Krysia Broda and Marcelo Finger. Ke-tableaux for a fragment of linear logic. Workshop on Theorem Proving and Analytic Tableaux and Related Methods, Stboar, Germany, 1995. Extended Abstract.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... in [17, 4, 5] and [7] The resulting theorem 1 Related work on tableau like methods for relevance logics is contained in [16, 23, 31] 2 For a related LDS based approach to categorial theorem proving, in terms of labelled proof nets, the reader is referred to [24] 3 prover is described in [9]. The use of unification enabled the development of resource abduction in which the instantiation of labels indicates the abductive data needed to prove a given theorem. The work of Russo [27] on modal logics introduces the possibility of a completely different approach, in which a given problem ....

Krysia Broda and Marcelo Finger. Ke-tableaux for a fragment of linear logic. Workshop on Theorem Proving and Analytic Tableaux and Related Methods, Stboar, Germany, 1995. Extended Abstract.

....S 3 based on the KE tableau methodology. KE tableaux were introduced by D Agostino [ D Agostino, 1992 ] as a principled computational improvement over Smullyan s Semantic Tableaux [ Smullyan, 1968 ] and have since been successfully applied to a variety of logics [ D Agostino and Gabbay, 1994; Broda and Finger, 1995; Broda et al. 1999 ] KE tableaux deal with T and F signed formulas. So if is a formula, T and F are signed formulas. T is the conjugate formula of F , and vice versa. An expansion of a tableau is allowed when the premises of an expansion rule are present in a branch; the expansion ....

K. Broda and M. Finger. KEtableaux for a fragment of linear logic. In Proceedings of the 4th International Workshop on Analytic Tableaux and Related Methods, Koblenz, May 1995.

....choice of labels to provide appropriate instantiations of the axioms, is transferred to the unification algorithm. For example, for LL an appropriate algorithm could be one which uses AC unification with identity [Sti85] A free variable tableau based theorem prover using this idea is described in [BF95] or a standard Model Elimination prover could be adapted, by incorporating a specialised unification algorithm, for example the one described in [BF95] Notice also that the clauses obtained from the axioms are quite specific, in that 45 the R literals are only used together with the properties ....

.... could be one which uses AC unification with identity [Sti85] A free variable tableau based theorem prover using this idea is described in [BF95] or a standard Model Elimination prover could be adapted, by incorporating a specialised unification algorithm, for example the one described in [BF95]. Notice also that the clauses obtained from the axioms are quite specific, in that 45 the R literals are only used together with the properties of the labelling algebra. In the case of the logic of elsewhere, these are the properties of an equality theory and for linear logic these are ....

K. Broda and M. Finger. KE-tableaux for a fragment of linear logic. Technical report, 4th Workshop on Theorem Proving with Analytic Tableaux and Related Methods, Ed. Peter Baumgartner, University of Koblenz, 1995.

....depends on the side condition x # y,whichcanbeprovedto hold using the properties of # of the underlying class of labelling algebras. However, the work in [DG94] does not cover the issue of finding algorithms for solving these kind of conditions. The first and only example has been given in [BF95] but only for the case of Linear Logic. Extending LKE The LKE system is here extended by adding an extra rule to those given in Table 3, called (Tch) Tch) TA : x TA : a where a is the Acharacteristic atomic label (11) This rule reflects the algebraic property given in clause (2) of ....

....in the ND system this approach is taken even further, allowing free variables to be used also in the # rule. Simple label inequations involving only the # operator generated by the closure rule can be solved in the LKE system using algorithms based on the AC unification technique[Sti81] See [BF95] for further details. For more complex inequations involving the operator no algorithm has, to the authors knowledge, yet been reported. In the ND approach, the solving process is much simpler. ND proofs are more structured. This structural feature facilitates the definition of an ordering ....

Krysia Broda and Marcelo Finger. KE-tableaux for a fragment of linear logic. Technical report, 4th Workshop on Theorem Proving with Analytic Tableaux and Related Methods, Ed. Peter Baumgartner, University of Koblenz, 1995.

....LDS has been used as a basis for other systems implementation, mainly for the construction of theorem provers. For example, D Agostino Gabbay 1994] presents a general LDS tableaux theorem prover for substructural logics whose implementation specialised for Linear Logic was described in [Broda Finger 1995]; LDS has been shown to gracefully apply to Natural Deduction theorem proving [Broda, Finger Russo 1996] and there are other works under way in the application of LDS to temporal modal logics [Russo 1996] All these implementations share with ours the basic LDS principles: a) both labels and ....

Broda, K & M Finger, 1995, KE-Tableaux for a Fragment of Linear Logic, in Proc 4th International Workshop on Analythic Tableaux and Related Methods. Koblenz.

....size of the input sentence. LDS has been used as a basis for other systems implementation, mainly for the construction of theorem provers. For example, 7] presents a general LDS tableaux theorem prover for substructural logics whose implementation specialised for Linear Logic was described in [3]; LDS has been shown to gracefully apply to Natural Deduction theorem proving [4] and there are other works under way in the application of LDS to temporal modal logics [42] All these implementations share with ours the basic LDS principles: a) both labels and formulas are jointly handled at ....

Broda, K & M Finger, 1995, KE-Tableaux for a Fragment of Linear Logic, in Proc 4th International Workshop on Analytic Tableaux and Related Methods. Koblenz.

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