Silicon Dale

Geological Reasoning.

This month I am turning over the column to Dr Cyril Pshenichny of the University of St.Petersburg, Russia, to introduce something completely different. There will be a workshop on 'geological reasoning' at IAMG2003 (the International Association of Mathematical Geology annual meeting, to be held in Portsmouth, England from 7 to 12 Sept, 2003). There will be an emphasis at IAMG2003 on geohazards of all types, including both natural hazards (e.g. volcanic) and artificial (e.g. hazards associated with mining or construction).

"Geological reasoning" includes mathematical and computer-aided methods but is by no means restricted to these fields. It includes formal methods from logic (including fuzzy logic and other non-classical variants) as well as from linguistics and philosophy.

Investigation of Geologic Reasoning as a New Objective of Geoscience and Geohazard Assessment

by Cyril A. Pshenichny - Petrography Dept., Faculty of Geology, St. Petersburg State University, Universitetskaya Naberezhnaya 7/9, 199034 St. Petersburg, Russia.

Conventional understanding of the evolution of a natural science is (i) accumulation of data, (ii) their summarization and, as a result, (iii) the development of conceptual models which are used then to interpret new data. However, is this the end of the story ?

Concepts accumulate, swarm, merge or repeat one another, or come to contradict each other, at times explicitly but often such contradictions are hidden by natural language, and thus eventually form a space one can hardly navigate. This is exactly the case in modern geology. Similar objects or data sets meet a number of diverse interpretations, and even a specialist in a narrow field can hardly encompass the ideas put forth in this very field. The choice of concepts becomes purely a matter of the scientist's intuition, taste or competence.

While possibly not that acute in academic research, this problem becomes urgent in hazard assessment, when non-professionals expect substantiated and bias-free solutions from scientists. Physical modeling or statistical methods claimed to be strict solutions of geologic problems cannot be taken as a remedy, because both are related to geologic objects by some simplifications of the latter, which, in turn, are determined by the researcher's intuition, taste or competence. Thus the problem becomes obscured, but not solved.

In general, it can be formulated as conceptual uncertainty. It accompanies other known types of uncertainty discussed, for example, in risk analysis - time, structural, metric, and translation uncertainties (Rowe, 1988) but, contrary to these, cannot be solved by the known methods of uncertainty elimination: Monte Carlo method, Bayesian approach, fuzzy arithmetic and others (Vaganov and Im, 2001).

To cope with conceptual uncertainty, knowledge processing methods are required. Obviously, they should be formal to the knowledge processed, i.e. should deal only with the form and not with the contents of statements. Meanwhile, the technologies of knowledge processing (e.g., expert systems, knowledge bases) applied so far in geoscience focus not on the relations between the statements, but on the relations between the objects these statements describe. Hence, these technologies in their modern state are not really formal and need to be accompanied by other, purely formal ways to investigate reasoning in natural sciences. Which are these ways?

First of all, there is classical logic. "Classical" means that it operates with two truth values only, TRUE and FALSE. It can unequivocally judge whether a statement can be inferred from a set of others solely by the form of the statements. Though developed since the time of Leibnitz, classical logic has had very limited application in descriptive science in general and in geology in particular. To the author's knowledge, few attempts have been made, by Sirotinskaya (1986), Pshenichny and Moukhachov (2001) and Pshenichny et al. (in press).

Next, there are some non-classical logical approaches which can be discussed. These originate from classical logic, but treat truth values more liberally, allowing transitional values between TRUE and FALSE. One such approach is fuzzy logic applied in geology by Cagnoli (1998), Klir (2002) and some other researchers.

Logic is an universal method of knowledge structuring, but is it unique ?

Possibly, some fields of geology can be fairly well translated into the language of mathematics - actually, this was the argument made by Vistelius (1992) and the idea behind the development of mathematical geology. However, herewith the question arises: what is the relationship between logic and mathematics? A violent discussion on what is primary, logic or mathematics, lasted throughout the 1940s and 1950s between the followers of logician David Hilbert and mathematician Luitzen Egbertus Jan Brouwer and has not reached final agreement. It seems plausible that both are complementary rather than competing and form a continuum of methods formal to any other human knowledge. Exactly this conclusion was reached four decades later by Lotfi Zadeh (1995) as a conclusion from the polemics of statisticians and fuzzy logicians. However, the "border" between logic and mathematics in any given domain of knowledge (e.g., geoscience) is an open question. What is better described by logic and what by mathematics? Anyway, while the party of "mathematicians" is rather numerous in geology, that of "logicians", as was stated above, is almost absent.

Still, logic and mathematics possibly do not exhaust the continuum of formal approaches. As another 'end-member', in the author's view, linguistics (or, generally speaking, philology) may appear. Isn't it a common feeling of field geologists that the nature is "speaking" with us in every outcrop, sample, or thin section? Aren't these just "texts", in which certain bodies (grains, inclusions, groundmass, etc.) are "words" and the structure/texture is the "grammar"? Isn't it possible, then, to view geology as a natural language? Robert Frodeman has introduced the terms "geo-poetry" and even "ecotheology" (relating them along with "geo-politics" and "geoscience" to a general field defined as "geo-logic", or "geology") in his recent lecture at the Colorado School of Mines (

Furthermore, describing the behavior of various objects, especially hazardous ones, aren't we recognizing the types of their "temper", or "spirit"? If so, the experience of psychology may appear appropriate, and this discipline could appear formal to geological knowledge.

Simultaneously, philology and psychology may have another application to reasoning research in geoscience. Every scientist possesses his/her national (cultural), gender and other backgrounds. It is unlikely that all of these do not influence the pathways the researcher's mind follows in investigation and the solutions he or she finds. The invention of computer in the West and rapid development of fuzzy logic in the East may be examples of that. The research of gender dimension in ecologic studies has already been carried out by Claudia Empacher and co-workers at ISOE (Institute for Social-Ecological Research, Frankfurt-am-Main,

And what do you think? What is your standpoint/your feeling about reasoning in geoscience? What formal pathways, in your view and experience, work best in geology? Maybe you have your own approaches, or an intuition that rarely betrays you? Have you tried to describe it? To explain it to someone else? To teach someone else?

This is exactly what we are going to think about all together through the new mailing list on GEOLOGICAL REASONING to be launched in early June 2002. To join the list, just send an email to the author of this article ( Try to state your point as formally (i.e., make it as independent of certain circumstances, which led to it) as possible - and do not be afraid that your ideas may be far from complete, or indeed 'half-baked'. Any contribution is appreciated, be you a modeler, a theoretician, or a field geologist never concerned with any formal methods, or a student ready to give us your first understanding of the science. We are at the very beginning, and the idea for now is not to exhibit our results to each other (it is too early to speak about them), but to share common problems and hesitations. This will be our joint (and hopefully, delightful) intellectual adventure aiming to outline the fundamentals, main directions and approaches of reasoning research in geoscience in general and geohazard research in particular. Three basic questions are, (i) what the continuum of formal approaches consists of, (ii) what are the relations between its parts and (iii) what geologic/geohazard tasks each of them fits best?

In a year, our talks and ideas will be summarized at the workshop directly following the IAMG conference "Modeling Geohazards" on September 14, 2003, in Portsmouth, UK. Even if you have not participated in the electronic discussion - nothing prevents you from joining us there!

Cagnoli, B., 1998, Fuzzy logic in volcanology: Episodes, Vol. 21, No. 2, pp 94-96.
Klir, G., 2002, Fuzzy Logic In Geology: Academic Press, 380 p.
Pshenichny, C.A., Moukhachov, V.P., and Khrabrykh, Z.V., Logical Assessment of Observational Knowledge in Volcanology: in press in Journal of Volcanology and Geothermal Research
Pshenichny, C.A., and Moukhachov, V.P., 2001, Volcano-Logic: reasoning research in volcanology: IAVCEI News, No. 1, p. 2.
Rowe, W.D., 1988, An Anatomy of Risk: Malabar, 416 p.
Sirotinskaya, S.V., 1986, Logical Methods of Analysis of Geologic Information: Nedra Publishers; 158 p. (in Russian).
Vaganov, P.A., and Im, M.-S., 2001, Ecological Risks (Second Edition): St. Petersburg University Publishers, 152 p (in Russian).
Vistelius, A.B., 1992, Principles of mathematical geology: Kluwer Academic Publishers, Dordrecht-Boston-London, 477 p.
Zadeh, L., 1995 Probability Theory and Fuzzy Logic are Complementary rather than Competitive: Technometrics, vol. 37, pp 271-276.

Further information on IAMG2003 can be found on or by emailing A geo-reasoning discussion group was set up in February 2003. It can be found at

Stephen Henley
Matlock, England

Copyright © 2002 Stephen Henley
Geological reasoning: Earth Science Computer Applications, v.17,no.11,p.1-3