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From the relationships between the notions of ordered m o n o i d and of quantale we de ne a new interpretation of ILL on Petri nets that is complete and veri es the property of nite models. ... In the latter case, the correspondence between Intuitionistic Linear Logic ILL and Petri nets illustrates the interest of e cient proof search methods for proving speci cations or properties of distributed ... . 2 From ordered monoids to quantales Quantales are to ILL what complete Boolean algebras are to classical logic, or what complete Heyting algebras are to intuitionistic logic. ...doi:10.1016/s1571-0661(05)01180-1 fatcat:grziahhbbjb5xgl5gtiz5e6lku
Summary: “We consider partially ordered algebraic structures aris- ing in the semantics of formulas of a noncommutative version of Girard’s linear logic. ... As a point of departure he uses intuitionistic propositional logic (IPL) and minimal intuitionistic propositional logic (MPL), which are widely admitted as proper models of informational structures. ...
(F-NANC-LRI; Vandoeuvre-les-Nancy) Quantales as completions of ordered monoids: revised semantics for intuitionistic linear logic. ... Therefore we obtain a new semantics based on ordered monoids and also new completeness results for ILL.” ...
In this paper we give relational semantics and an accompanying relational proof system for a variety of intuitionistic substructural logics, including (intuitionistic) linear logic with exponentials. ... of linear logic. To accomplish this, for each extension X of F L we develop a Kripke-style semantics, RelKripke X semantics, as a bridge to relational semantics. ... Francis Xavier University Council for Research Grant #91885. The author wishes to thank the referees for their comments and suggestions. 6. SOME OPEN PROBLEMS AND FUTURE DIRECTIONS 697 ...doi:10.1093/jigpal/5.5.673 fatcat:ccsg4hf63vctrexgxet3xmrqim
Focusing on the quantale semantics for dynamic operational quantum logic, we delineate some points of difference with the existing quantale semantics for (non)-commutative linear logic. ... On the other hand, an intuitionistic perspective on operational quantum logic, guides us in the direction of incorporating dynamics logically by reconsidering the primitive propositions required to describe ... Focusing on the quantale semantics for dynamic operational quantum logic, we delineate some points of difference with the existing quantale semantics for (non)-commutative linear logic. ...arXiv:math/0106059v6 fatcat:5n67ws3lbrgbndd2ikygnfjmj4
Galmiche, Quantales as completions of ordered monoids: revised semantics for intuitionistic linear logic (15 pp. ... Notin, Proof-search and proof nets in mixed linear logic (33 pp. (electronic)). ...
We present a complete pretopology semantics for a system of Intuitionistic Linear Logic (commutative or not) where the storage operator is split into a contraction and a weakening component and then recovered ... The canonical model construction of 3] is based on and extends the standard phase-space semantics for linear and substructural logics (Troelstra 22], Ono 21]). ... This report focuses on a bimodal version of intuitionistic linear logic. We prove a soundness and completeness theorem for the pretopology semantics for Linear Logic developed by G. ...doi:10.1093/jigpal/5.1.65 fatcat:npxhrwl6hvgjfidqda2nknxp6q
A number of examples underpin the universality of these constructions, the most prominent ones being separation logics, where convolution is separating conjunction in an assertion quantale; interval logics ... A Hoare logic can be constructed in a generic fashion on the power series quantale, which applies to each of these examples. ... We would like to thank Alasdair Armstrong, Kirill Bogdanov, John Derrick, Victor Gomes and Lindsay Groves for discussions of earlier versions. ...doi:10.1145/2874773 fatcat:czhzxgz5xne6xdfjsz2d6q3ka4
points of departure such as a deÿnition of a type-theoretic language or the relationship between languages and proof-objects. ... The strong connections between di erent proof-search methods in logics, type theories and logical frameworks, together with their impact on programming and implementation issues, are central in this context ... Acknowledgements We are grateful to Maurice Nivat for encouraging us to produce this article and for acting as a referee. Any remaining errors are our responsibility. ...doi:10.1016/s0304-3975(99)00169-3 fatcat:gy4nmmsupfeype23pw3jzbrvwu
Specifically, we present a new semantics for multiset rewriting founded on an alternative view of linear logic. ... In nearly all cases, the target of these investigations has been linear logic, a formal language that supports a view of formulas as consumable resources. ... Acknowledgments We are grateful to Frank Pfenning, Dale Miller, Mark-Oliver Stehr, Valeria de Paiva, Gerald Allwein, Steve Zdancevic and Vijay Saraswat for their comments on various aspects of this work ...doi:10.1016/j.entcs.2006.05.043 fatcat:eavrmrbudjbvbhnu2zlxecsd2e
Specifically, we present a new semantics for multiset rewriting founded on an alternative view of linear logic and specifically LV obs . ... of linear logic that we call LV obs . ... of this work. ...doi:10.1016/j.ic.2008.11.006 fatcat:p3nbvcukzbeqrfha4k32llbk4a
The Australasian Journal of Logic
Our main technical tool is to use residuated lattices as the algebraic semantics for them. ... In this paper, we will develop an algebraic study of substructural propositional logics over FLew, i.e. the logic which is obtained from intuitionistic logics by eliminating the contraction rule. ... The system FL e gives a sequent calculus for the intuitionistic linear logic. ...doi:10.26686/ajl.v8i0.1813 fatcat:3e5qatqxp5cixh3nheslskou4m
The space of truth values for this logic is the lattice of possibility functions, that, from an algebraic point of view, forms a quantal. ... A Gentzen calculus is presented, which is proved sound and complete with respect to the given semantics. The problem of truth functionality is discussed in this context. ... Acknowledgments We are grateful to Alessandro Saffiotti for several pre cious advices, and to Nino Trainito for a careful read ing of the paper. ...arXiv:1302.4931v1 fatcat:aeeu5dm2lfdrbk2eyyfiazd3je
linear logic, 3580 hardness, 3420 hyper (l)-AFL, 99 implicational dependencies, 1857 interpretations, 88 intuitionistic linear logic, 3257 linear logic, 3580 matrix equivalence problem, 355 ... 509,2175,2225,2317,2636 lazy functional languages, 2270 first-order linear differential systems, 3593 logic, 2574, 3580 first-order linear-time temporal logic, 3049 first-order logic, 823, 1057,2155,2156,2222,2407 ...doi:10.1016/s0304-3975(98)00319-3 fatcat:s22ud3iiqjht7lfbtc3zctk7zm
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