Francois Lamarche, Games semantics for full propositional linear logic, Proceedings of the 10th Annual Symposium on Logic in Computer Science (LICS'95) (San Diego, California) (D. Kozen, ed.), IEEE Computer Society Press, June 1995, pp. 464--473.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....an unpublished note [21] and ordered logic [25] but these did not incorporate possibility and related connectives ( #) To our knowledge, the double negation translation from classical into intuitionistic linear logic that can optionally account for MIX is also new in this paper. Lamarche [17] has previously given a more complex double negation translation from classical linear logic into intuitionistic linear logic using a onesided sequent calculus with polarities. The remainder of the paper has the following organization. In Sec. 2, we describe natural deduction for JILL in terms of ....

....a proof of # #A# where is the translation of A. It is more economical and allows some further applications if we instead parameterize the translation by a propositional parameter p and verify that ##A# p =# p#, an idea that goes back to Friedman [12] and was also employed by Lamarche [17] in the linear setting. It is convenient to introduce the parametric negation p A = A#p, where A is the usual negation in JILL. Since the translation of A becomes a linear hypothesis, all connectives except# , 1, and can simply be dualized. For the remaining three we need to introduce a ....

Francois Lamarche. Games semantics for full propositional linear logic. In D. Kozen, editor, Proceedings of the 10th Annual Symposium on Logic in Computer Science (LICS'95), pages 464--473, San Diego, California, June 1995. IEEE Computer Society Press.

....In this case, sequents are made of several antecedent formulas, but only one succedent formula. To deal with the intuitionistic notion with proof nets (since we consider one sided sequents) we use the notion of polarities with the input (ffl: negative) and the output (ffi: positive) Danos90, Lamarche95] to decorate formulas. Positive ones correspond to succedent formulas and negative ones to antecedent formulas. Given the links of table 1, we define proof structures as graphs made of these links such that: 1. any premise of any link is connected to exactly one conclusion of some other link; 2. ....

.... terms (with the Curry Howard isomorphism) and proof nets represent proofs of intuitionistic implicative linear logic. And indeed, the linear terms may be encoded as proof nets. On the other hand, given an intuitionistic implicative proof net, a simple algorithm (given in [dG et al..96] based on [Lamarche95] s dependency paths) we can obtain a term. This reading follows the algorithm: 1. enter the proof net by its unique output conclusion; 2. follow the output polarities until reaching an axiom link. This path is ascending and is made of par links corresponding to abstractions; Copyright c ....

F. Lamarche. -- Games semantics for full propositional linear logic. In : Proceedings, Tenth Annual IEEE Symposium on Logic in Computer Science. IEEE Computer Society Press, pp. 464--473. -- San Diego, California, 26--29 June 1995.

....states, events, and resources [15, 28, 29] A connection between linear logic and randomized interaction was investigated in [22] which introduced a game semantics of a fragment of linear logic by means of probabilistic games. Other notions of game semantics for linear logic were considered in [8, 1, 2, 17, 20, 19, 11]. Another direction is emphasized here: linear logic proof game simulations of probabilistic games from complexity theory. Such simulations are then used to show that certain problems in linear logic that are known to be hard to decide are also hard to approximate. We shall consider so called ....

F. Lamarche, Games semantics for full propositional linear logic, Proceedings of the 10-th Annual IEEE Symposium on Logic in Computer Science, San Diego, California, June 1995, pp. 464--473.

....particularly well suited to modelling linear GAMES AND DEFINABILITY FOR FPC 349 A # (A # B) # B b 1 b 1 a 1 a 1 a 2 a 2 b 2 b 2 . Figure 1. A winning strategy for A # (A # B) # B . logic [12] This was first noticed by Blass [8] whose ideas were refined by several others [2, 16, 22], leading to the first definability results. Games make the distinction between the additive conjunction ANB and the multiplicative conjunction A# B clear: in ANB , a play consists of a single play of either A or B , while in A# B , moves can be made on both sides. The linear arrow A # B ....

F. Lamarche, Games semantics for full propositional linear logic, In Proceedings, Tenth Annual IEEE Symposium on Logic in Computer Science [18], pp. 464--473.

.... rule. Proposition 3 If is provable in MALLP, contains at most one positive formula. Remark: There is a natural way to translate MALL formulas into MALLP: we just add the needed lifts when polarity changes. Lamarche described a game model for LL based on a notnot translation of LL in ILL [14]. His translation can be seen as a translation of MALL formulas into MALLP which adds double lifts # to our translation, every time we apply a positive connective to an already positive formula (and # in the negative case) 2.2 Interpretation of proofs De nition 13 (Total strategy) A ....

Francois Lamarche. Games semantics for full propositional linear logic. In Proceedings of the tenth annual IEEE symposium on Logic In Computer Science. IEEE Computer Society Press, 1995.

....In this case, sequents are made of several antecedent formulas, but only one succedent formula. To deal with the intuitionistic notion with proof nets (since we consider one sided sequents) we use the notion of polarities with the input (ffl: negative) and the output (ffi: positive) Danos90, Lamarche95] to decorate formulas. Positive ones correspond to succedent formulas and negative ones to antecedent formulas. Given the links of table 1, we define proof structures as graphs made of these links such that: 1. any premise of any link is connected to exactly one conclusion of some other link; 2. ....

.... terms (with the Curry Howard isomorphism) and proof nets represent proofs of intuitionistic implicative linear logic. And indeed, the linear terms may be encoded as proof nets. On the other hand, given an intuitionistic implicative proof net, a simple algorithm (given in [dG et al..96] based on [Lamarche95] s dependency paths) we can obtain a term. This reading follows the algorithm: 1. enter the proof net by its unique output conclusion; 2. follow the output polarities until reaching an axiom link. This path is ascending and is made of par links corresponding to abstractions; Copyright c ....

F. Lamarche. -- Games semantics for full propositional linear logic. In : Proceedings, Tenth Annual IEEE Symposium on Logic in Computer Science. IEEE Computer Society Press, pp. 464--473. -- San Diego, California, 26--29 June 1995.

....states, events, and resources [15, 28, 29] A connection between linear logic and randomized interaction was investigated in [22] which introduced a game semantics of a fragment of linear logic by means of probabilistic games. Other notions of game semantics for linear logic were considered in [8, 1, 2, 17, 20, 19, 11]. Another direction is emphasized here: linear logic proof game simulations of probabilistic games from complexity theory. Such simulations are then used to show that certain problems in linear logic that are known to be hard to decide are also hard to approximate. We shall consider so called ....

F. Lamarche. Games semantics for full propositional linear logic. In Proc. 10-th Annual IEEE Symposium on Logic in Computer Science, San Diego, pages 464--473, June 1995.

.... Linear logic, introduced in [10] is a refinement of classical logic often described as being resource sensitive because of its intrinsic ability to reflect computational states, events, and resources [11, 27, 28] Several notions of game semantics for linear logic are investigated in [6, 1, 2, 13, 17, 15, 9]. Connections between linear logic proof search and probabilistic games considered in complexity theory are investigated in [20, 21, 22] In particular, linear logic proof search may also be seen as a game. This game, the linear logic proof game, is played on linear logic formulas, and its moves ....

F. Lamarche. Games semantics for full propositional linear logic. In Proc. 10-th Annual IEEE Symposium on Logic in Computer Science, San Diego, pages 464--473, June 1995.

....in a proof structure, the inputs correspond to the formulas on the left hand side of the associated sequent and the unique output corresponds to the unique formula on the right hand side of the sequent. There is another representation of IILL using the one sided sequent calculus with polarities [Lam95]: in this representation, the ( input and ( output links are respectively replaced with links and O links, up and down formulas become input and output formulas but there is no essential di erence between the two representations. 1.2 Minimal labelling and correctness of proof nets Of course, ....

F. Lamarche. Games semantics for full propositional linear logic. In D. Kozen, editor, Tenth Annual IEEE Symposium on Logic in Computer Science, pages 464-473, San Diego, California, June 1995.

....the space that is necessary to P 2 is 2n 2 . 3 Transposition to the intuitionistic framework This decidability result can be transposed to the multiplicative and additive fragment of second order intuitionistic linear logic (IMALL2) via a translation of IMALL2 into MALL2 which uses polarities [8]. Each IMALL2 formula has two translations 20 into MALL2, a positive translation and a negative translation which correspond to its position as a member of the antecedent or the succedent of a sequent. Both translations are built inductively on the structure of the formulas according to the ....

F. Lamarche. Games Semantics for Full Propositional Linear logic. In D. Kozen, editor, Proceedings of Tenth Annual IEEE Symposium on Logic in Computer Science, San Diego, California, June 1995, pages 464--473.

....is resolved. 8. How to extract the semantic content from a net Until now we have not been explicit about how a proof determines a semantic reading. We shall show here how to extract from a proof net a functional term representing the semantics (see de Groote and Retor 1996, who reference Lamarche 1995). This is done by travelling from premises to conclusions and from conclusions to premises in a proof net following deterministic instructions. The proof nets are proof structures in which following these instructions visits each node exactly once. First one assigns a distinct index to each ....

Lamarche, F. (1995), `Games semantics for full propositional linear logic', in Ninth Annual IEEE Symposium on Logic in Computer Science, IEEE Press.

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Francois Lamarche. Games semantics for full propositional linear logic. In Proceedings of the 10th Annual IEEE Symposium on Logic in Computer Science (LICS 95),pages 464--473, 1995.

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Francois Lamarche. Games semantics for full propositional linear logic. In Proceedings of the 10th Annual IEEE Symposium on Logic in Computer Science (LICS 95),pages 464--473, 1995.

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Francois Lamarche, Games semantics for full propositional linear logic, Proceedings of the 10th Annual Symposium on Logic in Computer Science (LICS'95) (San Diego, California) (D. Kozen, ed.), IEEE Computer Society Press, June 1995, pp. 464--473.

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Francois Lamarche, Games semantics for full propositional linear logic, Proceedings of the 10th Annual Symposium on Logic in Computer Science (LICS'95) (San Diego, California) (D. Kozen, ed.), IEEE Computer Society Press, June 1995, pp. 464--473.

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Francois Lamarche, Games semantics for full propositional linear logic, Proceedings of the 10th annual symposium on logic in computer science (lics'95) (San Diego, California) (D. Kozen, editor), IEEE Computer Society Press, June 1995, pp. 464--473.

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Francois Lamarche, Games semantics for full propositional linear logic, Proceedings of the 10th Annual Symposium on Logic in Computer Science (LICS'95) (San Diego, California) (D. Kozen, ed.), IEEE Computer Society Press, June 1995, pp. 464--473.

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F. Lamarche. Games semantics for full propositional linear logic. In D. Kozen, editor, Tenth Annual IEEE Symposium on Logic in Computer Science, pages 464-473, San Diego, California, June 1995.

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F. Lamarche. Games semantics for full propositional linear logic. In D. Kozen, editor, Tenth Annual IEEE Symposium on Logic in Computer Science, pages 464--473, San Diego, California, June 1995.

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Francois Lamarche, Games semantics for full propositional linear logic, Proceedings of the 10th Annual Symposium on Logic in Computer Science (LICS'95) (San Diego, California) (D. Kozen, ed.), IEEE Computer Society Press, June 1995, pp. 464--473.

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F. Lamarche, Games semantics for full propositional linear logic, Proc. Logic In Computer Science '95, IEEE Computer Society Press (1995). 24

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Francois Lamarche, Games semantics for full propositional linear logic, Proceedings of the 10th annual symposium on logic in computer science (lics'95) (San Diego, California) (D. Kozen, editor), IEEE Computer Society Press, June 1995, pp. 464--473.

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Francois Lamarche. 1995. Games semantics for full propositional linear logic. In Proceedings, Tenth Annual IEEE Symposium on Logic in Computer Science, pages 464--473, San Diego, California, 26--29 June. IEEE Computer Society Press.

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Francois Lamarche. 1995. Games semantics for full propositional linear logic. In Proceedings, Tenth Annual IEEE Symposium on Logic in Computer Science, pages 464--473, San Diego, California, 26--29 June.

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Francois Lamarche. 1995. Games semantics for full propositional linear logic. In Proceedings, Tenth Annual IEEE Symposium on Logic in Computer Science, pages 464--473, San Diego, California, 26--29 June. IEEE Computer Society Press.

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