctive extension of smodels [75] which all provide this expressiveness, might be used, as well as theorem provers based on quantified Boolean formulas [20, 83, 32] However, efficient transformations of the problems to these logics remain to be designed. In the case of problems with ....

.... only prototype implementations handling small examples have been developed so far, see [12] Notice that in related areas such as nonmonotonic reasoning, knowledge about complexity results proved extremely useful for developing efficient implementations of reasoning systems such as DeReS [23], smodels [75] and DLV [78] Secondly, our work contributes on a refinement of the tractability intractability frontier of default reasoning from conditional knowledge bases, by establishing new tractable cases. In particular, we have introduced q Horn (resp. ff Horn) conditional knowledge ....

P. Cholewinski, V. W. Marek, A. Mikitiuk, and M. Truszczynski. Computing with default logic. Artificial Intelligence, 112(2--3):105--147, 1999.

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Pawe#l Cholewinski, V. Wiktor Marek, Artur Mikitiuk, and Miros#law Truszczynski. Computing with Default Logic. Artificial Intelligence, 112(2--3):105--147, 1999.

No context found.

Pawe#l Cholewinski, V. Wiktor Marek, Artur Mikitiuk, and Miros#law Truszczynski. Computing with Default Logic. Artificial Intelligence, 112(2--3):105--147, 1999.

No context found.

P. Cholewinski, V. W. Marek, M. Truszczynski, and A. Mikitiuk. Computing with default logic. Artificial Intelligence, 112:105--146, 1999.

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P. Cholewinski, V. W. Marek, A. Mikitiuk, and M. Truszczynski. Computing with Default Logic. Artificial Intelligence, 112(2--3):105--147, 1999.

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