A Survey of

Contents

1 The philosophy of CoL
1.2 Why game semantics?
1.3 CoL vs. classical logic
1.4 CoL vs. linear logic
1.5 CoL vs. intuitionistic logic
1.6 CoL vs. independence-friendly logic
1.7 The 'from semantics to syntax' paradigm

2 Games
2.2 Moves, runs and positions
2.3 Constant games
2.4 Not-necessarily-constant games

3 The CoL zoo of game operations
3.2 Prefixation
3.4 Choice operations
3.5 Parallel operations
3.6 Reduction
3.7 Blind operations
3.8 Branching operations
3.9 Sequential operations
3.10 Toggling operations

4 Interactive machines
4.2 Interactive complexity

5 The language of CoL and its semantics
5.2 Interpretations

6 Axiomatizations
6.2 The Gentzen-style system CL7
6.3 The Gentzen-style system Int
6.4 The cirquent calculus system CL15
6.5 The brute force system CL13
6.6 The brute force system CL4
6.7 The brute force system CL12

7 CL arithmetic (CoL-based arithmetic)
7.2 CL arithmetic vs. bounded arithmetic
7.3 Motivations
7.4 Common preliminaries for all our theories of CL arithmetic
7.5 CL arithmetics for polynomial time, polynomial space, elementary and primitive recursive computability
7.6 CL arithmetics for provable computability
7.7 Tunable CL arithmetic

8 CoL-based knowledge base and resource base systems