*Fourth Workshop on
Automated Reasoning* *AISB
Workshop Series, April 1997, Manchester, UK *
Michael Fisher
**1. INTRODUCTION**
The 1997 Automated Reasoning Workshop
was the fourth in the now well established series of workshops on Automated Reasoning held
in association with AISB. As in previous years, it was organised mainly as a set of panel
sessions, the aim being to stimulate discussion and to promote a true workshop atmosphere.
In addition we were fortunate to have a number of distinguished invited speakers,
particularly Jeff Paris (Victoria University of Manchester) and Ray Reiter (University of
Toronto).
The workshop was organised by a
committee chaired by Michael Fisher (Manchester Metropolitan University), and financial
support was provided by the AISB, the Manchester Metropolitan University, and the Compulog
network, whose generous sponsorship enabled us to invite Ray Reiter.
**2. INVITED PRESENTATIONS**
The invited speakers provided the
following presentations:
* "Use of Maths in AI" - Jeff Paris
* "Modeling Dynamical Systems in the Situation Calculus: Some Representational
and Computational Issues for Automated Reasoning" - Ray Reiter
The first talk was a plenary
presentation, being shared by all the AISB workshops. Professor Paris described his own
work on modelling belief, in particular his use of a "maximum entropy function"
for producing an agent's beliefs from its knowledge.
In the second talk, introduced and
reviewed by Tony Cohn (Leeds University), Professor Reiter described the use of Situation
Calculus in his "Cognitive Robotics" work. He showed how the Situation Calculus,
suitably extended, can be effective in modelling the actions and effects of robotic
agents, and described how an agent's behaviour can be animated by directly executing the
Situation Calculus formulae, an approach taken in the GOLOG programming language. In
manipulating agent descriptions, a form of automated reasoning is required although the
restricted form considered requires only rewriting using equivalences.
A third invited talk was planned, this
time by Ulrich Furbach on "Theorem Proving and Logic Programming".
Unfortunately, Professor Furbach suffered an accident immediately before the workshop and
was unable to attend. The slot scheduled for this talk was filled by a combination of an
overview of the COMPULOG Area on Automated Deduction Systems http://www.cs.
bham.ac.uk/~mmk/compulog/meeting
presented by Manfred Kerber (Birmingham University), an
additional presentation on "Automated Deduction and Rough Information",
presented by Laurent Vigneron (Nancy), and a report on the work of the Computer Science
Research Strategy Group both in general and with respect to Automated Reasoning http:
//www.dcs.gla.ac.uk/research/uk-cs-research/, presented by Alan Bundy (University of
Edinburgh).
**3. PANEL SESSIONS**
**Panel A:** "Bridging the Gap
between the AI Reasoning and the Automated Deduction Communities"
Chair: Alan Frisch (University of York)
Panelists: Alan Bundy (University of
Edinburgh);
Ian Gent (Strathclyde University);
Hans Juergen Ohlbach (Imperial
College);
Ray Reiter (University of Toronto);
Lincoln Wallen (Oxford University)
Alan Frisch opened the panel by
pointing out that the field of automated reasoning comprises two distinct communities: the
AI reasoning community centred around the International Conference on Principles of
Knowledge Representation and Reasoning (KR) and the automated deduction community centred
around the International Conference on Automated Deduction (CADE). He sensed that the
interests of the present workshop series were narrowing to a point similar to that of CADE
and pleaded for the series to maintain its original goal, as stated in the workshop's call
for papers, of bringing together a diversity of researchers.
Alan Frisch claimed that the AI
reasoning/automated deduction distinction was not merely a social one but also one of
research topic and methodology. His survey of KR and CADE publications showed that a
majority of KR papers are concerned substantially with representation issues, whereas only
a small percentage of CADE papers are. Furthermore, a large number of KR papers address
the question of what behaviour a reasoning system should exhibit, whereas only one CADE'94
paper does.
Alan Bundy continued this theme by
discussing the role of knowledge representation in automated reasoning. He claimed that in
automated mathematics the representation is given and the logic is standard, whereas in
formal methods the logics vary and, in automated commonsense reasoning, representation is
a research issue. However, in automated mathematics serious representation issues emerge
at the meta-level in representing and reasoning about proof search.
Lincoln Wallen argued that commonsense
reasoning as well as non-deductive reasoning was needed for automated theorem proving. He
also argued that the field of knowledge representation has reached the point where it
needs to evaluate its formalisms with respect to their contribution to systemic behaviour.
Formalisms used by reasoning systems, as distinct from those used for analysis, need to be
simple.
Ray Reiter further elaborated the claim
that commonsense reasoning must be simple and "shallow". His experience has led
him to conclude that the analysis of complex non-monotonic formalisms can result in simple
"closed forms," the most common of which is a database with a set of
definitions.
Hans Juergen Ohlbach discussed his
experience in building an automated reasoning service for a natural language processing
system. This system was also structured as a database with a hierarchy of definitions.
Although the system had implemented modal logics of knowledge and belief, it turned out
that the logical properties of these operators frequently addressed in the literature
where not needed at all. What was actually needed to build an agent's belief set was
essentially heuristical and outside the scope of such logics.
Ian Gent urged for increased
communication between the two communities. He used his research area, propositional
satisfiability, to illustrate the harmful effect of insufficient communication.
These presentations were followed by a
wide-ranging open discussion whose dominant topic was the role of representation in
mathematical reasoning. It was noted that the successful use of automated theorem provers
in solving open mathematical problems has been predominantly --- perhaps exclusively ---
in areas, such as group theory, where problems are essentially formal. But even here,
success has often required human expertise to properly configure the automated system.
Hence, OTTER, a system that accommodates substantial configuration has been among the most
successful. It was observed that formulating a problem is a crucial task that requires a
great deal of skill. The mapping of Euclidean geometry to analytic geometry is an example
of a case where a well-suited problem formulation has led to great progress in automation.
The formalisation of inference rules for partial functions was given as an example of an
area where progress was still needed. There appeared to be wide agreement that the
representation problem for mathematics was far from solved.
**Panel B:** "The Future of
Automated Reasoning Research"
Chair: Alan Bundy (University of
Edinburgh)
Panelists: & Rob Arthan (Lemma 1);
Dominic Semple (EPSRC);
Lincoln Wallen (Oxford University)
Lincoln Wallen emphasised the growing
importance of computer science practitioners being skilled professionals. Rob Arthan
discussed the role of automated reasoning systems in formal development of high-assurance
systems. Although there has been a lot of progress in the last decade or so, there is
still a great deal of work left to do before the potential of mechanized proof is realised
in practice. Much of what is needed is consolidation -- not so much building bridges as
filling in the ravines that the pioneers have already bridged. Dominic discussed the new
structure of EPSRC and the continued support within it for basic and theoretical research.
However, grant applicants must ensure they address the needs of the "users" of
their research. These users could be fellow academics. Automated reasoning research is
well supported by EPSRC. There are no figures for AR per se, but Theoretical Computer
Science takes about 30% of Dominic's budget and AI about 25%.
**Panel C:** "Can Formal
Methods Flourish without Automated Reasoning?"
Chair: Ursula Martin (University of St.
Andrews)
Panelists: Rob Arthan (Lemma 1);
Helen Lowe (Napier University);
Harrie de Swaart (Tilburg University);
Konrad Slind (Cambridge University).
A range of issues was discussed. A
related question was whether formal methods can flourish: it had been oversold in the
past, but was now emerging as a key component of specialised areas such as safety critical
systems and hardware designs, with Z emerging as the industry standard.
Arguments for the proposition included
the increasing interest in "light formal methods": using formal specification
without formal proof support as a means of clarifying system requirements and design at an
early stage, and the difficulty of using many automated tools which meant that many of the
most impressive work was obtained by highly skilled users using interactive systems.
Arguments against the proposition
included the importance of mechanically verified formal proof or what was the point of
formal methods at all, particularly for the verification of complicated designs where it
was impossible to rely on hand or informal proof, and the importance of increasing the
automation of such proofs so that tools could be used with confidence by non-expert users.
**Panel D:** "How 'Intelligent'
should Reasoning Systems be?"
Chair: Michael Fisher (Manchester
Metropolitan University)
Panelists: Andrew Adams (University of
St. Andrews);
Andrew Ireland (Heriot-Watt
University);
Manfred Kerber (Birmingham University);
Judith Underwood (Glasgow University)
Given that ("fast but dumb")
systems such as Otter have had such notable successes, for example results in Algebra, how
'intelligent' should we attempt to make our automated reasoning systems?
Most of the panelists felt that
considerable 'intelligence' was required within theorem-provers. In particular Andrew
Ireland listed areas in which he saw proof planning as being essential, for example
problems characterising huge search spaces, and where there was a need for user
interaction. Judith Underwood argued that there were two different application areas for
Automated Reasoning techniques, one where fast theorem-provers such as Otter were
required, the other where a deeper understanding of the problem space is required. Manfred
Kerber argued that, for our provers to be effective, then we would have to solve, at least
partially the general AI problem. He suggested a study of Polya's work in order to
characterise what kind of intelligence needed to be added to theorem provers.
In the discussion session following the
presentations, Alan Bundy defended the proof planning view. In addition, he claimed that
the Otter proof of the Robbins conjecture had required a large amount of human
pre-processing as well as a significant element of trial and error (i.e. tinkering with
parameters until proof ran quickly).
Michael Fisher agreed, but suggested
that Otter's success pointed to the importance of a fast underlying prover, together with
an appropriate representation of the problem, rather than any degree of planning within
the prover itself. He agreed with Manfred Kerber's view that in trying to prove very
complex theorems, we are essentially attacking the AI problem, and drew a parallel between
this debate and the cognitive/behavioural conflict in Robotics.
**4. FUTURE**
The fifth workshop in this series will
be held at the University of St. Andrews at the end of March 1998. The workshop will be
chaired by Ursula Martin, and will be co-located with, and immediately prior, to the
Fourteenth British Colloquium for Theoretical Computer Science. The two events will share
several sessions and combined registration.
**5. WWW Page**
Details of all these workshops can be
found at
http://www.cs.york.ac.uk/~frisch/AutoReason
Michael Fisher
Manchester Metropolitan University
Manchester, U.K. |