S. Cerrito and M. Cialdea Mayer. A polynomial translation of S4 into T and contraction-free tableaux for S4. Logic Journal of the IGPL, 5(2):287--300, 1997.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....we present a cubic time transformation from S4 into T, again using the cut free sequent style calculi for these respective logics. Both reductions proceed via an analysis of the proofs in cut free sequent calculi from the literature. The second reduction is a slight variant of the one presented in [4] (see also [7] The reduction announced in the title can be obtained by Also called GL (for Godel and Lob) KW, K4W, PrL. Also called transformation , see e.g. 23] 128 translating T into FO 2 , which is known to be decidable (see e.g. 18] Furthermore, the formula obtained by ....

....transformation from Grz into G is defined. By using renamings of subformulae, there also exists an O(n:log n) time transformation from Grz into G [3, Chapter 12] There exists an O(n) time transformation from G into K4 [2] There exists an O(n :log n) time transformation from K4 into K [4] (which uses renamings of subformulae) Finally, there exists an O(n) time transformation from K into FO 2 [27] Combining these results gives an O(n 5 into FO 2 , a decidable fragment of first order logic. The translation proposed in this paper is therefore a more refined alternative since ....

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S. Cerrito and M. Cialdea Mayer. A polynomial translation of S4 into T and contraction-free tableaux for S4. Logic Journal of the IGPL, 5(2):287--300, 1997.

....of logics into other logics have a long tradition in the area of mathematical logic (see, e.g. 7, 11, 13, 10] for some classical references) Some embeddings are practically motivated, some others are of theoretical interest. The embedding of the modal logic S4 into the modal logic T (see, e.g. [2, 6]) is an example for the former, because, due to the transitivity of the S4 accessibility relation, usual cut free Gentzen systems for propositional S4 require a loop check for termination, whereas similar systems for T do not. In the context of automated deduction, translations of modal logics ....

S. Cerrito and M. Cialdea Mayer. A Polynomial Translation of S4 into T and Contraction-free Tableaux for S4. Journal of the IGPL, 5(2):287-300, 1997.

....we present a cubic time transformation from S4 into T, again using the cut free sequent style calculi for these respective logics. Both reductions proceed via an analysis of the proofs in cut free sequent calculi from the literature. The second reduction is a slight variant of the one presented in [CCM97] (see also [Fit88] The reduction announced in the title can be obtained by translating T into FO 2 , which is known to be decidable (see e.g. Mor75] Furthermore, the formula obtained by reduction belongs to the decidable guarded fragment of classical logic (see e.g. ANB98] for which a ....

.... By using renamings of subformulae, it is easy to extract from that transformation, an O(n:log n) time transformation from Grz into G [Boo93, Chapter 12] There exists an O(n) time transformation from G into K4 [BH94] There exists an O(n 4 :log n) time transformation from K4 into K using [CCM97] and renamings of subformulae. Finally, there exists an O(n) time transformation from K into FO 2 [Ben83] Combining these results gives an O(n 4 : log n) 5 ) time transformation from Grz into FO 2 , a decidable fragment of first order logic. The translation proposed in this paper is ....

[Article contains additional citation context not shown here]

S. Cerrito and M. Cialdea Mayer. A polynomial translation of S4 into T and contraction-free tableaux for S4. Logic Journal of the IGPL, 5(2):287--300, 1997.

....for multiplicities in order to reduce as much as possible the search space for proofs. Moreover, it is obviously a crucial issue if the matrix method is to be used as a decision method. We exploit previous results establishing upper bounds on the number of contractions in tableau sequent proofs [4], in order to establish upper bounds for multiplicities in matrix systems. We obtain two kinds of upper bounds: in function of the size of the formula to be proved and in function of the number of the atomic paths through the unindexed formula tree. Such bounds may be non optimal. However, the ....

....concerned, the multiplicity of a 0 formula reflects also the number of times a contraction affects such a formula (or better, its parent) in a tableau proof. Now, such a number can be bounded polynomially in the length of the initial formula when single branches of the tableau are considered [4, 8, 9]. The possibility of exploiting this result in order to establish an upper bound for the multiplicity in modal matrix methods is the original inspiration of this work. However, the paths through a matrix do not preserve the tree structure of a tableau. Since a matrix is made of pointers to ....

[Article contains additional citation context not shown here]

S. Cerrito and M. Cialdea Mayer. A polynomial translation of S4 into T and contraction free tableaux for S4. Logic Journal of the IGPL, 5(2):287--300, 1997.

....we present a cubic time transformation from S4 into T, again using the cut free sequent style calculi for these respective logics. Both reductions proceed via an analysis of the proofs in cut free sequent calculi from the literature. The second reduction is a slight variant of the one presented in [4] (see also [7] The reduction announced in the title can be obtained by 1 Also called GL (for Godel and Lob) KW, K4W, PrL. 2 Also called transformation , see e.g. 23] translating T into FO 2 , which is known to be decidable (see e.g. 18] Furthermore, the formula obtained by reduction ....

....transformation from Grz into G is defined. By using renamings of subformulae, there also exists an O(n:log n) time transformation from Grz into G [3, Chapter 12] There exists an O(n) time transformation from G into K4 [2] There exists an O(n 4 :log n) time transformation from K4 into K [4] (which uses renamings of subformulae) Finally, there exists an O(n) time transformation from K into FO 2 [27] Combining these results gives an O(n 4 : log n) 5 ) time transformation from Grz into FO 2 , a decidable fragment of first order logic. The translation proposed in this paper is ....

[Article contains additional citation context not shown here]

S. Cerrito and M. Cialdea Mayer. A polynomial translation of S4 into T and contraction-free tableaux for S4. Logic Journal of the IGPL, 5(2):287--300, 1997.

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