Certain words in natural language are more amenable to logical formalization. The conjunction "and" or weak conditional "unless" are easily applied to break statements into their constituent atomic parts.
Other parts of language are less clear. For instance, it's hard to say what the logical status of the adjective "rambunctious" is. It clearly has internal, logical limits to its application. (a "rambunctious apple" is logically incoherent), but what those limits are may be subsceptible to too many vague edge cases to be assessed or applied the same way in which logical connectives are (a "rambunctious house").
I feel it may be possible to treat adpositions in a more formal manner, however. Although their internal limits of logical applicability may be more context-dependent than other connectives, or quantifiers, or modal operators, they don't necessarily suffer the same vagueness in applicability that adjectives or other parts of speech seem to.
Can anyone knock down this claim P and disabuse me of this idea? Or, alternatively, point me in the direction of any assessments or formalizations that have been done specifically with regards to classifying adpositional connectives?
I'm not after the formal linguistic treatment of adpositions and their use. I'm interested instead in qualifying the logical relationships these connectives exemplify, when they're extended to use in expressing concepts. For instance, that a member is "in" a set expresses a logical negation of "out" of that set (or vice-versa).