N. Peltier. A new method for automated finite model building exploiting failures and symmetries. J. Logic and Computation, 8(4):511--543, 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... proven by showing that Q is not a logical consequence of the program, in other words by constructing an interpretation in which the program clauses are true (i.e. which is a model of the program) and in which Q is false (or alternatively, the clause false Q is true) First order model generators [27, 28, 35, 24] can be used for this task. They search for an interpretation over a finite domain such that all clauses of a given set evaluate to true. This paper develops an alternative approach which exploits the fact that definite programs have least models. If Q is false in some model based on a ....

....uses abduction and failure analysis in the constraint checking. The second one 2 translates the constraints into finite domain constraints and uses a finite domain solver for the constraint checking. Section 5 discusses alternative approaches: the use of model generators for first order logic [27, 28, 35, 24], of type analysis [19, 10] a query fails if its inferred type is empty) and of program specialisation [22, 14] the query fails if the program for the given query can be specialised into the empty program) In section 6, the different approaches are compared. Finally, in section 7, we draw ....

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N. Peltier. A new method for automated finite model building exploiting failures and symmetries. J. Logic and Computation, 8(4):511--543, 1998.

.... Enumeration of Finite Models The Monadic Case Thierry Boy de la Tour LEIBNIZ IMAG 1 Introduction Few systems for finite model enumeration use pruning techniques based on the notion of isomorphism between finite interpretations (see [2] [1]) known to correspond to elementary equivalence of interpretations. These pruning techniques have two important restrictions: only special isomorphisms are considered, and only the last interpretation which has not been eliminated this way is tested for isomorphism with new candidate ....

....(see section 3) constructed by means of elementary general purpose successor functions. An important requirement of the enumeration is the possibility to switch to sub enumeration ensuring minimal changes with the next interpretation (this is the notion of refutation in an interpretation from [1]) and we give some promising hints about the application of this idea to our framework in section 5. Since the structure of IC of functions are very different whether image and range sets are equal or not, we adopt a many sorted account of finite semantics of first order logic. 46, avenue ....

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Nicolas Peltier. A new method for automated finite model building exploiting failures and symmetries. Journal of Logic and Computation, To appear.

.... 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 Satchmo [MB88] an early ....

Nicolas Peltier. A new method for automated finite model building exploiting failures and symmetries. Journal of Logic and Computation, 8(4):511-- 543, 1998.

....(R) FMC Atinf is a finite model builder based on enumeration of the set of interpretation. It uses some strategies, taking into account the failures of the previously tested interpretations and the isomorphism on interpretations, in order to reduce the number of candidates to be considered (see [6] for details) We obtain the following 2 elements model in 0:01 second. 8x; y:ln(x; y) 0 8x; y:pt(x; y) 0 8x; y:dipt(x; y) false diln(0; 0) diln(1; 1) false diln(1; 0) diln(0; 1) false 8x; y:con(x; y) false 8x; y:apt(x; y) false We also build a 3 elements model where ....

N. Peltier. A new method for automated finite model building exploiting failures and symmetries. To appear in the J. Logic and Computation, 1997.

....be solved by using theorem provers, often with some help of the user 1 (see, for example, 16,17] This is also true for model building: already fifteen years ago [15] striking results were obtained with the help of theorem provers. Most of these results concern finite mathematics [7,18,12], where finite model builders were used to show the existence or nonexistence of finite structures satisfying some properties. In this work, we show how model building methods can also be useful for showing the existence of infinite structures. More precisely, we show how to use an infinite model ....

....step, the method EQMC is used in order to build a model of F simp . Let us briefly recall the principle of this method. It is based on the enumeration of a particular class of Herbrand interpretations, called eq interpretations. Unlike all other enumeration based model builders (such as FMC ATINF [12,13], Finder [14] or Sem [19] it is able to build infinite models as well as finite ones. The method can be summarized as follows (see [13,3] for more details about EQMC) 1. Choose a finite partition S 1 ; S n of the Herbrand base. Each set S i belonging to the partition is represented ....

N. Peltier. A new method for automated finite model building exploiting failures and symmetries. Journal of Logic and Computation, to appear 1997.

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