scholarly journals Raciocínio Lógico e Escolarização

2019 ◽  
Vol 74 (176) ◽  
Author(s):  
Maria Dias ◽  
Antonio Roazzi
Keyword(s):  
Deductive Reasoning ◽  
Modus Ponens ◽  
Chance Level ◽  
Low Ses ◽  
Grand Nombre ◽  
Modus Tollens ◽  
Verbal Mode

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.

scholarly journals On Basic Probability Logic Inequalities

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1409
Author(s):  
Marija Boričić Joksimović
Keyword(s):  
Probability Theory ◽  
Inference Rule ◽  
Modus Ponens ◽  
Probability Logic ◽  
Modus Tollens ◽  
Short Overview ◽  
Basic Probability ◽  
Probabilistic Version ◽  
Hypothetical Syllogism

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.

scholarly journals Fuzzy Reasoning Method Based on Distance Measure and Its Reductive Property

2020 ◽  
Vol 8 ◽  
pp. 73-89
Author(s):  
Sonil Kwak ◽  
Unha Kim ◽  
Kumju Kim ◽  
Ilmyong Son ◽  
Chonghan Ri
Keyword(s):  
Fuzzy Control ◽  
Fuzzy Systems ◽  
Distance Measure ◽  
Fuzzy Reasoning ◽  
Modus Ponens ◽  
Information Loss ◽  
Modus Tollens ◽  
Criterion Function ◽  
Human Thinking ◽  
Fuzzy Modus Ponens

This paper shows a basic and original fuzzy reasoning method that can draw a novel study direction of the approximate inference in fuzzy systems with uncertainty. Firstly we propose a criterion function for checking of the reductive property about fuzzy modus ponens (FMP) and fuzzy modus tollens (FMT). Secondly unlike fuzzy reasoning methods based on the similarity measure, we propose a principle of new fuzzy reasoning method based on distance measure and then present two theorems for FMP and FMT. Thirdly through the several computational experiments, we show that proposed method is simple and effective, and in accordance with human thinking. Finally we pointed out conclusion that proposed method does satisfy the convergence of the fuzzy control and has not information loss.

scholarly journals ¿Hacia un replanteamiento del cálculo proposicional clásico?

1970 ◽  
Vol 32 (1) ◽  
Author(s):  
Enric Trillas ◽  
Itziar García-Honrado
Keyword(s):  
Modus Ponens ◽  
Modus Tollens

El cálculo proposicional se basa proposiciones que son tautologías, antilogías y de tipo contingente, construidas con las operaciones de disyunción, conjunción, y negación, así como con el llamado condicional material para trasladar los enunciados condicionales. Con todo ello se obtiene una estructura de álgebra de Boole, que permite equiparar el cálculo proposicional al cálculo algebraico booleano. En parte, la simplificación conceptual que se obtiene resulta de ser el orden parcial del álgebra equivalente a la afirmación del condicional material. Además, con tal metodología cabe ver qué partes del cálculo proposicional clásico pueden trasladarse, aun con limitaciones, a estructuras más débiles y, a la vez, más generales, como son los ortoretículos no booleanos o las álgebras de De Morgan.El cálculo proposicional trata con la deducción. Por ello, el artículo lo desarrolla a partir de un operador de consecuencias en el sentido de Tarski. Ampliado el modelo deductivo, es fácil ver otras consecuencias que las usualmente consideradas en los textos elementales; en particular, se analizan cuatro esquemas de razonamiento deductivo típicos y, entre ellos, se presta especial atención a los usuales Modus Ponens y Modus Tollens. En el caso de las estructuras algebraicas de conjuntos ‘borrosos’, ninguna es de álgebra de Boole ni siquiera de orto-retículo y sólo cabe trabajar, en algunos casos, con álgebras de De Morgan-Kleene. Por lo tanto el cálculo proposicional ‘fuzzy’ debe construirse de acuerdo con la estructura algebraica que corresponda en cada caso y una vez elegida como representación del condicional una función que verifique el Modus Ponens (‘condicional borroso’).

Inferences From Counterfactual Threats and Promises

2012 ◽  
Vol 59 (4) ◽  
pp. 227-235 ◽  
Author(s):  
Suzanne M. Egan ◽  
Ruth M. J. Byrne
Keyword(s):  
Cognitive Processes ◽  
Mental Representations ◽  
Ice Cream ◽  
Modus Ponens ◽  
Illocutionary Force ◽  
Modus Tollens

We examine how people understand and reason from counterfactual threats, for example, “if you had hit your sister, I would have grounded you” and counterfactual promises, for example, “if you had tidied your room, I would have given you ice-cream.” The first experiment shows that people consider counterfactual threats, but not counterfactual promises, to have the illocutionary force of an inducement. They also make the immediate inference that the action mentioned in the “if” part of the counterfactual threat and promise did not occur. The second experiment shows that people make more negative inferences (modus tollens and denial of the antecedent) than affirmative inferences (modus ponens and affirmation of the consequent) from counterfactual threats and promises, unlike indicative threats and promises. We discuss the implications of the results for theories of the mental representations and cognitive processes that underlie conditional inducements.

Tempered Pragmatism

2017 ◽  
Author(s):  
Ian Rumfitt
Keyword(s):  
Modus Ponens ◽  
Modus Tollens ◽  
Truth Conditions ◽  
Indicative Conditionals ◽  
Logical Basis ◽  
Theory Of Meaning

This chapter assesses the prospects of a pragmatist theory of content. It begins by criticizing the theory presented in D. H. Mellor’s essay ‘Successful Semantics’, then identifies problems and lacunae in the pragmatist theory of meaning sketched in chapter 13 of Dummett’s The Logical Basis of Metaphysics. It contends that the prospects are brighter for a tempered pragmatism, in which the theory of content is permitted to draw upon irreducible notions of truth and falsity. It sketches the shape of such a theory and illustrates the role of its pragmatist elements by showing how they point towards a promising account of the truth conditions of indicative conditionals. A feature of the account is that it validates Modus Ponens whilst invalidating Modus Tollens.

Modus Ponens, Modus Tollens, and Likeness

1998 ◽  
pp. 45-52
Author(s):  
Mustafa M. Dagli
Keyword(s):  
Modus Ponens ◽  
General Idea ◽  
Modus Tollens ◽  
Ordinary Life ◽  
Conditional Statements ◽  
Reasoning Patterns ◽  
Actual Life

Modus Ponens (MP) and Modus Tollens (MT) are taught as basic rules of inference related to conditional statements in introductory logic courses. In ordinary reasoning, MP and MT can have important roles in modes of argumentation. However, one can also distinguish counter-examples to such reasoning patterns when considered as ‘strictly’ valid rules (i.e., McGee’s counterattacks for MP, and Adams’ criticisms of MT). I suggest that this problem can be resolved if we revise MP and MT as basic tools of logic, assuming the above-mentioned counter-cases are valid, on the basis of nonmonotonicity. If the only thing that we know is ‘Tweety is a bird,’ we say ‘Tweety flies.’ But, after learning ‘Tweety is an ostrich,’ we (change our minds and) say, ‘Tweety does not fly.’ In actual life, we use ‘rules of logic’ in a limited sense; when we learn new facts, we change some of our beliefs sometimes. The question arises, ‘In which situation, which exception does not violate which rule?’ When reasoning about something, we use some semantic patterns in order to make inferences, or for the sake of argumentation. Two reasoning patterns employed in ordinary life scenes concerning conditional statements will be identified as MP-like and MT-like. These will be exemplified and discussed. The general idea guiding this tableau will be stated as likeness.

scholarly journals Logical Intuition Is Not Really About Logic

2021 ◽  
Author(s):  
Omid Ghasemi ◽  
Simon Handley ◽  
Stephanie Howarth ◽  
Ian Randal Newman ◽  
Valerie A Thompson
Keyword(s):  
Structural Feature ◽  
Modus Ponens ◽  
Structural Features ◽  
Modus Tollens ◽  
Logical Validity ◽  
Affirming The Consequent

Recent research suggest that reasoners are able to draw simple logical or probabilistic inferences relatively intuitively and automatically, a capacity which has been termed “logical intuition” (see, for example, De Neys & Pennycook, 2019). A key finding in support of this interpretation is that conclusion validity consistently interferes with judgments of conclusion believability, suggesting that information about logical validity is available quickly enough to interfere with belief judgments. In this paper we examined whether logical intuitions arise because reasoners are sensitive to the logical features of problem or another structural feature that just happens to aligns with logical validity. In three experiments (N = 113, 137, and 122), we presented participants with logical (determinate) and pseudo-logical (indeterminate) arguments and asked them to judge the validity or believability of the conclusion. Logical arguments had determinately valid or invalid conclusions, whereas pseudo-logical arguments were all logically indeterminate, but some were pseudo-valid (possible ‘strong’ arguments) and others pseudo-invalid (possible ‘weak’ arguments). Experiments 1 and 2 used simple Modus Ponens and Affirming the Consequent structures; Experiment 3 used more complex Denying the Antecedent and Modus Tollens structures. In all three experiments, we found that pseudo-validity interfered with belief judgments to the same extent as real validity. Altogether, these findings suggest that whilst people are able to draw inferences intuitively, and these inferences impact on belief judgments, they are not ‘logical intuitions.’ Rather, the intuitive inferences are driven by the processing of more superficial structural features that happen to align with logical validity.

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