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MPI-INF/SWS Research Reports 1991-2017

2. Number - only D2

MPI-I-92-242

Temporal logic: Mathematical foundations, part 2

Gabbay, Dov M. and Hodkinson, Ian M. and Reynolds, Mark A.

September 1992, 30 pages.

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The book ``Temporal Logic: Mathematical Foundations and Computational Aspects" which is an attempt to provide a comprehensive coverage of temporal logic as a topic which generates problems of general mathematical interest, which has many practical applications to computer science and linguistics and which is a source of various complex problems of computation and implementation. The report is the continuation of MPI Report MPI-I-92-213 which contains draft versions of chapters 1-6. Chapter 14 on temporalisation and 15 on decidability as well as perhaps volume two will appear in future reports. In Chapter 7, by looking at some specific examples of axiomatisation and expressive completeness of two and three dimensional logics, we illustrate some of the technical issues involved with many-dimensional logics. Chapter 8 introduces the idea of propositional quantifiers in temporal logic and examines the properties of a very useful fixed point language. In chapter 9 we show how the property of separation is related to expressive completeness so that in chapter 10 we can infer the expressive completeness of languages with until and since over various classes of flows of time. In chapter 11 we use separation to prove the expressive completeness of the Stavi connectives over the class of linear flows. Chapter 12 contains a direct proof of the same result and also considers languages appropriate to flows with ``gaps" in them. Chapter 13 is a very comprehensive account of the concepts of H-dimension and the $k$-variable property which are both concerned with the number of bound variables needed by the monadic language to be fully expressive but have surprising connections with expressive completeness of temporal languages. Since the publication of the book (Gabbay, D. M.; Hodkinson, L.; Reynolds, M.:"Temporal logic : mathematical foundations and computational aspects", Oxford : Clarendon 1994), this work is no longer available as report.
Note:
Since the publication of the book (Gabbay, D. M.; Hodkinson, L.; Reynolds, M.:"Temporal logic : mathematical foundations and computational aspects", Oxford : Clarendon 1994), this work is no longer available as report.
References to related material:

An Oxford University Press Book is available: Dov M. Gabbay, Mark Reynolds, Ian Hodkinson: Temporal Logic