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Optimization complexity of linear logic proof games

Patrick D. Lincoln, John C. Mitchell, Andre Scedrov
1999 Theoretical Computer Science  
A class of linear logic proof games is developed, each with a numeric score that depends on the number of preferred axioms used in a complete or partial proof tree.  ...  linear logic.  ...  Acknowledgements We would like to thank Mitsu Okada and the local organizers of the Linear Logic '96 Tokyo Meeting for the splendid arrangements at the conference.  ... 
doi:10.1016/s0304-3975(99)00057-2 fatcat:veu4bd5pznan3ncml3cwj2fod4

Page 47 of Mathematical Reviews Vol. , Issue 2001A [page]

2001 Mathematical Reviews  
complexity of linear logic proof games.  ...  Summary: “A class of linear logic proof games is developed, each with a numeric score that depends on the number of preferred axioms used in a complete or partial proof tree.  ... 

Optimal strategic reasoning with McNaughton functions

Tomáš Kroupa, Ondrej Majer
2014 International Journal of Approximate Reasoning  
Acknowledgements The work of both authors was supported by Grant No. P402/12/1309 of the Czech Science Foundation.  ...  Let f ∈ M 2 and let P( f ) be the complex of linear regions of f .  ...  The proof that ν * is an optimal strategy for the second player is completely analogous and we skip it. 2 Observe that in the proof we have not used the assumption about the integer values of linear coefficients  ... 
doi:10.1016/j.ijar.2014.04.009 fatcat:bbjkodmtrveolbpy4xg7y3n53i

Page 4614 of Mathematical Reviews Vol. , Issue 2000g [page]

2000 Mathematical Reviews  
The paper is written as a sequence of comments, definitions, results and proofs involving various aspects of linear logic. The main focus is on the game (dialogue) approach.  ...  We consider the lengths of proofs in nonclassical logics, in particular monotone and intuitionistic logics, and, in a similar way, show a relation to the complexity of sorting networks.”  ... 

Contents and abstracts of the electronic notes in theoretical computer science vol. 3

1998 Theoretical Computer Science  
Preface The field of linear logic has developed very rapidly during the last ten years. Linear logic is now one of the most active research areas in Logic and in Theoretical Computer Science.  ...  The Linear Logic 96 Tokyo Meeting provided a forum for an exchange of research results and a discussion of the future directions in the field.  ...  We present a novel semantics for Idealized Algol using games, which is quite unlike traditional denotational models of state.  ... 
doi:10.1016/s0304-3975(97)00246-6 fatcat:2skydvbtyvdq3mmxtqwo2hncgi

Index

1999 Theoretical Computer Science  
Scedrov, Optimization complexity of linear logic proof games (1}2) 299}331 McCusker, G., see S. Abramsky (1}2) 3} 42 MeH tayer, F., Polynomial equivalence among systems LLNC, LLNC ?  ...  Girard (1}2) 1 Okada, M., Phase semantic cut-elimination and normalization proofs of "rst-and higher-order linear logic (1}2) 333}396 Regnier, L., see V. Danos (1}2) 79} 97 Scedrov, A., see P.D.  ... 
doi:10.1016/s0304-3975(99)00259-5 fatcat:ryfkx56wxjaftoaar6dzvaivka

Page 8148 of Mathematical Reviews Vol. , Issue 2004j [page]

2004 Mathematical Reviews  
relational model of syntactic control of interference (247-261); Jerzy Marcinkowski and Tomasz Truderung, Optimal complexity bounds for positive LTL games (262-275); Antonin Kuéera [Antonin Kuéera’] and  ...  Hyland], Designs, disputes and strategies (442-457); Masahito Hasegawa, Classical linear logic of implications (458 472).  ... 

Scenario analysis based on linear logic

Frédéric Collé, Ronan Champagnat, Armelle Prigent
2005 Proceedings of the 2005 ACM SIGCHI International Conference on Advances in computer entertainment technology - ACE '05  
Linear logic facilitates the creation of the model: in the case of a complex scenario, the Petri net is difficult to build. However, we use the Petri net as an operational model.  ...  This approach consists in expressing a scenario by using a fragment of linear logic. This model is then translated into a Petri net model.  ...  A narrative is obtained in writing the proof of a sequent of Linear Logic.  ... 
doi:10.1145/1178477.1178583 dblp:conf/ACMace/ColleCP05 fatcat:f53tbd3bo5gvdcyw4paljekr3i

Page 5791 of Mathematical Reviews Vol. , Issue 91K [page]

1991 Mathematical Reviews  
Logic 48 (1990), no. 3, 277-297. The class of GH games [see Yu. Gurevich and L.  ...  The proof of the latter fact uses the relationship between Turing machine computations and domino- tiling games.  ... 

Page 10271 of Mathematical Reviews Vol. , Issue 2004m [page]

2004 Mathematical Reviews  
, Jerzy (PL-WROC-C; Wroclaw) ; Truderung, Tomasz (PL-WROC-C; Wroctaw) Optimal complexity bounds for positive LTL games.  ...  Summary: “We prove two tight bounds on the complexity of deciding graph games with winning conditions defined by formulas from fragments of LTL.  ... 

Page 3847 of Mathematical Reviews Vol. , Issue 98F [page]

1998 Mathematical Reviews  
Mitchell and Andre Scedrov, The complexity of local proof search in linear logic (extended abstract) (10 pp.  ...  Kanovich], Simulating computations in second order non- commutative linear logic (preliminary report) (11 pp. (electronic)); Francois Lamarche, From proof nets to games (extended abstract) (13 pp.  ... 

Personal mathematics and computing: Tools for the liberal arts

1992 Discrete Applied Mathematics  
A probability logic for statistical and propositional probabilities (Syntax. Semantics. The interpretation of the formulas). Examples of representation. Proof theory (An axiom system.  ...  The formalism (Representing direct inference in the combined probability logic. Proofs of the coherency theorems). Examples. Overly specific reference classes.  ... 
doi:10.1016/0166-218x(92)90237-5 fatcat:46rapx4f5jaytjpg3bq6wpt2ba

Book announcements

2000 Discrete Applied Mathematics  
Landing Fee Game 5.3.4 Trading Game 5.4 Activity Optimization Games 5.5 Examples of Activity Optimization Games 5.5.1 General Welfare Game 5.5.2 Production Game with Common Procurement of Inputs  ...  Problems 1.3.1 System of linear equations 1.3.2 System of nonlinear equations 1.3.3 Linear least-squares problem 1.3.4 System of linear inequalities 1.3.5 Linear programming (LP)  ... 
doi:10.1016/s0166-218x(00)90007-6 fatcat:cemhaoz7rzdmdoec7pjjqiur2a

Page 1596 of Mathematical Reviews Vol. , Issue 93c [page]

1993 Mathematical Reviews  
The calculus uses one logical connective > (implication) and a constant 1 (false). The calculus has deductions of linear length.  ...  On the basis of this calcu- lus we construct other extended calculi that also retain the linear complexity of deduction.” 93c:68093 68T27 03B50 deBessonet, Cary G. % A many-valued approach to deduction  ... 

Page 6286 of Mathematical Reviews Vol. , Issue 2003h [page]

2003 Mathematical Reviews  
We first present a polynomial space decision procedure of optimal worst-case space and time complexity for the fragment under consideration.  ...  In general, we expect many more results in the systematic study of McNaughton games with regard to complexity, logic, and structure.” 68 COMPUTER SCIENCE 2003h:68082 68Q60 03B44 68Q45 68Q85 Kupferman,  ... 
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