Mantel, Heiko and Kreitz, Christoph. (October 1998). A Matrix Characterization for MELL. In Dix, J., del Cerro, L. Farinas and Furbach, U., (eds.), Proceedings of Logics in Artificial Intelligence, European Workshop, JELIA '98, LNAI 1489, pages 169-- 183, Dagstuhl, Germany. Springer. Home/Search Document Details and Download
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linTAP: A Tableau Prover for Linear Logic - Mantel, Otten (1999) (5 citations) Self-citation (Mantel) (Correct)
....proof search in linear logic is dicult to automate. Various calculi have been developed for linear logic. Beginning with the sequent calculus and proof nets by Girard [12] several optimizations have been proposed. More recently, the connection method has been extended to fragments of linear logic [8,9,15,17]. In this article, we propose a tableau calculus for MELL and for M LL which is the theoretical basis for our theorem prover linTAP. linTAP is implemented in a very compact way but uses sophisticated techniques to reduce the search space and thus follows the idea of lean theorem proving . It was ....
....in ileanTAP, string uni cation is used to deal with the non permutabilities speci c to linear logic. This approach has been invented by Wallen in the context of matrix characterizations for non classical logics [25] The pre xes used by linTAP are motivated by a matrix characterization for MELL [17]. In our implementation of linTAP we use a leanTAP like technique for path checking and then try to unify the so called pre xes of atoms which are closing the branches of the tableau proof like in ileanTAP. Some additional checks are required because of the resource sensitivity of linear logic. ....
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H. Mantel, C. Kreitz. A Matrix Characterization for MELL. Logics in Articial Intelligence, JELIA '98, LNAI 1489, pp. 169-183, Springer, 1998.
Matrix-based Constructive Theorem Proving - Kreitz, Otten, Schmitt, Pientka (1999) (1 citation) Self-citation (Kreitz) (Correct)
....in a sequent proof, instead of the logical connectives of a proof goal. Although originally developed for classical logic, the connection method has recently been extended to a variety of non classical logics such as intuitionistic logic [18] modal logics [20] and fragments of linear logic [14, 17]. Furthermore, algorithms for converting matrix proofs into sequent proofs have been developed [23, 24] which makes it possible to view matrix proofs as plans for predicate logic proofs that can be executed within a proof assistant [6, 15] Viewing matrix proofs as proof plans also suggests the ....
H. Mantel and C. Kreitz. A matrix characterization for MELL. In 6 th European Workshop on Logics in AI (JELIA-98), LNAI, Springer, 1998.
Hierarchical Contextual Reasoning - Autexier (2003) (Correct)
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Mantel, Heiko and Kreitz, Christoph. (October 1998). A Matrix Characterization for MELL. In Dix, J., del Cerro, L. Farinas and Furbach, U., (eds.), Proceedings of Logics in Artificial Intelligence, European Workshop, JELIA '98, LNAI 1489, pages 169-- 183, Dagstuhl, Germany. Springer.
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