Some Effects of Negation on Adults' Conditional Reasoning Abilities

1971 ◽  
Vol 29 (3) ◽  
pp. 839-844 ◽  
Author(s):  
James J. Roberge

110 Ss evaluated conclusions for conditional reasoning arguments embodying 1 of 4 principles of inference: modus ponens, conversion, inversion, and modus tollens. The presence of the negative “not” was varied systematically within each major premise and conclusion. The results indicated that the form of the major premise had a significant ( p < .001) effect on reasoning. More importantly, it had a significant ( p < .001) differential effect according to the type of conclusion. The difference between Ss' mean error scores for conditional arguments with affirmative and negative conclusions was slight and nonsignificant ( p > .05).

1996 ◽  
Vol 49 (3) ◽  
pp. 828-844 ◽  
Author(s):  
In-mao Liu ◽  
King-chung Lo ◽  
Jei-tun Wu

This study proposes that subjects interpret thematic conditionals (“if p then q”) probabilistically in solving conditional reasoning problems. Experiment 1 found that subjects’ correct responses increased with the perceived probability of q, given p for each of the four forms of conditional arguments: modus ponens (MP), modus tollens (MT), denial of the antecedent (DA), and affirmation of the consequent (AC). Experiment 2 ruled out two alternative explanations based on the comprehensibility of conditionals and on subjects interpreting conditionals as biconditionals. In Experiment 3, subjects solved two types of problems: (a) complete probabilistic problems, such as “If p then q; knowing p; how probable is q?”, and (b) reduced probabilistic problems, such as “Knowing p; how probable is q?” Two sources of information that determine the observable reasoning responses are identified. One source of information is based on one's general knowledge, and another is based on taking all premises into account.


Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1409
Author(s):  
Marija Boričić Joksimović

We give some simple examples of applying some of the well-known elementary probability theory inequalities and properties in the field of logical argumentation. A probabilistic version of the hypothetical syllogism inference rule is as follows: if propositions A, B, C, A→B, and B→C have probabilities a, b, c, r, and s, respectively, then for probability p of A→C, we have f(a,b,c,r,s)≤p≤g(a,b,c,r,s), for some functions f and g of given parameters. In this paper, after a short overview of known rules related to conjunction and disjunction, we proposed some probabilized forms of the hypothetical syllogism inference rule, with the best possible bounds for the probability of conclusion, covering simultaneously the probabilistic versions of both modus ponens and modus tollens rules, as already considered by Suppes, Hailperin, and Wagner.


Problemos ◽  
2018 ◽  
Vol 93 ◽  
pp. 90-101
Author(s):  
Živilė Pabijutaitė

[full article, abstract in English; only abstract in Lithuanian] The paper deals with the problem of the “two Barbaras” in the Aristotelian modal syllogistic. The problem consists in Aristotle’s differing views on two at a first sight similar in nature syllogisms of mixed assertoric (X) and necessary (L) premises: Barbara LXL and Barbara XLL. The fact that Aristotle believed the first syllogism to be valid and the second one – not, has been received either 1) negatively, because both Barbaras have been held to be invalid, or 2) negatively, because both Barbaras have been held to be valid, or 3) positively, by giving a reason why the two Barbaras differ. We commit ourselves to the position (3) by proving that modal propositions for Aristotle have their modalities de dicto and that Aristotelian modal operators act according to their own separate rules where only the type of the modality of a major premise is relevant for the modal status of the conclusion.


1978 ◽  
Vol 30 (4) ◽  
pp. 705-716 ◽  
Author(s):  
James J. Roberge

An experiment is reported which demonstrates the effects of linguistic and psychometric factors on adults’ performance on a propositional reasoning task. The three linguistic factors were the semantic content in which the logical rule was embedded, the linguistic form of the logical rule, and the polarity of the major premise of the logical arguments. The two psychometric factors were the mode of response and the order of presentation of the different types of content. The results showed that the linguistic factors had a pronounced effect on adults’ propositional reasoning abilities, whereas the influence of the psychometric factors was negligible. These findings are discussed in relation to operational and interpretational factors in reasoning.


2021 ◽  
Vol 10 (1) ◽  
pp. 130
Author(s):  
Jayanti Jayanti ◽  
Jumroh Jumroh

<span lang="IN">This study aims to examine the improvement of prospective teacher Mathematical Reasoning (KPM) abilities through E-Learning-assisted Numeration learning. This study used a quasi-experimental method with a non-equivalent pretest and posttest control group design. The subjects of this study were mathematics prospective teachers at Universitas PGRI Palembang. namely the experimental class which received E-learning assisted numeracy learning (PNBE) and the control class which received conventional learning (PK). Based on the results of the analysis of the difference in the mean difference in the KPM increase of prospective teachers who received PNBE learning and prospective teacher who received conventional learning, the scores from the table of increasing KPM of students who received E-learning-assisted Numeration learning (PNBE) were better than a prospective teacher who received conventional learning. Based on the results of data analysis, it can be concluded that numeracy skills and mathematical reasoning abilities of fourth-semester prospective teacher PGSD at PGRI university are quite good. It is recommended for teaching staff/lecturers to be able to try out this learning model on other mathematical abilities.</span>


Author(s):  
Maria Dias ◽  
Antonio Roazzi

O objetivo deste estudo foi investigar o efeito do modo de faz-deconta, formas de silogismos e tipos de fatos, no desempenho de crianças inglesas de 5 anos de idade, escolarizadas, de nivel sócio-econômico (NSE) médio e de crianças brasileiras de 5 anos de idade, nao escolarizadas de NSE baixo. Os resultados mostraram que as crianças, independentemente se escolarizadas ou nao, produziram maior número de respostas corretas e maior número de justificativas teóricas na condição de brincadeira de faz-de-conta do que na condição verbal comum. Este efeito foi especialmente marcante para os fatos desconhecidos e para os fatos contrários às experiências das crianças. Este padrão foi mantido para ambas formas de silogismos, embora em geral o desempenho das crianças nos problemas envolvendo Modus Ponens tenha sido mais acurada do que nos problemas envolvendo Modus Tollens. As crianças não-escolarizadas obtiveram menores escores do que as escolarizadas. No entanto, esta diferença não foi tão forte como aquela relatada por Scribner (1977) onde as crianças não-escolarizadas obtiveram baixos escores adotando um viés empírico. Em nosso estudo, apesar das crianças não-escolarizadas terem freqüentemente recorrido a justificativas arbitrárias, puderam recorrer a uma atitude teórica quando a condição de faz-de-conta foi adotada. Abstract The main aim of this study was to investigate the effect of makebelieve mode, form of syllogisms and type of fact in 5-year-old schooled children from medium SES families in England and in non literate 5- year-old unschooled children from low SES families in Brazil. This study was a test of the claim that schooling is a pre requesite for deductive reasoning. The results showed that children, English or Brazilian, produced more correct responses and theoretical justifications in the makebelieve play condition than in the standard verbal mode. This was especially true for unknown facts and contrary facts. This pattern held for both form forms of syllogism, although in general children 's performance on Modus Ponens inferences was more accurate than on Modus Tollens inferences. Unschooled children s performance was poorer than schooled children s performance. However, this difference was not so strong as that found in the studies reported by Scribner (1977) where unschooled children performed at chance level, adopting the empirical bias. In this study, the unschooled children, although they very often appealed to arbitraty justifications, could adopt a theoretical attitude when the makebelieve mode was used. Résumé Ce travail de recherche a eu comme objectif principal l'investigation de Ì'effet du mode faire-semblant, des formes de syllogisme et des types défaits sur la réussite d'enfants anglais de cinq ans, scolarisés, niveau socio-économique moyen, et d'enfants brésiliens de même âge, nonscolarisés et de bas niveau socio-économique. Les résultats indiquent aue les enfants, scolarisés ou non, ont produit un plus grand nombre de réponses correctes, ainsi que de justificatives théoriques dans la condiction experimentale faire-semblant, par rapport à la condiction verbale commune. Cet effet a été plus net en ce qui concerne des faits nconnus et des faits contraires aux expériences des enfants. Ce résultat a été observé pour ¡ es deux formes de syllogisme étudiées, quoi que, en général, le nombre de réponses correctes a été plus important chez les enfants travaillant avec des problèmes em Modus Ponens, par raport à ceux travaillant sous modus Tollens. Les enfants non-scolarisés ont obtenu des scores plus bas que ceux des enfants scolarisés. Néanmoins, cette différence n 'a pas été aussi forte que celle mentionnée par Scribner (1977), qui a pu constater des scores bas chez des enfants non-scolarisés adoptant un biais empirique. Dans notre étude, bien que les enfants nonscolarisés aient fréquemment fait appel à des justifications arbitraires, ils ont, d'autre part, eu recours à une attitude théorique quand la condiction faire-semblant a été proposée. Resumen El objetivo principal de este estudio fue investigar el efecto del modo de fingir formas de silogismos y tipos de hechos en el rendimiento de niños ingleses de 5 anos de edad, escolarizadas, de NSE médio y de linos brasileños de 5 anos de edad, sin escolaridad de NSE bajo. Los resulados mostraron que ¡os niños, independientemente de si eran escolarizados o no, producían mayor número de respuestas correctas e mayor número de justificativas teóricas en la condición del juego de fingir que en la condición verbal común. Este efecto fue especialmente marcante para los hechos desconocidos y para los hechos contrários a Ias experiencias de los ninos. Este padrón fue conservado para ambas formas de silogismos, no obstante, en general el rendimiento de los ninos en los problemas envolviendo Modus Ponens haya sido mas preciso que en los problemas envolviendo Modus Tollens. Los ninos sin escolaridad obtuvieron resultados menores que los escolarizados. Sin embargo, esta diferencia no fue tan fuerte como aquella relatada por Scribner (1977) donde los ninos sin escolaridad obtuvieron bajos resultados adoptando una inclinación empírica. En nuestro estúdio, a pesar de los ninos sin escolaridad haber recurrido frecuentemente a justificativas arbitrarias, estos adoptaron una actitud teórica cuando fue usada Ia condición de fingir.


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