Possibilities of Cause-and-Effect Simulation in the Study of System Climate-Ocean-Sediments
213
In the case of blanks, the whole of Table 4 is expressed by four sets: 1,4,7; 1,
3,8; 1,2,3,5,6,7; 1,2,3,4,7, including the index numbers of blanks from the
four last lines of the table correspondingly.
3
Theoretical Principal of Cause-and-Effect Simulation
Apparently, different properties of sediments may have different relations to
oceanic and climatic phenomena. In particular, some properties may arise under the influence of only climatic or only oceanic factors, and the others may be
connected with both climatic and oceanic ones. In the latter case, climatic and
oceanic factors either have or have no cause-and-effect dependencies between
them. Additionally, any climatic and oceanic phenomenon may be expressed either by separate independent attributes or by a complex of interrelated attributes. In addition, types of CE dependencies can vary. Thus, one can formulate diverse hypotheses about CE relations in the system climate-ocean-sediments, each of them including propositions of three following groups: I. Connections between sediments and groups of oceanic and climatic phenomena; II.
Connections of climatic and oceanic phenomena between them; III. Relation of
mapped or observed attributes to a relevant phenomenon.
Besides the natural language, these propositions are expressed by formulas
of mathematical logic. Taking one formula from each group, one can compose a
formula set expressing a certain hypothesis on CE relations in the system climate-ocean-sediments ( Tables 5-7).Depending on the propositions of groups I
and II, these hypotheses have been divided into five main types A, B, C, D, E. Using, in addition, the different variants of proposition II (variants ILl - II.3 for
hypotheses B and C) and proposition III (variants III.l - IlIA for hypotheses A,
B, C and two of them for hypotheses D, E), it is possible to construct versions of
hypothesis A, 12 versions each of hypotheses Band C, and 2 versions each of hypotheses D and E.
Hypotheses described by Tables 5-7 include implicitly the assumption that
all oceanic (climatic) phenomena are connected with climatic (oceanic) phenomena and sediments by the same type of CE relations. However, it is clear that
more complicated cases are also possible (Fig. 1). In particular, in the case of the
hypotheses AB and C* two sets of climatic phenomena (Climate l , Climat 2 ) have
relations different from oceanic phenomena and sediments. In the case of the
hypotheses AC and B*, the same is true for two sets of oceanic phenomena
(Ocean!, Ocean 2 ). Complicated hypotheses usually represent combinations of
the main hypotheses expressed by Tables 5-7 (e.g., AB, AC) or are, in fact, some
of their modifications (f.i., B*, C*).
Any formula set describing some version of the hypotheses A, B, C, D, E can
be transformed into a Boolean algebraic equation, which is properly a mathematical model of CE relations for the given hypothesis. By means of this equation, a type of logical dependency between attributes (more exactly, between the
variable predicates corresponding to attributes) is described. The equation
213
In the case of blanks, the whole of Table 4 is expressed by four sets: 1,4,7; 1,
3,8; 1,2,3,5,6,7; 1,2,3,4,7, including the index numbers of blanks from the
four last lines of the table correspondingly.
3
Theoretical Principal of Cause-and-Effect Simulation
Apparently, different properties of sediments may have different relations to
oceanic and climatic phenomena. In particular, some properties may arise under the influence of only climatic or only oceanic factors, and the others may be
connected with both climatic and oceanic ones. In the latter case, climatic and
oceanic factors either have or have no cause-and-effect dependencies between
them. Additionally, any climatic and oceanic phenomenon may be expressed either by separate independent attributes or by a complex of interrelated attributes. In addition, types of CE dependencies can vary. Thus, one can formulate diverse hypotheses about CE relations in the system climate-ocean-sediments, each of them including propositions of three following groups: I. Connections between sediments and groups of oceanic and climatic phenomena; II.
Connections of climatic and oceanic phenomena between them; III. Relation of
mapped or observed attributes to a relevant phenomenon.
Besides the natural language, these propositions are expressed by formulas
of mathematical logic. Taking one formula from each group, one can compose a
formula set expressing a certain hypothesis on CE relations in the system climate-ocean-sediments ( Tables 5-7).Depending on the propositions of groups I
and II, these hypotheses have been divided into five main types A, B, C, D, E. Using, in addition, the different variants of proposition II (variants ILl - II.3 for
hypotheses B and C) and proposition III (variants III.l - IlIA for hypotheses A,
B, C and two of them for hypotheses D, E), it is possible to construct versions of
hypothesis A, 12 versions each of hypotheses Band C, and 2 versions each of hypotheses D and E.
Hypotheses described by Tables 5-7 include implicitly the assumption that
all oceanic (climatic) phenomena are connected with climatic (oceanic) phenomena and sediments by the same type of CE relations. However, it is clear that
more complicated cases are also possible (Fig. 1). In particular, in the case of the
hypotheses AB and C* two sets of climatic phenomena (Climate l , Climat 2 ) have
relations different from oceanic phenomena and sediments. In the case of the
hypotheses AC and B*, the same is true for two sets of oceanic phenomena
(Ocean!, Ocean 2 ). Complicated hypotheses usually represent combinations of
the main hypotheses expressed by Tables 5-7 (e.g., AB, AC) or are, in fact, some
of their modifications (f.i., B*, C*).
Any formula set describing some version of the hypotheses A, B, C, D, E can
be transformed into a Boolean algebraic equation, which is properly a mathematical model of CE relations for the given hypothesis. By means of this equation, a type of logical dependency between attributes (more exactly, between the
variable predicates corresponding to attributes) is described. The equation