scholarly journals Traditional Logic and Computational Thinking

Philosophies ◽  
2021 ◽  
Vol 6 (1) ◽  
pp. 12
Author(s):  
J.-Martín Castro-Manzano

In this contribution, we try to show that traditional Aristotelian logic can be useful (in a non-trivial way) for computational thinking. To achieve this objective, we argue in favor of two statements: (i) that traditional logic is not classical and (ii) that logic programming emanating from traditional logic is not classical logic programming.

2001 ◽  
Vol 22 (1) ◽  
Author(s):  
Jesse P. Bohl

There is a clash between some people's positive logical intuitions about traditional or Aristotelian logic and the assessment ofthat logic made by modem logic. In response to the clash, four sorts of reasons that might be given for referring one logic to the other are considered, but it is argued that none of them provides a decisive reason in favor of one rather than the other. A reformist and a radical response to the apparent inability to give reasons to prefer one logic to the other are considered and reasons given for preferring the radical response.


10.28945/4163 ◽  
2018 ◽  
Vol 17 ◽  
pp. 549-575
Author(s):  
Noa Ragonis ◽  
Gila Shilo

Aim/Purpose: Research shows that students encounter difficulties in identifying the structure of argumentation texts and in understanding the main message of the argument. The research examined the effect that learning Logic Programming (LP), while applying logic inference, has on students’ understanding of argumentation texts. Background: Understanding an argumentation text means exposure to its structure, which requires the ability to identify the argument presented and to distinguish between the argument and its justifications. Argumentation is an important cognitive capacity for handling conflicting information, viewpoints, and opinions. Students’ lack of ability to identify the structure of argumentation texts, and to understand its’ main message, affects the understanding of texts in general, the writing of texts, and the presentation of oral arguments. Since Logic Programming is based on inference that is similar to the way in which people commonly believe that human inferential thinking is performed, our research approach was to investigate how learning LP in Computer Science affects the understanding of argumentation texts in Linguistics. Methodology: The research population included 319 11th-grade students from five high schools, divided into a study group and a control group. Students’ understanding was tested using knowledge questionnaires after completing their language studies, before (pre-study) and after (post-study) a year of learning LP. The knowledge questionnaires included argumentation paragraphs where students were asked to give each paragraph a title and to analyze the argument structure. In addition, an attitudes questionnaire was administered at the end of the school year in order to examine the students’ attitudes towards the connection between the two disciplines. The research applied a mixed method approach, combining both qualitative and quantitative methods. Contribution: The research and its’ findings contribute to the previous body of knowledge with relation to students difficulties in understanding argumentation texts in Linguistics studies. Moreover, it suggests a new approach of using argumentation in the framework of inference as apply in LP to scaffold students’ conceptions. The use of an interactive computerized system (like the logic programming language Prolog) can scaffold students in constructing their knowledge, develop their computational thinking skills, and also enables to vary the teaching methods. Findings: Findings show that the students’ understanding of argumentation texts improved after learning LP. The study group students’ achievements were explicitly better compared with the control group students, who did not learn LP, though this was not always reflected with significant statistics. Students’ attitudes questionnaire revealed that students did not identify on their own the connections between the two disciplines and so could not explicitly use it to promote their understanding. Recommendations for Practitioners: Creative educators, who value challenges, can greatly benefit their students if they collaborate in aim for applying interdisciplinary learning while combining those two disciplines. The research conclusions shows that it is possible to improve students’ understanding if teachers explicitly mediate and guide students in drawing analogies. Recommendation for Researchers: The analysis tool we developed and apply can be used by educators and researchers to evaluate the understanding of argumentative texts by learners. It can be used in language classes at all levels as well as by educators in other disciplines in which the understanding of the argumentative structure is fundamental. Impact on Society: Developing argumentation skills and computational thinking skills. Future Research: Vary future possible research can follow the presented approach: examining how LP teachers expose the logical structure of an argumentation paragraph when they write logic programs that describe the inference represented in texts; examining how language teachers coupe with learning and using LP; examines the knowledge and skills of students that experienced a mediate learning process in the two disciplines in parallel.


2014 ◽  
Vol 7 (3) ◽  
pp. 548-578 ◽  
Author(s):  
WALTER CARNIELLI ◽  
MARCELO E. CONIGLIO ◽  
RODRIGO PODIACKI ◽  
TARCÍSIO RODRIGUES

AbstractThis paper investigates the question of characterizing first-orderLFIs (logics of formal inconsistency) by means of two-valued semantics.LFIs are powerful paraconsistent logics that encode classical logic and permit a finer distinction between contradictions and inconsistencies, with a deep involvement in philosophical and foundational questions. Although focused on just one particular case, namely, the quantified logicQmbC, the method proposed here is completely general for this kind of logics, and can be easily extended to a large family of quantified paraconsistent logics, supplying a sound and complete semantical interpretation for such logics. However, certain subtleties involving term substitution and replacement, that are hidden in classical structures, have to be taken into account when one ventures into the realm of nonclassical reasoning. This paper shows how such difficulties can be overcome, and offers detailed proofs showing that a smooth treatment of semantical characterization can be given to all such logics. Although the paper is well-endowed in technical details and results, it has a significant philosophical aside: it shows how slight extensions of classical methods can be used to construct the basic model theory of logics that are weaker than traditional logic due to the absence of certain rules present in classical logic. Several such logics, however, as in the case of theLFIs treated here, are notorious for their wealth of models precisely because they do not make indiscriminate use of certain rules; these models thus require new methods. In the case of this paper, by just appealing to a refined version of the Principle of Explosion, or Pseudo-Scotus, some new constructions and crafty solutions to certain nonobvious subtleties are proposed. The result is that a richer extension of model theory can be inaugurated, with interest not only for paraconsistency, but hopefully to other enlargements of traditional logic.


2012 ◽  
Vol 14 (1) ◽  
pp. 1-63 ◽  
Author(s):  
R. CABALLERO ◽  
M. RODRÍGUEZ-ARTALEJO ◽  
C. A. ROMERO-DÍAZ

AbstractUncertainty in logic programming has been widely investigated in the last decades, leading to multiple extensions of the classical logic programming paradigm. However, few of these are designed as extensions of the well-established and powerful Constraint Logic Programming (CLP) scheme for CLP. In a previous work we have proposed the proximity-based qualified constraint logic programming (SQCLP) scheme as a quite expressive extension of CLP with support for qualification values and proximity relations as generalizations of uncertainty values and similarity relations, respectively. In this paper we provide a transformation technique for transforming SQCLP programs and goals into semantically equivalent CLP programs and goals, and a practical Prolog-based implementation of some particularly useful instances of the SQCLP scheme. We also illustrate, by showing some simple – and working – examples, how the prototype can be effectively used as a tool for solving problems where qualification values and proximity relations play a key role. Intended use of SQCLP includes flexible information retrieval applications.


2014 ◽  
Vol 14 (4-5) ◽  
pp. 725-737 ◽  
Author(s):  
ANGELOS CHARALAMBIDIS ◽  
ZOLTÁN ÉSIK ◽  
PANOS RONDOGIANNIS

AbstractExtensional higher-order logic programming has been introduced as a generalization of classical logic programming. An important characteristic of this paradigm is that it preserves all the well-known properties of traditional logic programming. In this paper we consider the semantics of negation in the context of the new paradigm. Using some recent results from non-monotonic fixed-point theory, we demonstrate that every higher-order logic program with negation has a unique minimum infinite-valued model. In this way we obtain the first purely model-theoretic semantics for negation in extensional higher-order logic programming. Using our approach, we resolve an old paradox that was introduced by W. W. Wadge in order to demonstrate the semantic difficulties of higher-order logic programming.


2020 ◽  
Vol 34 (03) ◽  
pp. 2750-2757
Author(s):  
Ringo Baumann ◽  
Dov Gabbay ◽  
Odinaldo Rodrigues

The notion of forgetting, as considered in the famous paper by Lin and Reiter in 1994 has been extensively studied in classical logic and more recently, in non-monotonic formalisms like logic programming. In this paper, we convey the idea of forgetting to another major AI formalism, namely Dung-style argumentation frameworks. Our approach is axiomatic-driven and not limited to any specific semantics: we propose semantical and syntactical desiderata encoding different criteria for what forgetting an argument might mean; analyze how these criteria relate to each other; and check whether the criteria can be satisfied in general. The analysis is done for a number of widely used argumentation semantics. Our investigation shows that almost all desiderata are individually satisfiable. However, combinations of semantical and/or syntactical conditions reveal a much more interesting landscape. For instance, we found that the ad hoc approach to forgetting an argument, i.e., by the syntactical removal of the argument and all of its associated attacks, is too restrictive and only compatible with the two weakest semantical desiderata. Amongst the several interesting combinations identified, we showed that one satisfies a notion of minimal change and presented an algorithm that given an AF F and argument x, constructs a suitable AF G satisfying the conditions in the combination.


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