Anne Sjerp Troelstra, Lectures on linear logic, CSLI Lecture Notes, no. 29, Center for the Study of Language and Information, Stanford, CA, 1992. Home/Search Document Not in Database Summary Related Articles Check |
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Higher-Order Quantification and Proof Search - Miller (2002) (2 citations) (Correct)
....to establish. We now proceed to present some example of reasoning with higher order quantification. All of our examples involve some use of linear logic as well as higher order quantification. We will not attempt to describe the basics of linear logic, but rather refer the reader to, say, [Gir87,Tro92]. Our first two examples will make use of linear implication, written as (as as the converse # ) intuitionistic implication, written as #. The multiplicative conjunction appears as well. Our last example, starting in Section 5 will also make use of the multiplicative disjunction . ....
Anne S. Troelstra. Lectures on Linear Logic. CSLI Lecture Notes 29, Center for the Study of Language and Information, Stanford, California, 1992.
Cut Elimination for Classical Proofs as Continuation Passing.. - Ichiro Ogata (1998) (1 citation) (Correct)
....subsection, we briefly introduce LKT and LKQ and (linear and intuitionistic) decoration method[3, 4] on which our method is based. We shall assume the basics of multiplicative exponential part of classical linear logic(MELL) and the cut elimination procedure(linear procedure) for MELL; See e.g. [25] for introduction. LKT and LKQ are embeddable into the MELL by means of linear decoration of DJS [4] Under linear decoration, cut elimination for LKT LKQ becomes an immediate corollary to cut elimination for (second order) MELL, as reductions of the linear or intuitionistic decoration of a ....
Anne S. Troelstra. Lectures on Linear Logic. CSLI Lecture Notes 29, Center for the Study of Language and Information, Stanford, California, 1992.
Logical Aspects of Computational Linguistics: an.. - Blackburn, Dymetman.. (1997) (3 citations) (Correct)
....and two implications (because of the non commutativity) The properties of this calculus, once rather isolated from other calculi, are now easily observed and formulated in the linear logic framework. Linear logic was introduced ten years ago by Girard [53] see [54] for a recent survey and [118] for a textbook. Although it was conceived rather as a logic of computation and communication than for linguistic purposes, it explains the various aspects of logical calculi with restricted structural rules and their relations to the standard intuitionistic or classical logic, via the unary ....
....as a syntactical analysis, i.e. a proof in the Lambek calculus. This enables a particularly simple interface between syntax and semantics [85,88,27] which is especially clear in the proof net syntax [59] This proof net syntax is precisely another convenient tool provided by linear logic [53,118,54,73]. It is a very compact and elegant notation for proofs in these logical calculi, which avoids, for instance, the so called spurious ambiguities of categorial grammar analyses [100] The structure of a proof net is very much like a family of trees, and thus one is able to picture in this setting ....
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Anne Sjerp Troelstra. Lectures on Linear Logic, volume 29 of CSLI Lecture Notes. Center for the Study of Language and Information, Stanford CA, 1992. (distributed by Cambridge University Press)
A judgmental analysis of linear logic - Bor-Yuh Evan Chang Self-citation (Linear) (Correct)
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Anne Sjerp Troelstra, Lectures on linear logic, CSLI Lecture Notes, no. 29, Center for the Study of Language and Information, Stanford, CA, 1992.
A Judgmental Analysis of Linear Logic - Bor-Yuh Evan Chang (2003) (1 citation) Self-citation (Linear) (Correct)
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Anne Sjerp Troelstra, Lectures on linear logic, CSLI Lecture Notes, no. 29, Center for the Study of Language and Information, Stanford, CA, 1992.
A Judgmental Analysis Of Linear Logic - Bor-Yuh Evan Chang (2003) (1 citation) Self-citation (Linear) (Correct)
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Anne Sjerp Troelstra, Lectures on linear logic, CSLI Lecture Notes, no. 29, Center for the Study of Language and Information, Stanford, CA, 1992.
A Judgmental Analysis of Linear Logic - Chang, Chaudhuri, Pfenning (2003) (1 citation) Self-citation (Linear) (Correct)
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Anne Sjerp Troelstra, Lectures on linear logic, CSLI Lecture Notes, no. 29, Center for the Study of Language and Information, Stanford, CA, 1992.
A Judgmental Analysis of Linear Logic - Chang, Chaudhuri, Pfenning (2003) (1 citation) Self-citation (Linear) (Correct)
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Anne Sjerp Troelstra, Lectures on linear logic, CSLI Lecture Notes, no. 29, Center for the Study of Language and Information, Stanford, CA, 1992.
Temporal Linear Logic and Its Applications - Hirai (2000) Self-citation (Linear) (Correct)
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Anne S. Troelstra. Lectures on Linear Logic. CSLI Lecture Notes 29, Center for the Study of Language and Information, Stanford, California, 1992.
A Judgmental Analysis of Linear Logic - Chang, Chaudhuri, Pfenning (2003) (1 citation) Self-citation (Linear) (Correct)
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Anne Sjerp Troelstra, Lectures on linear logic, CSLI Lecture Notes, no. 29, Center for the Study of Language and Information, Stanford, CA, 1992.
Lógica Linear E a Especificação De Sistemas .. - Pimentel (2001) Self-citation (Linear) (Correct)
....sequent. Finally, the cut elimination theorem for FF Theorem 21 For every derivation of a sequent in FF , there is a cut free derivation of the sequent. Proof Corollary 20 deals with the atomic case. For the other cases, we perform the usual cut elimination procedure for linear logic (see e.g. [Tro92]) 7.4.3 Discussion It is easy to see that the application of Cut on formulas containing implication can be replaced by an implication free cut in FF Proposition 22 Let Pi the derivation: Note that the head of definitional clauses and the nat predicate are atomic and that atomic cuts ....
Anne S. Troelstra. Lectures on Linear Logic. CSLI Lecture Notes 29, Center for the Study of Language and Information, Stanford, California, 1992.
Temporal Linear Logic and Its Applications - Hirai (2000) Self-citation (Linear) (Correct)
.... models of concurrency are applications of LL [26, 2, 20] In particular, the relation between linear logic and Petri nets [11, 36] has been well studied [16, 35, 21, 4, 23] According to [25] the algebraic point of view of Petri nets seems to be related to the algebraic semantics for linear logic [28, 34]. LL has a modal storage operator which means an infinite resource. Using this operator, one can distinguish the treatment of a reusable resource from the treatment of a consumptive resource. For example, a token in Petri nets is treated as a consumptive resource and a transition is expressed ....
....operator which means always . S4 can be embedded into TLL. We can say that the time concept of this works in TLL. Theorem 3.3.1 (Cut Elimination) If a sequent # # # is provable in TLL, then it is cut free provable in TLL. Proof. The proof is as in the linear logic case (see, for example, [34] for details) Here we summarize the method. First, we add ( cut) and ( cut) to TLL. # # #, D ( D) n , # # # #, # # #, # ( cut) # # #, D) n D, # # # #, # # #, # ( cut) Here, n 0, and (D) n indicates n z D, D. cut) and ( cut) can be reduced to ordinary ....
Anne S. Troelstra. Lectures on Linear Logic. CSLI Lecture Notes 29, Center for the Study of Language and Information, Stanford, California, 1992.
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