Is ability a situational possibility?

While trying to establish a logical typology of modal meanings, I came across the problem of categorizing ability under situational possibility. Many authors group ability under dynamic modality, as it does not involve (or, at least, not more than tangentially) moral obligations, desirability or interdiction.

Dryer et al. (2011), however, state that “Both permission and ability have to do with a notion of possibility” (DRYER, 2011: Chapter 74). I’ll try to defend their point of view with some modal logic below.

(1) I can drive you to work.

Sentence (1) clearly denotes both ability and possibility, and may be understood as follows:

∃x （I (x) ∧ ♢Drive (x) ∧ ♢Drive (x,you) ⟷ ♢Drive (x) )

∃x (I (x) ⋀ ¬♢Drive (x) ➞ ¬♢Drive (x,you) )

The first possibility is the ability itself; the second, the actual possibility to drive you; the result is that the ability is a pre-requisite for the possibility to drive you.

This seems clear enough, the real problem is when there’s no apparent situational possibility, as in

(2) I can speak English.

However, this sentence can be understood as follows:

∃x (I (x) ∧ ♢Speak (x) ∧ ♢Speak (x,english) ➞ ♢Speak (x,english) ↔ ♢Speak (x,english) )

∃x ( I (x) ⋀ ¬♢Speak (x) ➞ ¬♢Speak (x,english) )

∃x ( I (x) ⋀ ¬♢Speak (x,english) ➞ ¬♢Speak (x,english) )

The possibility itself can be understood to be linked to the inherent ability which may or may not be utilized by the agent. In other words, if the possibility exists that I speak German with anyone, then the possibility exists that I speak German to someone because I am able to speak German. Following this interpretation, I can state that every dynamic modality that expresses ability also expresses a situational possibility, given the time and chance.

Therefore, I can conclude that dynamic modality expressing ability may also be grouped under situational possibility, together with

1. Possibility: You can take bus number 25 to the main station.
2. Permission: You may leave now. and
3. Request: May I leave now?

Reference: 

DRYER, Matthew S. & HASPELMATH, Martin (eds.), (2011) The World Atlas of Language Structures Online. Munich: Max Planck Digital Library. Available at http://wals.info/

Acessed on July 6th, 2013