J. Zhang. Search for models of equational theories. In Proceedings of ICYCS-93, pages 60--63, 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....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 ....

J. Zhang. Search for models of equational theories. In Proceedings of ICYCS-93, pages 60--63, 1993.

....Wos and Winker used a resolution based theorem prover in order to help the user in the search for a model. Since 1990, some methods have been proposed in order to build automatically models for first order formulae. Most of them are based on enumeration and backtracking (see for example [32, 38]) Their general principle is to perform an exhaustive search on the set of interpretations on a finite domain. Obviously a naive exploration of the search space is impossible in practice and powerful heuristics have to be used in order to prune the search space (for example to detect ....

J. ZHANG. Search for models of equational theories. In Proceedings of ICYCS-93, pages 60--63, 1993.

....as an assistant in the search for a model. Nevertheless, this approach did not define an algorithmic method for building models: all the crucial information was given by the user. Since 1990, other methods have been proposed. Most of them are based on enumeration and backtracking (see for example [26, 29]) Their general principle is to perform an exhaustive search on the set of interpretations on a finite domain. Obviously a naive exploration of the search space is impossible in practice and powerful heuristics have to be used in order to prune the search space (for example to detect isomorphic ....

J. Zhang. Search for models of equational theories. In Proceedings of ICYCS-93, pages 60--63, 1993. A Proof of Theorem 10 The proof of Theorem 5.2. needs the following lemmata. Lemma A1. There exists an algorithm transforming any equational formula X into a disjunction

....of T 1 T 4 that is not a model of T 5 , otherwise stated that satisfies: T 5 : 9x; y:f(x; y; y) 6= y. This problem was first solved by Wos and Winker (see [30] with assistance of a resolution based theorem prover. Fully automated solutions of this problem were given later (see for example [4, 33]) 4.2.2. Group Theory The following formula is a single axiom for group theory [34, 23] G 1 ) f(x; i(f(y; f(f(f(z; i(z) i(f(u; y) x) u The problem is to prove that the following axiom (which is an instance of G 1 , with x = u) is not a single axiom for group theory. G 2 ) f(u; ....

....a database containing the refutations previously obtained, in order to avoid backtracking twice for the same reasons. Results in Section 4 provide some elements of comparison between the two systems and show that FMC Atinf is faster than Finder on many examples. Falcon (previously known as Mod E) [33, 34] and Sem [35] are also quite powerful programs generating finite models based on an enumeration of the search space. A simple heuristic, called the Least Number Heuristic (LNH) is used in order to prune the search space. The LNH is based on a similar (though less general) idea than the one of our ....

J. Zhang. Search for models of equational theories. In Proceedings of ICYCS-93, pages 60--63, 1993.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC