======================================================================== Argument Analysis: Finding Missing Premises. ======================================================================== One of the trickiest parts of argument analysis can be identifying missing premises. Often, this is tricky because the missing premise seems so "obvious" that you're not even aware that it's missing. But, equally often, it's the missing premise that can make or break an argument. Here's an example from the "Textual Entailment Challenge", a competition for researchers interested in knowledge representation and in information extraction. For more information on TE in general, and the Challenge in particular, link to: http://pascallin.ecs.soton.ac.uk/Challenges/RTE3/ In a typical challenge, a system is given one or two premises and a conclusion (to use our terminology) and asked to determine whether the conclusion follows from the premise. And "follows" is taken fairly liberally to include all kinds of non-deductive inference. So here's an example: Premise 1 (P): Bountiful arrived after war's end, sailing into San Francisco Bay 21 August 1945. Premise 2: Bountiful was then assigned as hospital ship at Yokosuka, Japan, departing San Francisco 1 November 1945. Conclusion (C): Bountiful reached San Francisco in August 1945. The idea is that the 2 premises might be sentences from a news article, and the conclusion is something that a typical reader of the article might be expected to understand from reading it. I think we can all agree that this conclusion does, indeed, follow from these premises. In fact, it follows from Premise 1 alone. Premise 2 is a "distractor", in this case. But what rule of inference allows us to infer C from P? * P talks of "arrival" and "sailing into", but C talks only of "reaching" * P talks of "San Franciso Bay", but C talks only of "San Francisco" There are no logical rules that connect these concepts. Most people, I suspect, would think that no such rules would be needed; after all, isn't it "obvious" that, if you arrive somewhere, then you have reached it? And isn't it "obvious" that SF Bay must be in SF? Well, maybe. But, whereas people might know these things, computers won't unless we tell them. In other words, computers need some lexical knowledge and some simple geographical knowledge. (If you don't like the word "knowledge" here, you can substitute "information".) So, we need to supply some extra premises that link P with C more closely. These are the "missing premises". And the argument from P to C is called an "enthymeme" (because the missing premises are "in" (Greek "en-") the arguer's "mind" (Greek "thymos")). So, we might elaborate the argument as follows (there are other ways to do it; this is one that comes to my mind): P: Bountiful arrived after war's end, sailing into San Francisco Bay 21 August 1945. Pa: If something sails into a place, then it arrives at that place. .'. C1: B arrived at SFB 21 August 1945. In this first step, I've added a missing premise, Pa, and derived an intermediate conclusion C1. Hopefully, you agree that C1 follows validly (or at least logically in some way) from P and Pa. We have no way of knowing whether P is true, and must, for the sake of the argument, simply assume that it is true. (Well, we could look it up, I suppose; but we're not asked if the argument is *sound*, only if it is *valid*: Does C follow from P?) Pa, on the other hand, doesn't have to be accepted at all; after all, we are imposing it on the (unknown) author of the argument. So, we had better impose something that is likely to be true. Pa is offered as part of the meaning of "sail into". I won't defend its truth any further here, but if any of you think that it's *not* true, please let me know. Pb: If something arrives in a place named X Bay, then it arrives at a place named X. .'. C2: B arrived at SF 21 August 1945. C2 will follow from C1 and Pb, but is Pb true? Can you think of any bays named X Bay that are not located in a place named X? If you can, then we can't use Pb. Let's assume the worst: Then we'll need something like: Pb.1: If something arrives in SF Bay, then it arrives at SF. C2 will follow from C1 and Pb.1, and we can easily check the likely truth of Pb.1 by looking at a map. So far, so good. We've now got B arriving at SF on 21 August 1945. But what we need is B *reaching* SF in August 1945. So let's add... Pc: If something arrives somewhere, then it reaches that place. Again, this is proposed as an explication of part of the meaning of "arrive", and, in particular, of that part of its meaning that connects it to C. From Pc and C2, we can infer: C3: B reached SF 21 August 1945. Are we done? Does C3 = C? Look at them: C3: Bountiful reached San Francisco 21 August 1945. C: Bountiful reached San Francisco in August 1945. Think like a computer! What do you need to know in order to know whether C3 = C? You need to know whether the final missing premise, Pd, is true: Pd: If something occurs (on) DATE MONTH YEAR, then it occurs *in* MONTH YEAR. And that's true by virtue of the way (some) people talk. From Pd and C3, we can infer C. So, the simple argument that we started with, ignoring its irrelevant premise, becomes this rather more elaborate one: P: Bountiful arrived after war's end, sailing into San Francisco Bay 21 August 1945. Pa: If something sails into a place, then it arrives at that place. .'. C1: Bountiful arrived at San Francisco Bay 21 August 1945. Pb: If something arrives in a place named X Bay, then it arrives at a place named X. (or Pb.1: If something arrives in San Francisco Bay, then it arrives at San Francisco.) .'. C2: Bountiful arrived at San Francisco 21 August 1945. Pc: If something arrives somewhere, then it reaches that place. .'. C3: Bountiful reached San Francisco 21 August 1945. Pd: If something occurs (on) DATE MONTH YEAR, then it occurs *in* MONTH YEAR. .'. C: Bountiful reached San Francisco in August 1945.