The Logic of Distributed Protocols

A propositional logic of distributed protocols is introduced which includes both the logic of knowledge and temporal logic. Phenomena in distributed computing systems such as asynchronous time, incomplete knowledge by the computing agents in the system, and game-like behavior among the computing agents are all modeled in the logic. Two versions of the logic, the linear logic of protocols (LLP) and the tree logic of protocols (TLP) are investigated. The main result is that the set of valid formulas in LLP is undecidable.

[1]  Leslie Lamport,et al.  Reaching Agreement in the Presence of Faults , 1980, JACM.

[2]  Daniel Lehmann,et al.  Knowledge, common knowledge and related puzzles (Extended Summary) , 1984, PODC '84.

[3]  P. Naur.  Proof of algorithms by general snapshots , 1966 .

[4]  C. A. R. HOARE,et al.  An axiomatic basis for computer programming , 1969, CACM.

[5]  R. M. Wenley.  Foundations of Knowledge , 1901 .

[6]  Ronald Fagin,et al.  A Model-Theoretic Analysis of Knowledge: Preliminary Report , 1984, FOCS.

[7]  Mordechai Ben-Ari,et al.  The temporal logic of branching time , 1981, POPL '81.

[8]  John H. Reif,et al.  The Complexity of Two-Player Games of Incomplete Information , 1984, J. Comput. Syst. Sci..

[9]  Joseph Y. Halpern,et al.  Decision procedures and expressiveness in the temporal logic of branching time , 1982, STOC '82.

[10]  Richard E. Ladner,et al.  Propositional Dynamic Logic of Regular Programs , 1979, J. Comput. Syst. Sci..

[11]  Vaughan R. Pratt,et al.  A Near-Optimal Method for Reasoning about Action , 1980, J. Comput. Syst. Sci..

[12]  A. Prasad Sistla,et al.  Deciding branching time logic , 1984, STOC '84.

[13]  John H. Reif,et al.  Multiple-person alternation , 1979, 20th Annual Symposium on Foundations of Computer Science (sfcs 1979).

[14]  Danny Dolev,et al.  Cheating husbands and other stories (preliminary version): a case study of knowledge, action, and communication , 1985, PODC '85.

[15]  Ronald Fagin,et al.  A formal model of knowledge, action, and communication in distributed systems: preliminary report , 1985, PODC '85.

[16]  John H. Reif,et al.  A dynamic logic of multiprocessing with incomplete information , 1980, POPL '80.

[17]  Ramaswamy Ramanujam,et al.  Distributed Processes and the Logic of Knowledge , 1985, Logic of Programs.

[18]  Richard E. Ladner,et al.  The Complexity of Problems in Systems of Communicating Sequential Processes , 1980, J. Comput. Syst. Sci..

[19]  Robert W. Floyd,et al.  Assigning meaning to programs , 1967 .

[20]  John H. Reif,et al.  Universal games of incomplete information , 1979, STOC.

[21]  Nancy A. Lynch,et al.  Proceedings of the tenth annual ACM symposium on Theory of computing , 1978 .

[22]  Joseph Y. Halpern,et al.  Knowledge and common knowledge in a distributed environment , 1984, JACM.

[23]  Neil Immerman,et al.  Foundations of Knowledge for Distributed Systems , 1986, TARK.

[24]  Fred Kröger,et al.  Temporal Logic of Programs , 1987, EATCS Monographs on Theoretical Computer Science.

[25]  Vaughan R. Pratt,et al.  SEMANTICAL CONSIDERATIONS ON FLOYD-HOARE LOGIC , 1976, FOCS 1976.

[26]  A. Prasad Sistla,et al.  The complexity of propositional linear temporal logics , 1982, STOC '82.