J. Tiuryn. A survey of the logic of effective definitions. In E. Engeler, editor, Proceedings of the Workshop on Logics of Programs, pages 198--245, Springer LNCS, vol. 125, 1981.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....signature of some given module. We always refer to some fixed module, that is the modules themselves do not occur in the formulas of our new logic. In the terminology of [KT90] our logic is an endogenous logic about modules, not an exogenous one. The Logic of Effective Definitions (EDL) of [Tiu81] considers completely unstructered schemes that are a generalization of recursive program schemes. Model theoretic and proof theoretic properties of EDL are discussed in [Tiu81] In contrast to EDL our logic incorporates data structures defined by constructors. Furthermore we concentrate on the ....

....our logic is an endogenous logic about modules, not an exogenous one. The Logic of Effective Definitions (EDL) of [Tiu81] considers completely unstructered schemes that are a generalization of recursive program schemes. Model theoretic and proof theoretic properties of EDL are discussed in [Tiu81]. In contrast to EDL our logic incorporates data structures defined by constructors. Furthermore we concentrate on the relation between first order logic and the new logic as described above. This paper is organized as follows: In the next section we first shortly review the notions we use in the ....

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J. Tiuryn. A survey of the logic of effective definitions. In E. Engeler, editor, Proceedings of the Workshop on Logics of Programs, pages 198--245, Springer LNCS, vol. 125, 1981.

....the theory of program schemes, cf. 32, 39, 24] where abstract programs over classes of structures of related signatures are considered. Several relationships between definability of functions by programs, algebraic properties of the underlying structures and dynamic logic were pointed out, see [71, 34, 35]. Ideas of generalized computability were used to develop a logical basis for dealing with geometrical constructions, 59] Computational geometry [54] is also based on generalized models of computation. Finally, the several theories of effective analysis and type 2 computability should be ....

.... Delta ; s k ) iff it exists) S machine ( program ) Fig. 1: Computability in S, that means of functions : S k Gamma S with some arity k, has been considered by many authors, cf. 15, 31, 20, 61, 59, 34, 35, 21] It also plays a fundamental role in the theory of program schemes, see [39, 24, 71]. Figure 1 illustrates the underlying basic idea of so called finite algorithmic procedures. The input tuple is given to a machine which works according to a certain program and yields a result equal to the value of the 3 function if and only if the function is defined on that input. Such a ....

J. Tiuryn, A survey of the logic of effective definitions. in: Logic of Programs, ed. by E. Engeler, Lecture Notes in CS, v. 125, 1979, 198--245

....export signature of some given module. We always refer to some fixed module, that is the modules themselves do not occur in the formulas of our new logic. In the terminology of [KT90] our logic is an endogenous logic about modules, not an exogenous one. The Logic of Effective Definitions (EDL) of [Tiu81] considers completely unstructered schemes that are a generalization of recursive program schemes. Model theoretic and proof theoretic properties of EDL are discussed in [Tiu81] In contrast to EDL our logic incorporates data structures defined by constructors. Furthermore we concentrate on the ....

....[KT90] our logic is an endogenous logic about modules, not an exogenous one. The Logic of Effective Definitions (EDL) of [Tiu81] considers completely unstructered schemes that are a generalization of recursive program schemes. Model theoretic and proof theoretic properties of EDL are discussed in [Tiu81]. In contrast to EDL our logic incorporates data structures defined by constructors. Furthermore we concentrate on the relation between first order logic and the new logic as described above. This paper is organized as follows: In the next section we first shortly review the notions we use in the ....

[Article contains additional citation context not shown here]

J. Tiuryn. A survey of the logic of effective definitions. In E. Engeler, editor, Proceedings of the Workshop on Logics of Programs, pages 198--245, Springer LNCS, vol. 125, 1981.

....variables, and for discrete probabilities first order analysis with integer variables was shown to suffice. 14 OTHER APPROACHES Here we discuss briefly some topics closely related to Dynamic Logic. 14.1 Logic of Effective Definitions The Logic of Effective Definitions (LED) introduced by [Tiuryn, 1981a] was intended to study notions of computability over abtract models and to provide a universal framework for the study of logics of programs over such models. It consists of first order logic augmented with new atomic formulas of the form = where and are effective definitional schemes ....

....and t i are terms over a bounded set of variables, and the function i 7 ( i ; t i ) is recursive. The formula = is defined to be true in a state if both and terminate and yield the same value, or neither terminates. Model theory and infinitary completeness of LED are treated in [Tiuryn, 1981a] Effective definitional schemes in the definition of LED can be replaced by any programming language K, giving rise to various logical formalisms. The following result, which relates LED to other logics discussed here, is proved in [Meyer and Tiuryn, 1981; Meyer and Tiuryn, 1984] THEOREM 89. ....

J. Tiuryn. A survey of the logic of effective definitions. In E. Engeler, editor, Proc. Workshop on Logics of Programs, volume 125 of Lect. Notes in Comput. Sci., pages 198--245. Springer-Verlag, 1981.

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