Skip to main content
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 40
  • Cited by
    This (lowercase (translateProductType product.productType)) has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Spinks, Matthew and Veroff, Robert 2018. Don Pigozzi on Abstract Algebraic Logic, Universal Algebra, and Computer Science. Vol. 16, Issue. , p. 323.


    Acclavio, Matteo 2018. Proof Diagrams for Multiplicative Linear Logic: Syntax and Semantics. Journal of Automated Reasoning,

    Primas, Hans 2017. Knowledge and Time. p. 23.

    Crubillé, Raphaëlle Ehrhard, Thomas Pagani, Michele and Tasson, Christine 2017. Foundations of Software Science and Computation Structures. Vol. 10203, Issue. , p. 20.

    Terrés Villalonga, Pilar 2017. From Natural to Formal Language: A Case for Logical Pluralism. Topoi,

    Fermüller, Christian G. and Lang, Timo 2017. Automated Reasoning with Analytic Tableaux and Related Methods. Vol. 10501, Issue. , p. 98.

    SLAVNOV, SERGEY 2017. On Banach spaces of sequences and free linear logic exponential modality. Mathematical Structures in Computer Science, p. 1.

    KANOVICH, MAX 2016. The undecidability theorem for the Horn-like fragment of linear logic (Revisited). Mathematical Structures in Computer Science, Vol. 26, Issue. 05, p. 719.

    Porello, Daniele 2015. PRIMA 2015: Principles and Practice of Multi-Agent Systems. Vol. 9387, Issue. , p. 416.

    Perhac, Jan and Mihalyi, Daniel 2015. Coalgebraic modeling of IDS behavior. p. 201.

    Boniolo, Giovanni D’Agostino, Marcello Piazza, Mario and Pulcini, Gabriele 2015. Adding logic to the toolbox of molecular biology. European Journal for Philosophy of Science, Vol. 5, Issue. 3, p. 399.

    Papapanagiotou, Petros and Fleuriot, Jacques D. 2014. Formal verification of collaboration patterns in healthcare. Behaviour & Information Technology, Vol. 33, Issue. 12, p. 1278.

    Deng, Jianxun Jiang, Lihong and Ca, Hongming 2014. Complement Service Composition through Domain Template and Requirement Context. p. 320.

    Blute, Richard F. Guglielmi, Alessio Ivanov, Ivan T. Panangaden, Prakash and Straßburger, Lutz 2014. Categories and Types in Logic, Language, and Physics. Vol. 8222, Issue. , p. 90.

    Moot, Richard 2014. Categories and Types in Logic, Language, and Physics. Vol. 8222, Issue. , p. 297.

    Moot, Richard and Retoré, Christian 2012. The Logic of Categorial Grammars. Vol. 6850, Issue. , p. 193.

    Papapanagiotou, Petros Fleuriot, Jacques and Grando, Adela 2012. Rigorous process-based modelling of patterns for collaborative work in healthcare teams. p. 1.

    Moot, Richard and Retoré, Christian 2012. The Logic of Categorial Grammars. Vol. 6850, Issue. , p. 1.

    Papapanagiotou, Petros and Fleuriot, Jacques 2011. Formal Verification of Web Services Composition Using Linear Logic and the pi-calculus. p. 31.

  • Print publication year: 1995
  • Online publication date: February 2010

Linear Logic: its syntax and semantics



The connectives of linear logic

Linear logic is not an alternative logic ; it should rather be seen as an extension of usual logic. Since there is no hope to modify the extant classical or intuitionistic connectives, linear logic introduces new connectives.

Exponentials : actions vs situations

Classical and intuitionistic logics deal with stable truths:

if A and AB, then B, but A still holds.

This is perfect in mathematics, but wrong in real life, since real implication is causal. A causal implication cannot be iterated since the conditions are modified after its use ; this process of modification of the premises (conditions) is known in physics as reaction. For instance, if A is to spend $1 on a pack of cigarettes and B is to get them, you lose $1 in this process, and you cannot do it a second time. The reaction here was that $1 went out of your pocket. The first objection to that view is that there are in mathematics, in real life, cases where reaction does not exist or can be neglected : think of a lemma which is forever true, or of a Mr. Soros, who has almost an infinite amount of dollars. Such cases are situations in the sense of stable truths. Our logical refinements should not prevent us to cope with situations, and there will be a specific kind of connectives (exponentials, “!” and “?”) which shall express the iterability of an action, i.e. the absence of any reaction ; typically!A means to spend as many dollars as one needs.

Recommend this book

Email your librarian or administrator to recommend adding this book to your organisation's collection.

Advances in Linear Logic
  • Online ISBN: 9780511629150
  • Book DOI:
Please enter your name
Please enter a valid email address
Who would you like to send this to *