Chronometrical Evidence Supports the Model Theory of Negation

Abstract

We aimed to study how compound negation of conjunctions and disjunctions is understood and represented. In particular, we aimed to test time course predictions consistent with the Mental Models Theory of negation proposed in 2012 by Khemlani, Orenes, and Johnson-Laird. Consistent with this theory, we conjectured that the consideration of possibilities elicited by any given information regulates the processing of compound negation. We studied response type patterns to replicate previous findings as well as response time patterns to generate novel chronometrical evidence. We conducted a within-subjects experiment to test a set of five experimental hypotheses. We used a sentence-equivalence task. Participants were asked to find a logical equivalence for a given compound negation of a conjunction or a disjunction. Four possible response options were presented, but only one of them was correct according to sentential logic. We also tested predictions derived from theories that argue against the Mental Models Theory. The evidence resulted consistent with the model theory of negation and incompatible with alternative accounts. In particular, our results did not support the Psychology of Proof and the Dual-Process approach to negation.

Effect of personality on compound reasoning

“…In this way, the Theory of Negation works with the assumptions of the MMT and defines it as a function that takes the set of mental models as a single argument, and produces the complement for that set as a result (Khemlani et al, 2012(Khemlani et al, , 2014Macbeth et al, 2013;2014b, 2017a. In this sense, the meaning of negation coincides with that proposed by logic (Khemlani et al, 2012).…”

“…According to Khemlani et al (2012), while the goal of a Linguistic Theory of Negation is to explain its syntactic, semantic and pragmatic elements, the purpose of a Psychological Theory is to explain how such grammar, meaning, and knowledge are understood by people and how people represent them mentally. And here lies the central goal of the proposal: to decipher the meaning, representation, and use granted by people to negation (Khemlani et al, 2012(Khemlani et al, , 2014Macbeth et al, 2013Macbeth et al, , 2017a. Out of all these elements, meaning is the one which acquires fundamental value, due to its effect on negation (Khemlani et al, 2012(Khemlani et al, , 2014.…”

“…As these laws formally establish, the negation of a conjunction is equivalent to an inclusive disjunction (Law 1), while the negation of an inclusive disjunction is equivalent to a conjunction (Law 2) (De Morgan, 1847;Suppes & Hill, 1992). Since the representation of a conjunction requires a single mental model, and the representation of an inclusive disjunction involves three mental models, the theory predicts greater difficulty in processing Law 1 than Law 2 (Macbeth et al, 2014b;2017a).…”

“…Thus, we chose an experimental paradigm that was specifically designed to evaluate propositional reasoning regarding compound negations. It is a selection test used in previous studies (Macbeth et al, 2015;2017a), in which subjects are asked to select a response option that they consider appropriate. Given that the paradigm was also based on the MMT, it presupposes a close relationship between each specific response and specific mental models leading to such selection.…”

“…A paradigmatic example of this issue can be found when studying the processing of negation. This phenomenon, easily explained by mathematical logic (Macbeth, Crivello, Fioramonti, Razumiejczyk, 2017a), nevertheless presents some difficulties when processed by the human mind. Some approaches tried to account for this complexity and proposed the intervention of pragmatic (Horn, 1989;Horn & Ward, 2005;Orenes, Moxey, Scheepers, & Santamaría, 2016), contextual (Sperber & Wilson, 1986;Wilson & Sperber, 1994) and conversational (Bott & Noveck, 2004;Grice, 1989) factors.…”