Richard Zach

Deadly Ambiguity

Several of the commenters on my previous post on motivating the study of logic in my intro class have suggested that one important aspect of logic is the precision it affords, and hence the usefulness of logic in avoiding ambiguities. So I tried to find some nice examples of where ambiguity in natural language—and the resulting different interpretations—can have important consequences. (I’m still looking for examples, especially form philosophy!) I happened upon a paper entitled “Syntactic Ambiguity” by Paul Conway, which gives some very nice actual examples from law. I picked one of the examples that can be dealt with in propositional logic (no quantifiers used yet).

a is a cube in front of b, or a tetrahedron in front of b, or to the left of b.

That’s ambiguous between*

(Cube(a) ∧ FrontOf(a, b)) ∨
(Tet(a) ∧ (FrontOf(a, b) ∨ LeftOf(a, b))

and

(Cube(a) ∧ (FrontOf(a, b) ∨ LeftOf(a, b))) ∨
(Tet(a) ∧ (FrontOf(a, b) ∨ LeftOf(a, b))

Here’s the real-life example from the above paper:

In R v. Casement, Sir Roger Casement was charged with high treason contrary to Treason Act, 1351 (Eng.). It was alleged that during World War I he incited British subjects who were prisoners of war in Germany to renounce their allegiance to the King. The statute declared that treason was committed ‘… if a man do levy war against our Lord the King in his realm, or be adherent to the King’s enemies in his realm, giving to them aid and comfort in the realm, or elsewhere, and thereof be properly attainted of open deed by the people of their condition: …’. The charge alleged adhering to the King’s enemies elsewhere than in the King’s realm, namely in the empire of Germany. The defence unsuccessfully submitted that the Crown had failed to prove an offence in law. ‘The contention is that those words “or elsewhere” govern only the words “aid and comfort in the realm” and have no application to the words “be adherent to the King’s enemies in his realm.’

I believe that part of the reason that the trial and conviction caused such an outcry, aside from the fact that Casement was famous as a humanitarian exposing human rights abuses in the Congo and Peru, was that it wasn’t clear if the original document of the Treason Act contained the last comma or not.

* A third reading would be

(Cube(a) ∧ FrontOf(a, b)) ∨ (Tet(a) ∧ FrontOf(a, b)) ∨ LeftOf(a, b)

but that isn’t a possible reading of the clause in the Treason Act.

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2 responses to “Deadly Ambiguity”

  1. Helmut

    Buf if you insist on precision as a virtue of logic, your course has to be just that – precise. I always found this to be the most annoying part – so much to tell, and you got these chains on your feet.

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  2. keet

    For the CS students, a good motivation appeared to be the link between first order logic and the (sometimes informal) graphical conceptual data modelling languages they have to learn for software and database development anyway (UML, ER, ORM, etc): the experts in those conceptual modelling languages tend to be finicky when it comes to the shapes of the entity type, the relationship, how the constraints are represented etc.. The first order logic gives a nice and unambiguous formalisation of those languages: learn one formal language and use the graphics of the conceptual modelling languages as “syntactic sugar”–the sugar can change but the core they will learn serves them for a longer period—and the graphics can be used as a ‘bridge’ to communicate with non-logicians who have to provide input for development of conceptual data models and ontologies whereas the CS-person will have the precise specification to develop a good information system.Regarding the ambiguity, then: if you have to conceptual data model without the formal foundation, conceptual modellers and domain experts (or domain experts with slightly different backgrounds) easily misunderstand each other and the system won’t do what was expected, which requires a lot of costly and time-consuming re-engineering. For instance, a relationship “located in” without proper typing of the relata doesn’t tell you if it is about one region located in another region (i.e., a kind of part-whole relation), or an object located in a region, which easily can mess up, say, a Geographic Information System.From philosophy, and mereology and meronomy in particular, there are many examples on ‘problematic’ things that can be solved with being more precise. E.g., the classic example of the musician’s hand that is part of the musician, the musician part of the orchestra, but the musician’s hand is not part of the orchestra, as if part-of is not transitive; but, in fact, the musician is not part-of the orchestra, but member-of, where member-of is a meronymic relation but not a mereological part-of. There are many more ‘sloppy’ natural language examples regarding part-whole relations that can be disambiguated with a mix of logic and ontology (see, e.g., here).

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