A process model of the understanding of uncertain conditionals

Abstract

To build a process model of the understanding of conditionals we extract a common core of three semantics of if-then sentences: (a) the conditional event interpretation in the coherencebased probability logic, (b) the discourse processingtheory of Hans Kamp, and (c) the game-theoretical approach of Jaakko Hintikka. The empirical part reports three experiments in which each participant assessed the probability of 52 if-then sentencesin a truth table task. Each experiment included a second task: An n-back task relating the interpretation of conditionals to working memory, a Bayesian bookbag and poker chip task relating the interpretation of conditionals to probability updating, and a probabilistic modus ponens task relating the interpretation of conditionals to a classical inference task. Data analysis shows that the way in which the conditionals are interpreted correlates with each of the supplementary tasks. The results are discussed within the process model proposed in the introduction.

Imprecise Uncertain Reasoning: A Distributional Approach

“…For a speaker who expresses imprecise uncertainties the if-then and the and have practically the same “meaning.” This throws a new light on the conjunctive interpretation of conditionals. In Fugard et al ( 2011 ) and Kleiter et al ( 2018 ) we observed that about twenty percent of the participants give conjunctive interpretations of the conditional. We also observed a higher frequency of conjunctive interpretations in female participants.…”

“…For not too extreme probabilities these differences may be small, so small that it will be impossible to distinguish the two interpretations empirically. We observed that in typical truth table tasks about twenty percent of the participants interpret if-then sentences as conjunctions (Fugard et al, 2011 ; Kleiter et al, 2018 ). In the context of everyday conversation, say, the different interpretations would not matter.…”

“…The smallest value of D ( P ; Q ) = 0.14 is obtained for the distance between if and and for P ( A ) ~ Be (30, 3) and P ( B ) ~ (20, 20), that is, for one distribution with a high mean of 0.91 and one distribution with a mean of 0.5. This may be related to the empirical finding that about twenty percent of the interpretations of if-then sentences are conjunction interpretations (Fugard et al, 2011 ; Kleiter et al, 2018 ).…”

Conditionals, Causality and Conditional Probability

“…2 This proposal is compatible with the view that indicative conditionals can be (taken to be) true or false in some situations. In particular, one can adopt de Finetti's (1936Finetti's ( /1995 proposal [as done by psychologists like Over and Evans (2003) and Kleiter et al (2018), philosophers (Belnap 1970;Milne 2004) and linguists (Huitink 2008)], according to which 'If i, then e' is taken to be true if i and e hold, false, if i holds, but not e, and has no (classical) truth value otherwise. The probability P(e|i) then measures the conditional probability that the conditional is true, the 'i ∧ e' outcome, given that the conditional has a (classical) truth value at all, the i case, for P(i ∧ e|i) = P(e|i).…”

Cancellation, negation, and rejection

“…Conditionals with false antecedents can be compared to called-off bets: a bet that if you throw a fair coin it will land heads is neither won, nor lost -it is called off -when the coin is not thrown at all (see, e.g., Politzer, Over, & Baratgin, 2010). A more refined version of the de Finetti's system can be obtained by replacing the third, "void" value with the conditional probability itself (Jeffrey, 1991; see also Baratgin, Politzer, Over, and Takahashi, 2018;Pfeifer, 2018, andOver &.…”