Michael J. Maher. Complete axiomatisations of the algebra of finite, rational and infinite trees. In Third Anual Symposium on Logic in Computer Science, pages 348-- 357, IEEE, Edinburgh, Scotland, july 1988.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....a module with NFm = and = a domain operator. Then for each w 2 WFFm there exists a = m weakest parameter condition. Furthermore for each formula w the weakest parameter condition is computable. Proof: The proof follows from procedures for solving equational problems in term algebras ( CL89] [Mah88]) See [Tre91] and [Buh91] for details how to apply these results to the semantics of modules. 2 5 Properties of the New Logic We now consider two basic model theoretic properties of our new logic. Lindstrom ( Lin69] has shown that first order logic is the only logic fulfilling countable ....

Michael J. Maher. Complete axiomatisations of the algebra of finite, rational and infinite trees. In Third Anual Symposium on Logic in Computer Science, pages 348-- 357, IEEE, Edinburgh, Scotland, july 1988.

....those infinite feature trees that are rational (i.e. have only finitely many subtrees) For the results of this paper this would not make a difference. We also conjecture that the rational feature tree structure and T are elementarily equivalent, analogous to the situation with constructor trees [18]. 3 The Theory CFT We will now define a first order theory CFT having the feature tree structure T as one of its models. All results of this paper actually hold for every model of CFT. We conjecture that CFT is a complete axiomatization of the feature tree structure T and expect that this can be ....

M. J. Maher. Complete axiomatisations of the algebra of finite, rational and infinite trees. In Proceedings of the Third Annual Symposium on Logic in Computer Science, pages 348--357. IEEE Computer Society, 1988.

....within a single tree relate to each other; that is, it is often the internal perspective that is fundamental. By way of contrast, most work on logics of trees in the computer science literature takes an external perspective on tree structure. For example, in the work of Courcelle [7] and Maher [11], variables range over entire trees. This is a natural choice for work on the semantics of programming languages, but unsuitable for the applications mentioned below. And although the internal perspective on trees has been explored in the logical literature (the classic example is Rabin s [14] ....

M. Maher. Complete axiomatisations of the algebras of finite, rational and infinite trees. In Proceedings of the 3rd International Symposium on Logic in Computer Science, pages References 19 348--357, Edinburgh, Scotland, 1988.

....a module with NFm = and = a domain operator. Then for each w 2 WFFm there exists a = m weakest parameter condition. Furthermore for each formula w the weakest parameter condition is computable. Proof: The proof follows from procedures for solving equational problems in term algebras ( CL89] [Mah88]) See [Tre91] and [Buh91] for details how to apply these results to the semantics of modules. 2 5 Properties of the New Logic We now consider two basic model theoretic properties of our new logic. Lindstrom ( Lin69] has shown that first order logic is the only logic fulfilling countable ....

Michael J. Maher. Complete axiomatisations of the algebra of finite, rational and infinite trees. In Third Anual Symposium on Logic in Computer Science, pages 348-- 357, IEEE, Edinburgh, Scotland, july 1988.

....set of constants (called the theory of finitely generated multisets in Comon (1991) can as well be reduced to the theory of Presburger arithmetic. Furthermore the theory of a ground term algebra modulo an empty set of equations has been shown to be decidable in Comon Lescanne (1989) and Maher (1988). 2 The decidability of the Sigma 1 fragment of the theory of ground term algebra modulo associativity and commutativity has been proved in Comon (1988) While we have shown the undecidability of the Sigma 3 fragment the Sigma 2 case is still unsolved. 3 Comon (1990) shows the decidability ....

Maher, M. J. (1988). Complete axiomatisations of the algebra of finite, rational and infinite trees. In Proceedings of the Third Annual Symposium on Logic in Computer Science, pages 348--357. IEEE Computer Society.

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