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Switch to: Citations
References in:
Proof and refutation in MALL as a game
Annals of Pure and Applied Logic 161 (5):654-672 (2010)
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Investigating Girard's new propositionnal calculus which aims at a large scale study of computation, we stumble quickly on that question: What is a multiplicative connective? We give here a detailed answer together with our motivations and expectations. |
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This book is a specialized monograph on the development of the mathematical and computational metatheory of reductive logic and proof-search including proof-theoretic, semantic/model-theoretic and algorithmic aspects. The scope ranges from the conceptual background to reductive logic, through its mathematical metatheory, to its modern applications in the computational sciences. |
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We present a game semantics for Linear Logic, in which formulas denote games and proofs denote winning strategies. We show that our semantics yields a categorical model of Linear Logic and prove full completeness for Multiplicative Linear Logic with the MIX rule: every winning strategy is the denotation of a unique cut-free proof net. A key role is played by the notion of history-free strategy; strong connections are made between history-free strategies and the Geometry of Interaction. Our semantics incorporates a (...) |
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Linear logic, introduced by Girard, is a refinement of classical logic with a natural, intrinsic accounting of resources. This accounting is made possible by removing the ‘structural’ rules of contraction and weakening, adding a modal operator and adding finer versions of the propositional connectives. Linear logic has fundamental logical interest and applications to computer science, particularly to Petri nets, concurrency, storage allocation, garbage collection and the control structure of logic programs. In addition, there is a direct correspondence between polynomial-time computation (...) |
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This book is a specialized monograph on the development of the mathematical and computational metatheory of reductive logic and proof-search, areas of logic that are becoming important in computer science. A systematic foundational text on these emerging topics, it includes proof-theoretic, semantic/model-theoretic and algorithmic aspects. The scope ranges from the conceptual background to reductive logic, through its mathematical metatheory, to its modern applications in the computational sciences. Suitable for researchers and graduate students in mathematical, computational and philosophical logic, and in (...) |
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We give a very brief introduction to how concurrent systems can be modelled within process calculi, as terms of an algebraic language whose behaviours are described using transitions. Reasoning has centred on two kinds of questions. One is relationships between descriptions of concurrent systems. The other is appropriate logics for describing crucial properties of concurrent systems. Bisimulation equivalence is briefly described. It can also be characterised in terms of modal logic . However as a logic it is not very expressive. (...) |
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We present a game semantics in the style of Lorenzen for Girard's linear logic . Lorenzen suggested that the meaning of a proposition should be specified by telling how to conduct a debate between a proponent P who asserts and an opponent O who denies . Thus propositions are interpreted as games, connectives as operations on games, and validity as existence of a winning strategy for P. We propose that the connectives of linear logic can be naturally interpreted as the (...) |
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Go back to An-fang, the Peace Square at An-Fang, the Beginning Place at An-Fang, where all things start (… ) An-Fang was near a city, the only living city with a pre-atomic name (… ) The headquarters of the People Programmer was at An-Fang, and there the mistake happened: A ruby trembled. Two tourmaline nets failed to rectify the laser beam. A diamond noted the error. Both the error and the correction went into the general computer. Cordwainer SmithThe Dead Lady (...) |
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We present an infinite-game characterization of the well-founded semantics for function-free logic programs with negation. Our game is a simple generalization of the standard game for negation-less logic programs introduced by van Emden [M.H. van Emden, Quantitative deduction and its fixpoint theory, Journal of Logic Programming 3 37–53] in which two players, the Believer and the Doubter, compete by trying to prove a query. The standard game is equivalent to the minimum Herbrand model semantics of logic programming in the sense (...) |
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