H. Fujita and R. Hasegawa. A model generation theorem prover in KL1 using a ramified-stack algorithm. In K. Furukawa, editor, Proc. 8th Int. Conf. on Logic Programming, Paris/France, pages 535--548. MIT Press, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Problems division of CASC 13, 1996, where they could solve 6 of the 50 problems. With a timeout of 60s KRHyper can solve 15 of them. A Satchmo variant also participated in the SAT division of CASC 15, 1998, where it solved 11 of the 30 problems. KRHyper, with a timeout of 20s, solved 12. MGTP [5] is another family of systems descending of Satchmo with advanced implementations. In [6] a variant of MGTP is described, that, like ours, adapts techniques like semi naive evaluation to model generation theorem proving. SModels [11] is a model generating system, which computes stable models with ....

H. Fujita and R. Hasegawa. A model generation theorem prover in KL1 using a ramified-stack algorithm. In K. Furukawa, editor, Proc. 8th Int. Conf. on Logic Programming, Paris/France, pages 535--548. MIT Press, 1991.

.... In the syntax advocated by CCP, one should first ask B(q(S) q( read(A) B] or equivalently, B(S = read(A) B] first and then tell q(S) q( read(A) B] Kazunori Ueda Parallel Inference Machine (PIMOS) 6] a parallel theorem prover (MGTP) that discovered a new fact in finite algebra [10]. genetic information processing, and so on. People found the communication and synchronization mechanisms of GHC KL1 very natural. Bugs due to concurrency were rather infrequent and people learned to model their problems in an object based manner using concurrent processes and streams. At the ....

Fujita, H. and Hasegawa, R., A Model Generation Theorem Prover in KL1 Using a Ramified-Stack Algorithm. In Proc. Eighth Int. Conf. on Logic Programming (ICLP'91), The MIT Press, Cambridge, MA, 1991, pp. 535--548.

....the user in identifying and solving errors in the implementation. A theoretical framework for counter example generation based on abstract data types is presented in [1] The usefulness of this approach has already been shown in a prototype which is based on a model generation theorem prover [26]. A current version of the KeY tool can be downloaded at http: i12www.ira.uka.de key download.htm. A further step to improve the usability of the KeY tool is the integration of an authoring tool for OCL constraints [30] This tool is already available as a stand alone version and offers ....

H. Fujita and R. Hasegawa. A model generation theorem prover in KL1 using a ramified-stack algorithm. In K. Furukawa, editor, Proceedings 8th International Conference on Logic Programming, Paris/France, pages 535--548. MIT Press, 1991.

....Model Reasoning In [BFN96] a variant of clausal tableau calculus called hyper tableaux has been introduced. In the ground case, which we consider here as the basis for our view deletion algorithm, hyper tableaux coincide with the calculi underlying the SATCHMO prover [MB88] and the MGTP system [FH91]. More recent developments in the SATCHMO tradition are described in [BY96] concerning minimal model reasoning) and in [BT98] concerning finite models) Improvements for first order hyper tableaux have been suggested in [Bau98] We apply the usual notions of first order logic, in a way ....

H. Fujita and R. Hasegawa. A Model Generation Theorem Prover in KL1 using a Ramified-Stack Algorithm. In Proc. of the Eighth International Conference on Logic Programming, pages 535--548, Paris, France, 1991.

.... amenable to study due to its simple presentation form (a nineteen line Prolog implementation is presented in [MB88] Furthermore, the approach adopted by SATCHMO has been amplified with considerable success, for example in the Model Generation Theorem Prover (MGTP) developed at ICOT in Japan [FH91]. This research was partially supported by NSF Grants IRI 8805696 and CCR 9116203. y This paper is a major revision of [WL89] 1 The SATCHMO prover is applicable to theorems which have the property known as range restriction. If we present a problem using positive implication clauses, i.e. ....

H. Fujita and R. Hasegawa. A model generation theorem prover in KL1 using a ramified-stack algorithm. In K. Furukawa, editor, Logic Programming: Proc. of the Eighth Int'l Conf. MIT Press, 1991.

.... into a rule of a disjunctive logic program (p a) a 0 q 14 A description of this work can also be found in [51] 56 where a 0 is a new atom that stands for the complement of a, as expressed by the integrity constraint : a a 0 ) 7) A model generator (like SATCHMO or MGTP [37]) can then be applied to compute all the minimal models that satisfy the integrity constraints (7) 6 Abduction and Truth Maintenance In this section we will consider the relationship between truth maintenance (TM) and abduction. TM systems have historically been presented from a procedural ....

Fujita, M., Hasegawa, R., A model generation theorem prover in KL1 using a ramified-stack algorithm. Proc. 8th International Conference on Logic Programming, Paris (1991) 535--548

....fail. Figure 2: The fair SATCHMO program. In [44, 45] where SATCHMO was first presented, it is described in terms of positive unit hyperresolution and splitting and not as a tableaux method. This presentation has been retained by most authors referring to SATCHMO or extensions of it, e.g. [60, 26, 67, 43, 31, 38]. In fact, SATCHMO has been conceived as a tableaux method, as early publications [9, 8] on this project report. This is because enhancing a tableaux method with resolution was a new idea and because tableaux methods were considered inefficient that this view is not explicitly mentioned in [44, ....

....atoms, as it is considered in this paper, this objection does not apply to a model generation procedure. As model generation procedures, the approaches to minimal model generation proposed in this paper compare well with those reported in the literature, many of which generate nonminimal models [66, 35, 44, 25, 45, 34, 26, 24, 36, 5, 67, 73, 74, 39, 42, 43, 30, 23, 3, 37, 69, 31, 1, 29, 52, 27, 11]. Compared with approaches based on blind model construction then testing for minimality as e.g. the methods reported in [24, 63, 64] the approaches proposed here avoid nonminimal model generation altogether. The construction of nonminimal models is aborted as soon as possible, in general ....

H. Fujita and R. Hasegawa. A Model Generation Theorem Prover in KL1 Using a Ramified Stack Algorithm. In Proc. Eighth Int. Conf. on Logic Programming, MIT Press, 1991.

....complexity issues for those kinds of calculi have been considered in [19] We propose a new technique for the design of proof procedures for rigid variable methods. The proposed technique should also be applicable to calculi which avoid rigid variables in the first place, like SATCHMO [16] MGTP [10], hyper tableaux [4] and ordered semantic hyper linking [17] Usually the price for getting around rigid variables in these approaches is that they involve some uninformed ground instantiation in special cases. These calculi are likely to profit from techniques enabling them to handle rigid ....

H. Fujita and R. Hasegawa. A Model Generation Theorem Prover in KL1 using a Ramified-Stack Algorithm. In Proc.8 th of the Eighth International Conference on Logic Programming, pages 535--548, Paris, France, 1991.

....The second and the third satisfy all the qualifying properties. Hence, stable( Pi 1 ) consists of two stable models which are obtained from the second and the third one and which are fpg and fqg. 2 There are several approaches to compute the minimal models of a positive disjunctive program [FH91, FM91]. Fernandez et al. FLMS93] use model trees to compute minimal models. Inoue et al. IKH92] use an extension of the model generation theorem prover (MGTP) FH91] to directly compute the minimal models of the formulas obtained using tr 1 . Obviously much more work is needed to find efficient ....

....third one and which are fpg and fqg. 2 There are several approaches to compute the minimal models of a positive disjunctive program [FH91, FM91] Fernandez et al. FLMS93] use model trees to compute minimal models. Inoue et al. IKH92] use an extension of the model generation theorem prover (MGTP) [FH91] to directly compute the minimal models of the formulas obtained using tr 1 . Obviously much more work is needed to find efficient methods of answering queries and computing the stable models of general logic programs. 2.4 Other Semantics of General Logic Programs In this section we briefly ....

[Article contains additional citation context not shown here]

H. Fujita and R. Hasegawa. A model generation theorem prover in KL1 using a ramified stack algorithm. In Eight International Conference in Logic Programming, pages 535--548, 1991.

....parallel ausgewertet werden, das den Keller mittels Akkumulationslisten darstellt. Der Beweiser MGTP [FHKF92] ist eine Ausnahme. Um das Satchmo Verfahren im Datenbankstil in der parallelen Sprache der Logikprogrammierung KL1 zu implementieren, wird eine besondere Datenstruktur, ramified stack [FH91] genannt, verwendet. 1 Lee Naish hat gegen Ende der 80er Jahre das Programm im Internet erwahnt. 6 Implementierungen der Breitensuche Bekanntlich entspricht die Warteschlange bei der Breitensuche, dem Keller bei der Tiefensuche. Es stellt sich also die Frage, wie die oben erwahnten ....

Hiroshi Fujita and Ryuzo Hasegawa. A model generation theorem prover in KL1 using a ramified-stack algorithm. In Proc. 8th Int. Conf. on Logic Programming, 1991.

....and simply structured variant of Satchmo in a purely functional subset of Scheme. From this implementation the variant that participated in the competition has been developed. 1.2. Related Systems There are several other approaches for generating models of clausal theories. One such approach, MGTP [5], is based on the calculus of Satchmo. Its developers have, however, put emphasis on other aspects, e.g. parallel execution. MGTP can, like Satchmo, be used as a theorem prover. Model generators like FINDER [16] SEM [19] and MACE [11] differ from Satchmo and MGTP in that they attempt to ....

H. Fujita and R. Hasegawa. A model generation theorem prover in KL1 using a ramified-stack algorithm. In K. Furukawa, editor, Proceedings of the 8th International Conference on Logic Programming, pages 535--548. MIT Press, 1991.

.... have J P = a i 1 ; a i k ) Ij=P (a i 1 ; a i k ) k j=1 x i 2 A i j where a(P ) k and x P = x 1 ; x 2 ; x k ) Then we have J j= S iff I j= S (this is a straightforward consequence of the definition of J ) 4 A parallel and optimized version of SATCHMO is described in [18]. Theorem 6.2. Let I be an interpretation representable by an atomic representation. Then I is G representable, for any regular term grammar G. Proof: In [5] it is proven than atomic representation are a particular case of equational formulae. Moreover, an equational formula is a particular ....

M. FUJITA and R. HASEGAWA. A model generation theorem prover in KL1 using a ramified stack algorithm. In Proceedings of 8th International Conference Symp. Logic Programming, pages 1070--1080, 1991.

....programming framework. To compute stable models of a general logic program or answer sets [GL91] of an extended disjunctive program, Inoue et al. [IKH92] have shown a constructive definition of stable models and answer sets, and provided a bottomup procedure based on model generation techniques [MB88, FH91]. Inoue and Sakama [IS92] have proved that this procedure has a formal fixpoint semantics for general and extended (disjunctive) logic programs. The basic idea of this technique is to transform a program into a semantically equivalent positive disjunctive program not containing negation as ....

....proving the result corresponding to Lemma 3. 5 (a) 2 5 Bottom Up Evaluation of Abductive Programs In this section, we investigate the procedural aspect of the fixpoint theory for abductive programs in the context of a particular inference system called the model generation theorem prover (MGTP) [FH91, IKH92]. MGTP is a parallel and refined version of SATCHMO [MB88] which is a bottomup forward reasoning system that uses hyperresolution and case splitting on non unit hyperresolvents. Let P be a positive disjunctive program consisting of clauses of the form: H 1;1 . H 1;k1 ) H l;1 . ....

H. Fujita and R. Hasegawa. A model generation theorem prover in KL1 using a ramified-stack algorithm. In: Proc. 8th Int. Conf. Logic Programming, pages 494--500, 1991.

....The second and the third satisfy all the qualifying properties. Hence, stable(5 1 ) consists of two stable models which are obtained from the second and the third one and which are fpg and fqg. 2 There are several approaches to compute the minimal models of a positive disjunctive program [FH91, FM91]. Fernandez et al. FLMS93] use model trees to compute minimal models. Inoue et al. IKH92] use an extension of the model generation theorem prover (MGTP) FH91] to directly compute the minimal models of the formulas obtained using tr 1 . Obviously much more work is needed to find efficient ....

....one and which are fpg and fqg. 2 There are several approaches to compute the minimal models of a positive disjunctive program [FH91, FM91] Fernandez et al. FLMS93] use model trees to compute minimal models. Inoue et al. IKH92] use an extension of the model generation theorem prover (MGTP) [FH91] to directly compute the minimal models of the formulas obtained using tr 1 . Obviously much more work is needed to find efficient methods of answering queries and computing the stable models of general logic programs. 2.4 Other Semantics of General Logic Programs In this section we briefly ....

[Article contains additional citation context not shown here]

H. Fujita and R. Hasegawa. A model generation theorem prover in KL1 using a ramified stack algorithm. In Eight International Conference in Logic Programming, pages 535--548, 1991.

....Satchmo suffers from, has also shown up in other rule processing AI systems and in deductive databases. Solutions like the Rete algorithm [9] and semi naive fixpoint iteration [3, 1] have been developed. For the Satchmo like theorem prover MGTP solutions to the problem have also been developed [10, 14], which are, however, more complex than ours and less suited for compilation. Many theorem provers perform some preprocessing on their input formulas before the central inference mechanism is started. However, to our knowledge there is no preceding work on similarly far reaching compilation for ....

H. Fujita and R. Hasegawa. A model generation theorem prover in KL1 using a ramified-stack algorithm. In Logic Programming, Proc. of the 8th Int. Conf., pages 535--548, 1991.

....and no goal to achieve, but an interest in models corresponding to some given information. From the standpoint of theorem proving, automatically constructed models can be used, e.g. as successful theorem provers [12] or for guiding other theorem provers [24] Several recent approaches (e.g. [20, 11, 9, 2, 17]) to the generation of Herbrand models come from this field. 7 this is the case if there is a A1 Sigma 2 I where A is an instance of A1 , but not an instance of some A1 oe where oe 2 Sigma All the latter approaches use some kind of iterated hyperresolution [23] for generating models of ....

....head atoms and negative body literals are grounded by the variable bindings to positive body literals. Therefore, only finite sets of ground atoms are generated. On the other hand, this means that no generalizing inference can be modeled, what is quit unsatisfying wrt intelligent behaviour. MGTP[11] basically is a parallel implementation of SATCHMO. The approach presented in [9] uses positive hyperresolution and subsumption, and computes models of sets of clauses from the class PDC, which is a weaker restriction than range restrictedness. The latter approaches compute models of considered ....

H. Fujita and R. Hasegawa. A model generation theorem prover in KL1 using a ramified stack algorithm. In Proceedings of the International Conference on Logic Programming, pages 535--548, 1991.

.... appears in [BEST98] Other successful applications of model generation include model based diagnosis [BFFN97] planning [EG98] and even the solution of previously open problems in finite algebra [FSB93] Among the various approaches for building models of first order formulas (e.g. CZ91,FH91,Sla92,ZZ95,FL96,BFN96,Pel98] we concentrate in this paper on the positive unit hyper resolution (PUHR) tableau method [BY96] It combines positive hyper resolution with unit clauses and a beta or splitting tableau rule. The PUHR tableau method is actually a formalisation of the theorem prover ....

Hiroshi Fujita and Ryuzo Hasegawa. A model generation theorem prover in KL1 using a ramified-stack algorithm. In Logic Programming, Proc. of the 8th Int. Conf., pages 535--548, 1991.

....range restricted 1 , which is usually imposed on programs in the field of deductive databases. Inoue et al. IKH92] have proposed bottom up computation methods to compute all the stable models of a general logic program. We quickly review the procedure. MGTP (model generation theorem prover) [FH91] performs the bottom up computation using clauses of the form: A l 1 ; 1 1 1 ; Am A 1;1 ; 1 1 1 ; A 1;k 1 j 1 1 1 j A l;1 ; 1 1 1 A l;k l ; 2) where m l 0, k i 1 (1 i l) According to [IKH92] we use the connective j instead of also. Let S be a set of model candidates in some stage, ....

H. Fujita and R. Hasegawa. A Model Generation Theorem Prover in KL1 using a Ramified-Stack Algorithm. In Proc. of ICLP'91, pp. 535--548, 1991.

....method Ramcet in two directions. First we define a new simplification rule allowing to prune the search space. Second, we propose a new method for extracting a model from an open (possibly infinite) branch. The new method is based on 1 A parallel and optimized version of Satchmo is described in [14]. generalization techniques and inductive reasoning. It is proven to be strictly more powerful than the simpler one proposed in the original work [9] The models built by the method are expressed by equational formulae interpreted on the finite terms algebra (i.e. where equality is interpreted ....

.... b) 8x; y : x 6= y:P (f(x) f(y) 8x:P (f(x) f(x) g Then, the set gen(S p ; A) is gen(S p ; A) f8x: P (b; f(x) P (b; b) 8x:P (f(x) b) 8x; y : x 6= y: P (f(x) f(y) 8x: P (f(x) f(x) g: Again, the standard tableaux method as well as refinements of it (such as Satchmo [22] Mgtp [14], Hyper Tableaux [1] cannot build a model for this formula. Indeed, they generate the sets of facts fP (b; b) P (f(b) b) P (f n (b) b) g and fP (b; b) P (f(b) b) P (f n (b) b) g but cannot generate the facts 8x:P (x; b) and 8x; y: P (x; f(y) that ....

M. Fujita and Hasegawa. A model generation theorem prover in kl1 using a ramified stack algorithm. In Proceedings of 8th International Conference Symp. Logic Programming, pages 1070---1080, 1991.

.... model reasoning [Niemel a, 1996] for diagnosis applications [Baumgartner et al. 1997] and to compute database updates [Aravindan and Baumgartner, 1997] Hyper tableau like calculi have been also applied in provers like SATCHMO [Manthey and Bry, 1988; Loveland et al. 1995] and the MGTP system [Fujita and Hasegawa, 1991] . However, these calculi ground instantiate all clauses during the tableau construction. The hyper tableau calculus of [Baumgartner et al. 1996] improves on this by allowing branch local universally quantified variables. Consider for instance, a disjunction p(x;y) q(x) When brought into the ....

H. Fujita and R. Hasegawa. A Model Generation Theorem Prover in KL1 using a Ramified-Stack Algorithm. In Proc. of the Eigth International Conference on Logic Programming, pages 535--548, Paris, France, 1991.

....propositional problem considered grows to much and they become practically intractable. In [22] the model builder Satchmo is described. It is based on the use of hyperresolution, splitting of non Horn clauses and backtracking. A parallel and refined version of Satchmo, called Mgtp, is presented in [19]. The three programs that are the closest to FMC Atinf are Finder, Sem, and Falcon (a former version of Sem) Finder [26] is a model generator based on enumeration and backtracking. Unlike FMC Atinf it does not use any strategy to prune the search space but instead builds as long as the search ....

M. Fujita and Hasegawa. A model generation theorem prover in KL1 using a ramified stack algorithm. In Proceedings of 8th International Conference Symp. Logic Programming, pages 1070---1080, 1991.

.... A description of this work can also be found in [76] where a is abducible, into DLP clauses (p a) a 0 q where a 0 is a new atom that stands for the complement of a, as expressed by the integrity constraint : a a 0 ) 3) A model generation theorem prover (such as SATCHMO or MGTP [58]) can then be applied to compute all the minimal models that satisfy the integrity constraints (3) This transformation is related to a similar transformation [82] for eliminating NAF. Elsewhere [167] Sakama and Inoue demonstrate a one to one correspondence between generalised stable models for ....

Fujita, M., Hasegawa, R., A model generation theorem prover in KL1 using a ramified-stack algorithm. Proc. 8th International Conference on Logic Programming, MIT Press, Paris (1991) 535--548

....a set of model candidates for S that are neither extendable nor rejected. 1 We employ rule notation p1 ; pn q1 ; qm for first order clauses of the form f:p1 ; pn ; q1 ; qmg. 2 The following definition is a slightly more precise variant of the definition in [2]. 3 In connection with the implementation of model generation also the expression term memory is sometimes used for a model candidate. 4 The symbol denotes falsity that is D = Soundness and completeness of MG may now be formulated as follows: a range restricted first order CNF formula S ....

....2 above: first, it is easy to formulate a backtracking free MG proof search procedure, in other words an AND search tree is sufficient; second, matching of clauses is sufficient as opposed to unification. Therefore, an efficient implementation of MG called MGTP (Model Generation Theorem Prover) [2, 5] in KL1 is possible. KL1 is a committed choice concurrent logic programming language [11] developed at ICOT and has just the required features. One of the applications of MGTP is the search for models in finite domains, for instance in finite quasigroups [3] Experiments in such domains showed ....

H. Fujita and R. Hasegawa. A model generation theorem prover in KL1 using a ramified-stack algorithm. In K. Furukawa, editor, Proceedings 8th International Conference on Logic Programming, Paris/France, pages 535--548. MIT Press, 1991.

....SATCHMO [14] written in Prolog compactly. SATCHMO adopts the model generation method as the proof procedure. It checks the satisfiability of a given set of clauses by trying to generate models for the given clause set. Triggered by this work, a parallel model generation based theorem prover MGTP [9, 13] has been developed in KL1 [20] and exhibits good performance on a parallel inference machine PIM [15] and a UNIX workstation [11, 12] The basic model generation method detects a violated clause that is not satisfied by a certain interpretation (a set of atoms) called a model candidate, then ....

Hasegawa, R. and Fujita, H.: A model generation theorem prover in KL1 using ramified-stack algorithm, Proc. 8th ICLP, pp. 535--548 (1991). L A T E X style file for Lecture Notes in Computer Science -- documentation 15

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