1. What is the concept of universal logic and its significance in the study of logic systems?
Universal logic is a general study of various systems of logic, considered as logical structures, similar to how universal algebra studies algebras as algebraic structures. It promotes unity in diversity by developing concepts in a general framework to better understand the universe of logic systems. Universal logic generalizes concepts used in classical or non-classical logic systems, such as the pivotal notion for an abstract version of the completeness theorem and the notion of maximal non-trivial theory. It also introduces new definitions and understandings of notions, like substitution, leading to the notion of structural consequence relation. Furthermore, it includes concepts like fibring, which is key in the theory of combining logics. Universal logic offers a new philosophical perspective and understanding of logic, breaking the dichotomy of syntax/semantics. It is not just a reflection of what exists but also the transformation and evolution of the science of logic. The UNILOG event, launched in 2005, has been a platform for discussions and contests related to fundamental problems regarding relationships between logic systems.
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2. How to define identity between logics?
Defining identity between logics involves establishing a common ground or criteria to determine when two logics are considered equivalent or identical. This process requires a deep understanding of the underlying principles, axioms, and rules of each logic system. Researchers explore various approaches, such as isomorphism, homomorphism, and equivalence, to establish a formal relationship between logics. By defining identity between logics, researchers can analyze the similarities and differences between different logic systems, facilitating the development of new theories and applications in fields like computer science, mathematics, and philosophy. The UNILOG contests, such as the 1st UNILOG in Montreux, 2005, have focused on addressing this fundamental question, contributing to the advancement of universal logic and the unification of logic research worldwide.
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3. What is the concept behind the journal Logics?
The journal Logics, proposed by the author in July 2021, aims to address all kinds of logic systems and different perspectives on logic. It emphasizes unity among the diversity of logic systems, contrasting with journals devoted to specific families of logic systems. The title 'Logics' signifies plurality, similar to 'languages', focusing on the study of various linguistic phenomena. The author's experience with MDPI's plural journal Philosophies influenced the concept. The journal Logics was launched by MDPI, with Valentin Goranko appointed as Editor-in-Chief. The author expresses support for the journal's success and willingness to contribute as a member of the editorial board. The research was funded by the Brazilian Research Council (CNPq).
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4. What is the significance of dates in historical accounts?
Dates of birth and death are crucial in historical accounts as they provide a precise timeline and emphasize the human development of sciences. By knowing when key personalities were born and died, we can better understand the context and progression of ideas. This approach also highlights that logic, as a science, has been developed by humans, not robots. It allows us to trace the evolution of different logical systems, such as Aristotelian logic, and their influences on other proposals like Indian logic, Talmudic logic, and Stoic logic. The systematization of Aristotelian syllogistic logic, including the theory of square opposition and the introduction of singular terms, showcases the complexity and variations within the field. Additionally, recognizing the contributions of individuals like Carroll, who was both a logician and author of Alice's Adventures in Wonderland, further enriches our understanding of the interplay between logic and literature.
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