K. Broda, S. Eisenbach, H. Koshnevisan and S. Vickers, Reasoned Programming, Prentice Hall, (1995)  Home/Search   Document Not in Database   Summary   Related Articles   Check

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K. Broda, S. Eisenbach, H. Koshnevisan and S. Vickers, Reasoned Programming, Prentice Hall, (1995)

.... the combination of two lines of research: the methodology of Labelled Deductive Systems [19] and the recent developments in the field of theorem proving based 1 on analytic methods, such as the method of analytic tableaux or the system KE [14] or procedural approaches to Natural Deduction (ND) [3]. The methodology of Labelled Deductive Systems (LDS for short) is a unifying framework for the study of logics and of their interactions. It was proposed by Gabbay a few years ago in response to conceptual pressure from various application areas and their needs, and is now proving a very ....

....well understood proofs, which, although derived backwards from the goal, can be read forwards from the data. It seemed interesting, therefore, to compare the KE approach with that of natural deduction, and in particular with a format for natural deduction developed by Gabbay in [19] and Broda in [3] There is, indeed, a close correspondence between procedural natural deduction and KE tableaux, if the latter are formed in a particular way. This was initially described and applied to substructural logics in [8] It is described fully in [2] leading to the completeness theorem for ND. A sound ....

K. Broda, S. Eisenbach, H. Khoshnevisan, and S. Vickers. Reasoned Programming. Prentice Hall, 1994.

....processes. There is in fact no reason for restricting the attention only to tableau methods and sequent calculi [DG94, Dos93] Natural deduction systems can be equally expressive. A formal definition of the inference rules is given in Table 2, adopting a presentation style first introduced in [BEKV94] for the definition of a classical natural deduction style proof system. A solo parameter is an atomic label such that any other atomic occurrences within a structural derivation labels only the formula it is first introduced with, and which may occur (as atomic 6 Rules for # #I A : a . ....

K. Broda, S. Eisenbach, H. Khoshnevisan, and S. Vickers. Reasoned Programming. Prentice Hall, 1994.

.... synthesis . He agreed with the nowadays ATP community that the analysis involves reasoning backwards, from the theorem that one wants to prove to the axioms (or the data) while the synthesis requires us to retrace our steps, somehow inverting them, from the axioms to the theorem. See (Broda et al. 1994) for a description of a goal directed approach to Natural Deduction. TRANSFORMATION METHODS 9 of L will be denoted by F , and F will denote the set of all sequences of elements of F . Sequences of formulae will be denoted by enclosing formulae, separated by commas, within square brackets, ....

....reasoning in a natural deduction style. This algorithm could be useful in applications of substructural logics to all the areas where a human oriented interface, based on natural deduction, is required. 6.1. SUBSTRUCTURAL NATURAL DEDUCTION Following the framework developed in (Gabbay, 1994; Broda et al. 1994) we define in Table 4 six Natural Deduction (ND) inference rules which correspond to the tree expansion rules for f ; Omega Gamma 10 , and to the closure and PB rules. The ND rules can be proved to be complete and sound with respect to the LKE rules (see Section 6.3) We will restrict our ....

Broda, K.; Eisenbach, S.; Khoshnevisan, H.; and Vickers, S. (1994). Reasoned Programming.

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Broda, K., et. al., Reasoned Programming, Prentice Hall, 1994.

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