K. Broda, M. Finger, and A. Russo. LDS-natural deduction for substructural logics (extended abstract). Logic Journal of the IGPL, 4(3):486489, 1996.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....treatment of constraints in our method. A rst step consists in computing the BI substitutions (from a set of connections) As illustrated in the example, it mainly requires an uni cation algorithm on labels. First, we could use an existing T string uni cation algorithm [9] or an AC algorithm [4,13] on our labels. Further work will focus on this step in order to analyze if it is necessary to propose other uni cation algorithms, specially dedicated to our constraint based method. The second step consists in proving the admissibility of such a substitution, i.e. whether requirements hold ....

K. Broda, M. Finger, and A. Russo. LDS-natural deduction for substructural logics (extended abstract). Logic Journal of the IGPL, 4(3):486489, 1996.

.... this semantics only holds for BI without the unit , denoted BI [27, 34] The LDS approach aims to provide a general deductive framework [9] and has been previously combined with tableau methods or analytic systems in order to obtain such a framework for a wide range of substructural logics [4, 6]. According to this approach, we deal with labelled formulae, the labels being used 1 to incorporate information such as semantics into syntax. Moreover, labels can be used in a speci c way in order to prove completeness theorems with the proof search method [28] and then allow to directly ....

....the tableau construction procedure terminates with a tableau containing a H branch. This H branch is necessarily nite and it is obvious that the construction given in de nition 7.5 results in a nite Kripke model whenever the given H branch is nite. Compared to the standard LDS approach in IL [4] and also to more standard tableaux methods [8] our derived tableau method for IL is based on a spe cic treatment of the labels with a direct construction of the countermodels. It involves an original use of the Kripke semantics through labels constraints. The introduction of assertions and ....

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K. Broda, M. Finger, and A. Russo. LDS-natural deduction for substructural logics (extended abstract). Logic Journal of the IGPL, 4(3):486489, 1996.

....in a given class of algebras, a problem we addressed by means of unification like techniques (especially AC unification) So far, this objective has been fully achieved for the special, if important, case of (multiplicative) propositional Linear Logic. The algorithms developed are described 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 ....

K. Broda, M. Finger, and A. Russo. LDS -- natural deduction for substructural logics. Journal of the Interest Group in Pure and Applied Logics (ISSN 0945-9103), 1996. (Abstract).

....in a given class of algebras, a problem we addressed by means of unification like techniques (especially AC unification) So far, this objective has been fully achieved for the special, if important, case of (multiplicative) propositional Linear Logic. The algorithms developed are described 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 ....

....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 theorem prover based on the same idea is presented in [4]. In addition the extra structure led us to develop a very simple algorithm for solving abductive style problems [ 5 Multi Implication Logics The last decade has seen a proliferation of different logical systems proposed for a variety of different purposes, both theoretical and practical. ....

K. Broda, M. Finger, and A. Russo. Lds -- natural deduction for substructural logics. In WOLLIC, Proceedings of the IIIrd Workshop on Logic, Language, Information and Computation, volume (ISSN 0945-9103) of Journal of the Interest Group in Pure and Applied Logics, 1996. (Submitted).

....properties of their related semantic accessibility relation [Fit83, HC68] A new logical approach, called Labelled Deductive System has been proposed by Gabbay [Gab92] which, taking into account this observation, facilitates logics of the same family to have a common 1 formalisation. Results in [DG94, BFR97] have already shown that uniform labelled proof systems can be developed for a family of substructural logics, using respectively tableaux and natural deduction proof style. This paper takes a further step. It provides a logical approach, based on Labelled Deductive System, in which logics ....

....labelling algebra A. In [Rus96] examples derivations are given for the di#erent labelling algebrae associated with the di#erent normal modal logics and it is shown how the CLDS approach (called in [Rus96] MLDS) facilitates the development of a uniform proof system for any normal modal logic. In [BFR97] a similar approach, also based on LDS, is described in which a common set of natural deduction rules are developed for a given family of substructural logics. The di#erence between one logic and another in [BFR97] is not 8 embedded explicitly in the derivation process in terms of inference ....

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K. Broda, M. Finger, and A. Russo. LDS-Natural Deduction for Substructural Logics. Technical Report DOC. 97/11, Imperial College, Department of Computing, 1997.

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