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**MPI-I-92-242**. September** **1992, 30 pages. | Status:** **distribution forbidden | Next --> Entry | Previous <-- Entry

Abstract in LaTeX format:

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.

Acknowledgement:** **

References to related material:

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