Wolfgang Schwarz

An RSA model of SDA

In this post, I'll develop an RSA model that explains why 'if A or B then C' is usually taken to imply 'if A then C' and 'if B then C', even if the conditional has a Lewis/Stalnaker ("similarity") semantics, where the inference is invalid.

I'll write 'A>C' for the conditional 'if A then C'. For the purposes of this post, we assume that 'A>C' is true at a world w iff all the closest A worlds to w are C worlds, by some contextually fixed measure of closeness.

It has often been observed that the simplification effect resembles the "Free Choice" effect, i.e., the apparent entailment of '◇A' and '◇B' by '◇(A∨B)', where the diamond is a possibility modal (permission, in the standard example). But there are also important differences.

An RSA model of free choice

Let's continue. I'm going to present a new (?) model of free choice. Free choice is the phenomenon that a disjunction embedded in a possibility modal conveys the possibility of both disjuncts. 'You may have tea or coffee', for example, conveys that you may have tea and you may have coffee. Champollion, Alsop, and Grosu (2019) present an RSA model of this effect, drawing on the "lexical uncertainty" account from Bergen, Levy, and Goodman (2016). I'll present a model that does not rely on lexical uncertainty.

RSA vs IBR

In this post, I want to compare the Rational Speech Act approach with the Iterated Best Response approach of Franke (2011). I'm also going to discuss Franke's IBR model of Free Choice, turn it into an RSA model, and explain why I find both unconvincing.

Let's back up a little.

Lewis (1969) argued that linguistic conventions solve a game-theoretic coordination problem.

RSA models with partially informed speakers

Let's model a few situations in which the hearer does not assume that the speaker has full information about the topic of their utterance.

Goodman and Stuhlmüller (2013) consider a scenario in which a speaker wants to communicate how many of three apples are red. The hearer isn't sure whether the speaker has seen all the apples. Chapter 2 of problang.org gives two models of this scenario. The first makes very implausible predictions. The second is very complicated. Here's a simple model that gives the desired results.

var states = ['RRR','RRG','RGR','GRR','RGG','GRG','GGR','GGG'];
var meanings = {
  'all': function(state) { return !state.includes('G') },
  'some': function(state) { return state.includes('R') },
  'none': function(state) { return !state.includes('R') },
  '-': function(state) { return true }
}
var observation = function(state, access) {
    return filter(function(s) {
        return s.slice(0,access) == state.slice(0,access);
    }, states);
}
var hearer0 = Agent({
    credence: Indifferent(states),
    kinematics: function(utterance) {
        return function(state) {
            return evaluate(meanings[utterance], state);
        }
    }
});
var speaker1 = function(obs) {
    return Agent({
        options: keys(meanings),
        credence: update(Indifferent(states), obs),
        utility: function(u,s){
            return learn(hearer0, u).score(s);
        }
    });
};
showChoices(speaker1, [observation('RRR', 2), observation('GGG', 2)]);

Pragmatic non-equivalence despite semantic equivalence

Bergen, Levy, and Goodman (2016) assert that "the rational speech acts model, and neo-Gricean models more generally, cannot derive distinct pragmatic interpretations for semantically equivalent expressions".

In the previous post, I gave a counterexample. I presented an RSA model that explains why 'pockets' is interpreted as plural and 'a pocket' as singular, even though the two expressions are semantically equivalent.

RSA models of scalar implicature

In this post, we'll model different kinds of scalar implicature. I'll introduce several ideas and techniques that prove useful for other topics as well.

Let's begin with the textbook example, the inference from 'some' to 'not all' (for which Goodman and Stuhlmüller (2013) give an RSA-type explanation).

A speaker wants to communicate the results of an exam. The available utterances are 'all students passed', 'some students passed', and 'no students passed'; for short: 'all', 'some', and 'none'. We can represent their meaning as functions from states to truth values:

var states = ['∀', '∃¬∀', '¬∃'];
var meanings = {
    'all': function(state) { return state == '∀' },
    'some': function(state) { return state != '¬∃' },
    'none': function(state) { return state == '¬∃' }
};

Exploring the Rational Speech Act framework

I've been playing around with the Rational Speech Act framework lately, and I want to write a few blog posts clarifying my thoughts. In this post, I'll introduce the framework and go through a simple application.

The guiding idea behind the Rational Speech Act framework is to model speakers and hearers as rational (Bayesian) agents who think strategically about each other's behaviour. A hearer doesn't just update on the literal content of an utterance, but on the fact that the utterance has been made, by a speaker who anticipated that the speaker would update in some such way.

In its purest form, this kind of reasoning leads to an infinite regress. To interpret your utterance, I need to figure out why you made it. To do that, I need to figure out how you thought I would interpret the utterance, which depends on what you believe about what I believe about why you made it, and so on.

The semantic blindness of scalar implicatures

Magri (2009) points out that the computation of scalar implicatures appears to be insensitive ("blind") to contextual knowledge. This is indicated by the oddness of sentences like (1) and (2):

(1) Some Italians come from a warm country.
(2) John is sometimes tall.

Plausibly, these sound odd because their implicature-strengthened meaning clashes with our background knowledge that – in the case of (1) – all Italians come from the same country and – for (2) – that people's height is a stable property.

The independence of free choice alternatives

It is well-known that disjunctive possibility and necessity statements appear to imply the possibility of the disjuncts:

(FC) \( \Diamond(p \lor q) \Rightarrow \Diamond p \land \Diamond q \).
(RP) \( \Box(p \lor q) \Rightarrow \Diamond p \land \Diamond q \).

The first kind of inference is known as a "free choice" inference, the second is "Ross's Paradox".

For example, (1a) seems to imply (1b) and (1c):

(1a) Alice might [or: must] have gone to the party or to the concert.
(1b) Alice might have gone to the party.
(1c) Alice might have gone to the concert.

In chapter 3 of his dissertation, Booth (2022), Richard Booth points out that (FC) and (RP) underdescribe the true effect.

Negative exhaustification?

Here's an idea that might explain a number of puzzling linguistic phenomena, including neg-raising, the homogeneity presupposition triggered by plural definites, the difficulty of understanding nested negations, and the data often assumed to support conditional excluded middle.

An utterance of

(1a) We will not have PIZZA tonight

conveys two things. Unsurprisingly, it conveys that we will not have pizza tonight. But it also conveys, due to the focus on 'PIZZA', that we will have something else. By comparison,

On neg-raising

Neg-raising occurs when asserting ¬Fp (or denying Fp) tends to communicate F¬p. For example, 'John doesn't believe that he will win' tends to communicate that John believes that he won't win.

There appears to be no consensus on why this happens. Some think ¬Fp really does entail F¬p. Others think the effect is an implicature. Still others think it's caused by a presupposition of opinionatedness or "settledness": when we talk about whether Fp holds, we presuppose that F holds either for p or for an alternative to p, denying Fp therefore commits us to F¬p.

Indefinites and implicatures

Suppose I say (*), with respect to a particular gambling occasion.

(*) A gambler lost some of her savings. Another lost all of hers.

There is an implicature here that the first gambler, unlike the second, didn't lose all her savings. How does this implicature arise?

On the standard account of scalar implicatures, we should consider certain alternatives to the uttered sentences. In particular, I could have said 'A gambler lost all of her savings' instead of 'A gambler lost some of her savings'. If true, this alternative would have been more informative. Since I chose the weaker sentence, you can infer that I wasn't in a position to assert the stronger sentence. Assuming I am well-informed, you can further infer that the stronger sentence is false.

Pragmatic intrusion, validity, and compositional pragmatics

Sometimes, implicatures appear to survive under embedding. Take

1) the column will fail and the bridge will collapse,

which in a suitable context implicates that (the speaker believes that) the bridge will collapse as a result of the column failing. This implicature is still present if (1) gets embedded in, say, a conditional:

2) if it rains, the column will fail and the bridge will collapse;

3) if the column will fail and the bridge will collapse, you'll be in trouble.

(2) is likely to convey that if it rains, the bridge will collapse as a result of the column failing, and (3) that if the bridge will collapse as a result of the column failing, then you'll be trouble.

Diamond Implicature II

I've thought a little more about this thing I called 'diamond implicature', and I've come up with the following explanation. I don't know if it's original, and unfortunately, I don't see how exactly it applies to the antecedent of counterfactuals, which is what I am most interested in.

The explanandum is that in many contexts, appears to imply . For example,

Diamond implicature

If I say "", you would often take me to have asserted both "" and "". A quick internet search didn't come up with any useful literature on this, so I'd be grateful for pointers.

What does the Wason Selection Task test?

I'm doing a visual memory test. On the table in front of me are twelve green and fourteen red apples, and an empty basket. The lights go out, and the instructor says to me:

"Put all the green apples into the basket". (1)

I try to do what he says. When the lights go on, you, the instructor's assistant, are given a form on which you are to tick whether I've correctly or incorrectly fulfilled the task. You see twelve green and two red apples in the basket. What do you tick?