M. Dalal, `Tractable reasoning in knowledge representation systems ', Technical Report CUCS-017-95, Department of Computer Science, Columbia University, New York, NY, (July 1995). file://ftp.cs.columbia.edu/reports/reports-1995/cucs-017-95.ps.gz.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....Methods for exact compilation (many of them with experimental results) a) Definition of original methods (for propositional formulae) i. efficient basis: Moses Tennenholtz 1993) ii. unit refutation completeness: del Val 1994) iii. directional extension: Dechter Rish 1994) iv. vivid form: (Dalal 1995) v. theory prime implicates: Marquis 1995) b) Definition of original methods (for non propositional formulae) i. propositional default logic propositional logic: Ben Eliyahu Dechter 1992) ii. propositional disjunctive logic programs propositional logic: Ben Eliyahu Dechter 1994) ....

Dalal, M. 1995. Tractable reasoning in knowledge representation systems. Technical Report CUCS-017-95, Department of Computer Science. Columbia University. New York.

....complete for any base of fact which will be used later. This provides us with a knowledge compilation method whose cost will be eventually amortized because forward chaining is faster than a complete inference method. Several other knowledge compilations have been defined since then [SK91] KS92] [Dal95], dV94] Mar95] SK96] Sch96] MS96] dV96] MM96] but only [Dal95] deals with a production algorithm. All methods but the approximate knowledge compilations of [SK91] dV96] SK96] are restricted to the propositional case. This paper describes an exact knowledge compilation method for the ....

....us with a knowledge compilation method whose cost will be eventually amortized because forward chaining is faster than a complete inference method. Several other knowledge compilations have been defined since then [SK91] KS92] Dal95] dV94] Mar95] SK96] Sch96] MS96] dV96] MM96] but only [Dal95] deals with a production algorithm. All methods but the approximate knowledge compilations of [SK91] dV96] SK96] are restricted to the propositional case. This paper describes an exact knowledge compilation method for the first order case. This compilation is dedicated to forward chaining but ....

Mukesh Dalal, Tractable Reasoning In Knowledge Representation Systems, Ph.D. thesis, Graduate School, New Brunswick, New Jersey, May 1995.

....the algorithm was not able to determine the satisfiability of S; but guaranteeing that S is satisfiable iff R is satisfiable. In the next section, we will show how to improve the speed of these algorithms at the cost of additional spaceused to cache results. Several basic ideas are taken from [13, 10, 9]. All algorithms presented in this paper are sound, that is, they never return an incorrect answer. An algorithm is called complete for a class of formulas iff it returns either fg or f2g for every formula in the class. For any formula S, let BinSat(S) returns S if S has a non binary clause, else ....

M. Dalal, `Tractable reasoning in knowledge representation systems ', Technical Report CUCS-017-95, Department of Computer Science, Columbia University, New York, NY, (July 1995). file://ftp.cs.columbia.edu/reports/reports-1995/cucs-017-95.ps.gz.

....start by reviewing clausal boolean constraint propagation (BCP) 12] an incomplete but sound and linear time method for deduction from clausal propositional theories. We will develop a model theoretic semantics for BCP [8] and study fact propagation (FP) that extends BCP to non clausal theories [2, 5]. FP will be specified using a confluent rewriting systems, for which we will present an algorithm that has quadratic time complexity in general, but is still linear time for clausal theories. FP performs strictly more inferences than CNF BCP, a previously proposed extension of BCP to nonclausal ....

M. Dalal, `Tractable reasoning in knowledge representation systems ', Technical Report CUCS-017-95, Department of Computer Science, Columbia University, New York, NY, (July 1995). file://ftp.cs.columbia.edu/reports/reports-1995/cucs-017-95.ps.gz.

....which model theoretic or proof theoretic semantics are not yet known (see 0 This work is supported by NSF Grant No. IRI 9410117 and ARPA ARL Contract No. DAAL01 94 K 0119. 1 For the purposes of this paper, a problem is tractable iff the corresponding decision problem is known to be in PTIME. (Dalal 1995)) Since not all equivalence relations on theories and formulas provide reasoners suitable for tractable reasoning with logical knowledge bases, we restrict our attention to admissible relations, which satisfy the properties listed in Section . For example, consider the equivalence relation =BCP ....

....f(ff) ff ff 1 : ff n )g [ Gamma =BCP f(ff) ff 1 : ff n )g [ Gamma; where Gamma is any clausal theory, ff s are any literals, and n is any natural number. A clause is inferable from a clausal theory Gamma using =BCP , denoted by Gamma BCP , iff Gamma [ f: g =BCP ffg. (Dalal 1995) shows that BCP is the well known linear time incomplete propositional reasoner called clausal boolean constraint propagation (BCP) McAllester 1990) which is a variant of unit resolution (Chang Lee 1973) BCP is known to be complete for inferring clauses from theories containing only Horn ....

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Dalal, M. 1995. Tractable reasoning in knowledge representation systems. Technical Report CUCS-017-95, Department of Computer Science, Columbia University, New York, NY.

....to the relaxed liner programmingproblem. Although their approach is similar in spirit to ours, they do not consider arbitrary grouping and multiple occurrences of literals. Cadoli and Schaerf [SC95] obtained several reasoners by parameterizing j= RP by sets of propositions. However, we have shown [Dal95] that none of their incomplete reasoners is stronger than j . In a related work [Dal96] we have extended j to an anytime family 0 ; 1 ; of reasoners such that each i is tractable, each i 1 is at least as complete as i , and each theory has a i complete for reasoning with it. ....

M. Dalal. Tractable reasoning in knowledge representation systems. Technical Report CUCS-017-95, Department of Computer Science, Columbia University, New York, NY, July 1995. file://ftp.cs.columbia.edu/reports/reports1995 /cucs-017-95.ps.gz.

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