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FOL Review by Leonard Jacuzzo 20120514
Here are my comments on the FOL rendering of BFO.
#. For ease of locating terms, primitves should be listed in alphabetical order. #. Definitions which utilize a term should not occurr before the term is defined or listed as primitive, e.g., "RelationalQuality(a)" uses 'qualityOf(a,b,t)' before it is mentioned. #. 'projectsOnto' should be 'ProjectOnTo' #. Sometimes it reads "where a and b are occurrents etc. Some times it doesn't this should be uniform. #. Enlgish Translations of the Axioms would be nice. #. 't' is always used for a time, but 'r' needs to be explicitly asserted as an instance of a Region (Some times 'r' is asserted to be a region and sometimes it is not..see next comment.....why is there only one sorted variable? Why is this never explicitly stated? #.In the definition of 'temporalPartOf' 'r' is the subject of the predicate 'TemporalRegion' But 'r1' is not designated as a region...slipping into multi-sorted? Should add predicate for 'r1' This also occurrs in definition 14. #. We should either use a single sorted language or a properly multi-sorted language and not just wing it....The range of variables should be set in advance of the use of them. #. Since the Universe of discourse is the class of Entities...Entity(x) is trivially true and should not occurr in any sentence as, when coupled with a quantifying expression it is redundant. If it is informative then all axioms should have Entity(x) or 'y' or whatever as a conjunct in their antecedent. #. Maybe this is a problem with BFO? but axiom 33 says that if x is a continuant then there is a temporal region and a time and that temporal region exists at that time and x exists at that time too....but don't temporal regions always exist? #. "axiom" 49 (041 -002) is incorrect. It implies that only independent continuants can be located in a region... Also it's source number from BFO document is a primitive relation..
Final Comment: The use of a first-order language here is suboptimal. The
definitions mix Meta linguistic variables with object language variables in
a manner that produces confusion. For example in the 'continuantPartOfAt'
elucidation' 'a' and 'b' are specified at contiuants. That is a use of 'a'
and 'b'. When predicates are defined 'a' and 'b' are metalinguistic
variables. This is evident from the use of '=df' which is a meta-linguistic
operator that is used to define an entire class of sentences/ phrases that
use that particle being defined. Then when, as in axiom 51 the terms are
being used.. there is no mention of the fact that 'x' and 'y' are used to
refer to continuants as in 'Continuant(x)', nor is there any indication
that 'r' refers to a region in axiom 50.
In order to adequately express BFO in a First Order language, and specify
what that expression means.. we need to be much more careful in keeping the
object language and the meta-language distinct. We also need to either
specify a multi-sorted language, and use variables like 'r' for regions
and 't' for times 'p' for process...etc.. or we need to Stay single sorted
and use phrases like 'Continuant(x)' or 'Region(r)'. As it stands there is
no way that this can be understood as an ideographic representation of BFO
in a FOL.