# 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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##### Status: distribution forbidden

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