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Focuses on the significant connection between logic and information retrieval. Introduces the formalisms used in logical models for information retrieval, shows the use of logic to build the models, and presents a brief overview of some of the current logical models in information retrieval. (Author/AEF)

Beginning geometry students misunderstand the requirements of formal proof because of confusion between deductive reasoning and argumentation. Presented is a cognitive analysis of deductive organization versus argumentative organization of reasoning and the applications of this analysis to learning. Implications of a study analyzing students' written proofs is given. (MDH)

Provides four examples for testing the validity of logical arguments by using the method of truth trees. (YP)

A previous article argued that the tradition of teaching sentential logic in geometry should be challenged and suggested that sentential logic be moved to algebra and replaced by inferential logic. Specific inferential logic topics were also suggested. This article elaborates on the inference schemes suggested and describes general proof strategies. (JN)

Challenges traditional use of logic in the mathematics curriculum, indicating how it may be better used. Explicit suggestions and justification for placing inferential logic in high school geometry and relegating most of the sentential logic to algebra are provided. Overviews of both forms of logic are also provided. (JN)

A test of logic using implicational and disjunctive sentences was given to Chinese and English speakers. No differences were found on "if-then" sentences, but differences were found on "or" sentences. (MNS)

The authors argue that mathematics curricula and teachers should set as objectives the development of logical processes, concepts, and language. The teaching materials described in this article have been used to help second, fourth, and seventh graders become skillful in the use of logic. (PK)

The Logic Box, a mathematics laboratory device, is described. Students can solve simple problems, then go on and design moderately complex digital logic circuits in the program presented. (MP)

The thought processes of 507 elementary, secondary, and university students engaged in problem-solving situations are examined in this study. Results indicated that pupils who got correct answers often showed incorrect reasoning justifications. No significant sex differences were indicated. (MP)

The concept of proof is discussed from a "human" viewpoint. The author concludes that "a good proof is one which makes us wiser." (MP)

A project designed to stimulate analytical reasoning skills in elementary school students is described, with a sample of the developed exercises. The materials were found to generate and maintain an enthusiastic response from the group of gifted eight-year-olds with which they were used. (MP)

Traditional mathematics curriculum is unsuitable for gifted children. Computing, statistics, operations research, and logic are suggested as suitable new topics. (MP)

This study extends research of college students' comprehension of implication into the area of conjunction and disjunction. The results indicated that the majority of the students did not comprehend conjunction and disjunction well enough to correctly respond to most subtest components. (MP)

Activities are proposed which are designed to aid the development of formal reasoning processes in middle and junior high school pupils. It is felt the materials presented can be easily adapted by an instructor to many audience levels. The puzzle format is designed to increase student motivation for participation. (MP)

Increasing the amount of problem-solving training in the preservice education of mathematics teachers is promoted. Such problems should be designed to help preservice teachers acquire an "open search" frame of mind, according to the authors. (MP)

Discusses the postage rate increases in recent years and notes that if the trend continues the rate will reach three dollars an ounce by the year 2017. (GA)

The article titled "Evald Ilyenkov: 'On the State of Philosophy [Letter to the Central Committee of the Party]'" provides an analysis of the current state of philosophy and its role in the communist transformation of the world. The author argues that philosophy's influence is diminishing, with other schools and concepts gaining more prominence. They criticize the dominance of neopositivism in the natural sciences and the rise of anthropological and existential approaches in the humanities. The author also highlights the confusion surrounding the understanding of philosophy as a distinct science and calls for the development of a theory of dialectics before philosophers can intervene in other sciences. The text also discusses the training of philosophical cadres at Moscow State University, criticizing the lack of clarity and neglect of dialectical materialism in current philosophical education. [Extracted from the article]

Semi-overlap functions as a generalization of left-continuous t-norms also have residua. In this paper, we develop a new residuated logic, SOL-logic, based on semi-overlap functions and their residua. The corresponding algebraic structures, SOL-algebras, are defined, and the completeness of SOL with respect to SOL-algebras is proved. [ABSTRACT FROM AUTHOR]

Most people, evidence suggests, have a hard time thinking straight. Symbolic logic is a tool that can help remedy this problem. Unfortunately, it is highly abstract and uses symbols whose meanings rely on unintuitive arbitrary conventions. Without sacrificing rigor, iconic logic is more concrete and uses icons that resemble what they stand for and whose meanings are thus easier to picture, process, and remember. Here I review and critique iconic existential graphs and concept diagrams--the former link iconic logic to iconic mathematics; the latter expand popular Euler or Venn diagrams and have, to some degree, been empirically investigated for user-friendliness. I lay out how expertise in perception, cognition, and genetics can inform and improve such empirical research to help make iconic logic more ergonomic. After all, logic is a tool, and tools should not only suit their use but also their user. [ABSTRACT FROM AUTHOR]

In this paper, the predicate counterparts, defined both axiomatically and semantically by means of Kripke frames, of the modal propositional logics |$\textbf {GL}$|⁠ , |$\textbf {Grz}$|⁠ , |$\textbf {wGrz}$| and their extensions are considered. It is proved that the set of semantical consequences on Kripke frames of every logic between |$\textbf {QwGrz}$| and |$\textbf {QGL.3}$| or between |$\textbf {QwGrz}$| and |$\textbf {QGrz.3}$| is |$\Pi ^1_1$| -hard even in languages with three (sometimes, two) individual variables, two (sometimes, one) unary predicate letters, and a single proposition letter. As a corollary, it is proved that infinite families of modal predicate axiomatic systems, based on the classical first-order logic and the modal propositional logics |$\textbf {GL}$|⁠ , |$\textbf {Grz}$|⁠ , |$\textbf {wGrz}$| are not Kripke complete. Both |$\Pi ^1_1$| -hardness and Kripke incompleteness results of the paper do not depend on whether the logics contain the Barcan formula. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of similarity monadic MTL-algebras and study some of their related basic algebraic properties. Then we introduce and investigate similarity monadic filters of similarity monadic MTL-algebras. In particular, by means of similarity monadic filters, we give some characterizations of representable similarity monadic MTL-algebras. Finally, we introduce the logic of similarity monadic MTL-algebras and prove the completeness of them. [ABSTRACT FROM AUTHOR]

Łukasiewicz introduced a new methodological approach to the history of logic. It consists of the use of modern formal logic in the research of the history of logic. Although he was not the first to use formal logic in his historical research, Łukasiewicz was the first who used it consistently and formulated it as a requirement for a historian of logic. The aim of this paper is to present Łukasiewicz's contribution and the history of its formulation. In addition, the paper will present its reception. There are two main themes in Łukasiewicz's work on the history of logic. He discussed Stoic logic and Aristotle's syllogistic. The second part of the paper focuses on current reception of Łukasiewicz's contribution and on the question of whether there is a difference between knowledge about his contribution to Stoic logic and to Aristotle's syllogistic, given that it has been hypothesised that Łukasiewicz's contribution is currently more known among Aristotelian scholars than among those who focus on Stoic logic. Based on the papers that have appeared in the last five years at Web of Science and Scopus this hypothesis has not been confirmed. [ABSTRACT FROM AUTHOR]

The twentieth-century logical mainstream, derived from works by Łukasiewicz and Scholz, pictures the history of logic for the most part as the prehistory of Boolean–Fregean mathematical logic. Particularly, with respect to classical propositional calculus, the Stoic logic has been pictured as an early stage of it and Aristotle's or the Peripatetics' logic as a theory that assumes it. Although it was not emphasised, it follows that the ancient logics contain the principle of explosion. In the endmost quarter of the twentieth century, a competitive view began to spread to the effect that the ancient systems of logic were paraconsistent or relevantistic. In the twenty-first century, the latter view prevails and has every chance of becoming a new orthodoxy. It is claimed that although in Łukasiewicz's argument for the classicality of ancient logics, there are gaps, it may be demonstrated that the ancient logics contain the principle of explosion. [ABSTRACT FROM AUTHOR]

This interview was given by Yaroslav Shramko (b. 1963), professor of the Department of Philosophy and rector of the Kryvyi Rih State Pedagogical University (Ukraine). His main research interests lie in the fields of logic and analytical philosophy. He has carried out several projects on modern non-classical logic: 1996–1998, within the Alexander von Humboldt Foundation Fellowship at Humboldt University in Berlin (Germany); 1999–2000, within the Fulbright Program at Indiana University in Bloomington (USA); and 2003–2004, as a Wilhelm Bessel Awardee at Dresden University of Technology (Germany), among others. He has been a frequent invited speaker at international conferences and congresses. He is a member of the editorial boards of several international logic journals, such as Logic and Logical Philosophy (Torun, Poland), Bulletin of the Section of Logic (Łódź, Poland), European Journal of Mathematics (Springer), and Studia Logica (Springer). Prof Shramko is the author of "Truth and falsehood: An inquiry into generalized logical values" (Springer, 2011, joint work with Heinrich Wansing) and a number of articles on logic and analytic philosophy in peer-reviewed international journals. [ABSTRACT FROM AUTHOR]

This paper presents a concrete and a symbolic rewriting logic semantics for parametric time Petri nets with inhibitor arcs (PITPNs), a flexible model of timed systems where parameters are allowed in firing bounds. We prove that our semantics is bisimilar to the "standard" semantics of PITPNs. This allows us to use the rewriting logic tool Maude, combined with SMT solving, to provide sound and complete formal analyses for PITPNs. We develop and implement a new general folding approach for symbolic reachability, so that Maude-with-SMT reachability analysis terminates whenever the parametric state-class graph of the PITPN is finite. Our work opens up the possibility of using the many formal analysis capabilities of Maude—including full LTL model checking, analysis with user-defined execution strategies, and even statistical model checking—for such nets. We illustrate this by explaining how almost all formal analysis and parameter synthesis methods supported by the state-of-the-art PITPN tool Roméo can be performed using Maude with SMT. In addition, we also support analysis and parameter synthesis from parametric initial markings, as well as full LTL model checking and analysis with user-defined execution strategies. Experiments show that our methods outperform Roméo in many cases. [ABSTRACT FROM AUTHOR]

Hyperlogic is a hyperintensional system designed to regiment metalogical claims (e.g., "Intuitionistic logic is correct" or "The law of excluded middle holds") into the object language, including within embedded environments such as attitude reports and counterfactuals. This paper is the first of a two-part series exploring the logic of hyperlogic. This part presents a minimal logic of hyperlogic and proves its completeness. It consists of two interdefined axiomatic systems: one for classical consequence (truth preservation under a classical interpretation of the connectives) and one for "universal" consequence (truth preservation under any interpretation). The sequel to this paper explores stronger logics that are sound and complete over various restricted classes of models as well as languages with hyperintensional operators. [ABSTRACT FROM AUTHOR]

The book "Aristotle's Syllogism and the Creation of Modern Logic: Between Tradition and Innovation, 1820s–1930s" edited by Lukas M. Verburgt and Matteo Cosci is a valuable contribution to the history of logic. The collection of 14 papers aims to reassess the origins of modern formal logic and challenges the common narrative that modern logic began with Gottlob Frege in 1879, erasing lesser-known logicians, including women. The book provides a more accurate and complex narrative of the origins of modern logic by exploring the contributions of various logicians and their relation to traditional syllogistic logic. The chapters are organized chronologically and provide condensed overviews of the logicians' work, allowing for cross-readings and further exploration. However, it should be noted that the book does not discuss Aristotle's logic but focuses on logicians' relation to traditional syllogistic logic in the 19th and 20th centuries. Overall, the book challenges the traditional narrative and offers a richer understanding of the origins of modern logic. [Extracted from the article]