Towards a Consistent Logical Framework for Ontological Analysis
https://www.cs.rochester.edu/~schubert/projects/papers/fois01.pdf
Abstract
In their framework for ontological analysis, Guarino and Welty provide a number of insights that are useful for guiding the design of taxonomic hierarchies. However, the formal statements of these insights as logical schemata are flawed in a number of ways, including inconsistent notation that makes the intended semantics of the logic unclear, false claims of logical consequence, and definitions that provably result in the triviality of some of their property features. This paper makes a negative contribution, by demonstrating these flaws in a rigorous way, but also makes a positive contribution wherever possible, by identifying the underlying intuitions that the faulty definitions were intended to capture, and attempting to formalize those intuitions in a more accurate way.
Conclusions
(1) Guarino and Welty’s notation and associated descriptions indicate a confusion between between modal logic on the one hand, and temporal logic with explicit tem- poral arguments on the other, with the result that their formulae are uninterpretable by any standard semantics. The way to alleviate this confusion with the least disturbance to their framework would seem to be to replace all modal operators with explicit quan- tification over times, and to state explicitly that terms like “necessary,” “rigid,” and “essential” are related to persistence over time, rather than across worlds. (2) The claim that an anti-rigid property can’t subsume a rigid one is false. Incorrect intuitions about this issue probably indicate a confusion between subsumption and necessary subsumption, since it is true that an anti-rigid property can’t subsume a rigid one necessarily. (3) The meta-properties +/-I and +/-/∼U, indicating whether or not a property car- ries identity or unity conditions, turn out to be useless for constraining taxonomic relationships, as they are defined by Guarino and Welty. However, the property of carrying a particular identity or unity condition does place useful constraints on taxo- nomic relations between properties
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