Yves Lafont. The finite model property for various fragments of linear logic. The Journal of Symbolic Logic, 62(4):1202--1208, 1997.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... 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 ....

Y. Lafont. The finite model property for various fragments of linear logic. J. Symb. Logic, 62(4):1202--1208, 1997.

.... 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 ....

Y. Lafont. The finite model property for various fragments of linear logic. J. Symb. Logic, 62(4):1202--1208, 1997.

....the corresponding linear logic theorems. Two aspects of this proof are of particular interest. First, we are able to show completeness by assigning to variables only Chu spaces with at most 4 points. Although there are other completeness results where finite objects are assigned to variables, e.g. [7], this is the first for which the objects assigned to variables are of uniformly bounded finite size. We expect that this property survives lifting the CNF restriction, but have no expectations either way for when the restriction to two occurrences per variable is lifted. Second, we introduce the ....

Y. Lafont. The finite model property for various fragments of linear logic. Available as http://hypatia.dcs.qmw.ac.uk/authors/L/LafontYGA/papers/model.ps.Z, 1996.

....LC2 and LLW2. This encoding is like as the encodings in [Kan1, Laf1, LS] In order to obtain the faithfulness of the encoding we use (as in [Laf1, LS] the phase semantic, but here we need the phase semantic for linear ane logic. 2 Phase semantic Let us remind some de nitions about phase semantic [Gir, Laf2]. Phase space is the triple (M; K) where M is a commutative monoid, M and K is a submonoid of the submonoid J(M) fx 2 j x 2 fx 2 g g. For instance, K may be f1g. Let X;Y M , then, by de nition, XY = fxy j x 2 X; y 2 Y g; X Y = fz 2 M j 8x 2 X xz 2 Y g; X = X : We ....

....of A, when = X. By de nition, a formula A is satis ed, if 1 2 A . A sequent A 1 ; A n B 1 ; B k is satis ed, if the formula (A 1 : A n ) B 1 : B k ) is satis ed. It is equal to that (A 1 : A n ) B 1 : B k ) De nition ([Laf2]) We say that the phase space is an ane phase space if is an ideal, i.e. M . Theorem 1 ( Laf2] If a sequent is derivable in LLW2, then any ane phase space (M; K) satis es . 3 Remark For quanti er free linear ane logic without modalities the converse theorem holds too. If (M; is ....

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Y. Lafont. The Finite Model Property for Various Fragments of Linear Logic.

....classes of logics in a uniform framework. He shows that the contraction rule and the distribution rule are the two main sources which give rise to higher complexity in decision procedures or to undecidability. He also discusses recent results on the finite model property by Meyer and Ono 1994, Lafont 1995 and Buszkowski 1996. Zaslavsky studies the relationship between logical completeness and functional completeness for logical calculi in three valued predicate logics. Here functional completeness means that all three valued (true, undefined, false) logical functions can be expressed in terms ....

Lafont, Y. 1995. The finite model property for various fragments of linear logic. Manuscript.

....and ( W X) ffi X ffi . On the other hand, X 6 W X. Thus we have X ( W X) ffi and finally X ffi ( W X) ffi . Theorem 2.13 The class of quantales of the form (M ffi ; ffl) is a complete class of models of ILL. Moreover, finiteness is preserved by our construction. From [9], we know that ILL is complete with respect to finite quantales and thus we can deduce another complete class of quantales. Theorem 2.14 The class of finite quantales of the form (M ffi ; ffl) where M is finite, is complete class of models of ILL. 2.8 Back to the example Remember the ....

Yves Lafont. The finite model property for various fragments of linear logic. Journal of Symbolic Logic, 62(4):1202--1208, 1997.

.... Restricted Powerset Models for the Lambek Calculus and Its Extensions Wojciech Buszkowski Faculty of Mathematics and Computer Science Adam Mickiewicz University Pozna n Poland Abstract Lafont [11] gives an elegant proof of finite model property (fmp) for Multiplicative Additive Linear Logic (MALL) and suggests it can be adapted to noncommutative linear logics of Abrusci [1] In [4, 6, 9] fmp for certain fragments of MALL (e.g. BCI, BCI[ and weaker systems (e.g. the product free Lambek ....

....L1[ as well as commutative versions of these systems (the commutative L1 equals the BCI logic and is a fragment of MALL) The proof for L[ has been arranged in such a form that all further modifications are straightforward. In section 6 we show that our methods also yield the result of Lafont [11]; we use a syntactic interpretation of MALL in system L1E[ and the completeness of the latter with respect to finite restricted powerset models over commutative monoids. Quite likely, the completeness of L1[ Omega ; and richer noncommutative linear logics with respect to finite ....

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Y. Lafont, The finite model property for various fragments of linear logic, manuscript, 1995.

....x 2 A Gamma ffl B. Let a 2 A and y 2 B ; a Delta x 2 B so y Delta a Delta x 2 , thus x 2 A rB = B Delta A) Conversely, assume x 2 A rB, and take a 2 A. For all y 2 B , y Delta a Delta x 2 , thus a Delta x 2 B = B, whence x 2 A Gamma ffl B. Xi As in [7, 9], we extend the semantics to exponential connectives. If P is a phase space, define J(P ) fx 2 1 j x 2 fx xg g. Note that x 2 J(P ) x 2 fx Delta xg , because fx xg fx Delta xg . Definition 5.11 An enriched phase space consists in a phase space P and a subset K of ....

Y. Lafont. The finite model property for various fragments of linear logic. J. Symb. Logic, 62(4):1202--1208, 1997.

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Yves Lafont. The finite model property for various fragments of linear logic. The Journal of Symbolic Logic, 62(4):1202--1208, 1997.

No context found.

Yves Lafont. The finite model property for various fragments of linear logic. The Journal of Symbolic Logic, 62(4):1202--1208, 1997.

No context found.

Y. Lafont. The finite model property for various fragments of linear logic. J. Symb. Logic 62(4):1202--1208, 1997.

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