P. Lincoln. Deciding Provability of Linear Logic Formulas. In J.-Y. Girard, Y. Lafont, L. Regnier (eds). Advances in Linear Logic, London Mathematical Society Lecture Note Series, Vol. 222, pp. 109-122, 1995.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....of these languages. Algorithmic aspects for veri cation of properties of the resulting linear logic speci cations are not considered in the works mentioned above. The problem of the decidability of provability in fragments of linear logic has been investigated in several works in the last years [31 33]. Speci cally, in [29] Kopylov has shown that the full propositional linear ane logic containing all the multiplicatives, additives, exponentials, and constants is decidable. Ane logic can be viewed as linear logic with the weakening rule. Propositional LO belongs to such a substructural logic. ....

....to such a substructural logic. Provability in full rst order linear logic is undecidable as shown by Girard s translation of rst order logic into rst order linear logic [Girard, 1987] The same holds for rst order ane logic (Girard s encoding can also be viewed as an encoding into ane logic [31]) First order linear logic without modalities, i.e. without the possibility of re using formulas, is decidable [33] In [12] Cervesato et al. use a formalism based on multisetrewriting and existential quanti cation that can be embedded into our fragment of linear logic to specify protocol ....

Lincoln, P. (1995). Deciding provability of linear logic formulas. Advances in linear logic. London Mathematical Society Lecture Notes Series, vol. 222.

.... include the decidability and the finite model property for propositional BI [19] Note that full propositional linear logic, with exponentials, is undecidable even when restricted to the intuitionistic fragment, that the status of MELL is unknown, and that neither has the finite model property [26, 29]. Note also that the releveant logic R is undecidable [45] In 4, after further discussion of resource modelling, we present a number of concrete models, which illustrate a range of features of resources, including: distribution (Petri nets, Ambients) resource allocation, deallocation and access ....

P. Lincoln. Deciding provability of linear logic formulas. In Y. Lafont J.-Y.Girard and L. Regnier, editors, Advances in Linear Logic, pages 109--122. Cambridge University Press, 1995.

.... include the decidability and the finite model property for propositional BI [18] Note that full propositional linear logic, with exponentials, is undecidable even when restricted to the intuitionistic fragment, that the status of MELL is unknown, and that neither has the finite model property [27, 30]. Note also that the releveant logic R is undecidable [46] In 4, after further discussion of resource modelling, we present a number of concrete models, which illustrate a range of features of resources, including: distribution (Petri nets, Ambients) resource allocation, deallocation and access ....

P. Lincoln. Deciding provability of linear logic formulas. In Y. Lafont J.-Y.Girard and L. Regnier, editors, Advances in Linear Logic, pages 109--122. Cambridge University Press, 1995.

.... watashi , is still applicable in formal settings. 3.3 Transforming objects under context We have to be careful not to push our fragment of linear logic beyond the boundary of decidable fragments. It is known that the decidability of multiplicative exponential linear logic (MELL) is unknown [Lincoln (1995)] We therefore lose the decidability unless we impose some restriction on the use of the exponential. We observe that the source of difficulty lies in allowing for both unlimited supply and consumption of resources. For our purpose, however, we can happily give up with the latter, the unlimited ....

Lincoln, Patrick. 1995. Deciding provability of linear logic formulas. In Jean-Yves Girard, Yves Lafont, and Laurent Regnier, editors, Advances in Linear Logic. Cambridge University Press, pages 109--122.

....since a lot of results have been obtained already in some restricted classes of substructural logics, like relevant logics, and therefore it is impossible to cover all of them. As for surveys of decision problems and the finite model property of relevant logics, see e.g. 1, 2, 7] Also, see [16] for a survey of decision problems of logics related to linear logic. Our aim of the present paper is to try to compare results from different classes of substructural logics with each other and discuss them as a whole, in order to get a perspective of them. 1 2 Decidability and undecidability ....

P. Lincoln, Deciding provability of linear logic formulas, Advances in Linear Logic, J.-Y. Girard, Y. Lafont and L. Regnier eds., London Mathematical Society, Lecture Note Series 222, Cambridge University Press (1995), 109-122.

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P. Lincoln. Deciding Provability of Linear Logic Formulas. In J.-Y. Girard, Y. Lafont, L. Regnier (eds). Advances in Linear Logic, London Mathematical Society Lecture Note Series, Vol. 222, pp. 109-122, 1995.

No context found.

P. Lincoln. Deciding provability of linear logic formulas. In Advances in Linear Logic, J.-Y.Girard, Y. Lafont and L. Regnier (editors), Cambridge Univ. Press, 1995, 109--122.

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