On full abstraction for PCF: I, II, and III
Information and Computation
CSL '02 Proceedings of the 16th International Workshop and 11th Annual Conference of the EACSL on Computer Science Logic
Locus Solum: From the rules of logic to the logic of rules
Mathematical Structures in Computer Science
Mathematical Structures in Computer Science
Interactive observability in Ludics: the geometry of tests
Theoretical Computer Science - Automata, languages and programming: Logic and semantics (ICALP-B 2004)
Theoretical Computer Science - Logic, language, information and computation
Ludics with Repetitions (Exponentials, Interactive Types and Completeness)
LICS '09 Proceedings of the 2009 24th Annual IEEE Symposium on Logic In Computer Science
Ludics is a model for the finitary linear pi-calculus
TLCA'07 Proceedings of the 8th international conference on Typed lambda calculi and applications
The separation theorem for differential interaction nets
LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
Theoretical Computer Science
On the meaning of focalization
Ludics, dialogue and interaction
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Gödel's completeness theorem is concerned with provability, while Girard's theorem in ludics (as well as full completeness theorems in game semantics) is concerned with proofs. Our purpose is to look for a connection between these two disciplines. Following a previous work [1], we consider an extension of the original ludics with contraction and universal nondeterminism, which play dual roles, in order to capture a polarized fragment of linear logic and thus a constructive variant of classical propositional logic. We then prove a completeness theorem for proofs in this extended setting: for any behaviour (formula) A and any design (proof attempt) P , either P is a proof of A or there is a model M of ${\mathbf{A}}^{\bot}$ which beats P . Compared with proofs of full completeness in game semantics, ours exhibits a striking similarity with proofs of Gödel's completeness, in that it explicitly constructs a countermodel essentially using König's lemma, proceeds by induction on formulas, and implies an analogue of Löwenheim-Skolem theorem.