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Bimbo, Katalin, , . Proof Theory: Sequent Calculi and Related Formalisms
2015, CRC Press, Boca Raton, FL
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Added by: Berta Grimau, Contributed by:

Publisher’s Note: Although sequent calculi constitute an important category of proof systems, they are not as well known as axiomatic and natural deduction systems. Addressing this deficiency, Proof Theory: Sequent Calculi and Related Formalisms presents a comprehensive treatment of sequent calculi, including a wide range of variations. It focuses on sequent calculi for various non-classical logics, from intuitionistic logic to relevance logic, linear logic, and modal logic. In the first chapters, the author emphasizes classical logic and a variety of different sequent calculi for classical and intuitionistic logics. She then presents other non-classical logics and meta-logical results, including decidability results obtained specifically using sequent calculus formalizations of logics.

Comment: This book can be used in a variety of advanced undergraduate and postgraduate courses. Chapters 1, 2, 3 and 8 may be useful in an advanced undergraduate or beginning graduate course, where an emphasis is placed on classical logic and on a range of different proof calculi (mainly for classical logic). Chapters 4, 5 and 6 deal almost exclusively with non-classical logics. Chapters 7 and 9 are rich in meta-logical results, including results that have been obtained specifically using sequent calculus formalizations of various logics. These last five chapters might be used in a graduate course that embraces classical and nonclassical logics together with their meta-theory. To facilitate the use of the book as a text in a course, the text is peppered with exercises. In general, the starring indicates an increase in difficulty, however, sometimes an exercise is starred simply because it goes beyond the scope of the book or it is very lengthy. Solutions to selected exercises may be found on the web at the URL www.ualberta.ca/˜bimbo/ProofTheoryBook.

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Bobzien, Susanne, , . Ancient Logic
2016, The Stanford Encyclopedia of Philosophy
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Added by: Berta Grimau, Contributed by: Giada Fratantonio

Summary: A comprehensive introduction to ancient (western) logic from the 5th century BCE to the 6th century CE, with an emphasis on topics which may be of interest to contemporary logicians. Topics include pre-Aristotelian logic, Aristotelian logic, Peripatetic logic, Stoic Logic and a note on Epicureans and their views on logic.

Comment: This paper would be ideal as an introductory overview for a course on ancient logic. Alternatively, it could serve as an overview for a module on ancient logic within a more general course on the history of logic. No prior knowledge of logic is required; formalisms are for the most part avoided in the paper. Note that this is a SEP entry, so it’s completely accessible to students.

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Bobzien, Susanne, , . Stoic Syllogistic
1996, Oxford Studies in Ancient Philosophy 14: 133-92.
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Added by: Berta Grimau, Contributed by: Giada Fratantonio

Abstract: For the Stoics, a syllogism is a formally valid argument; the primary function of their syllogistic is to establish such formal validity. Stoic syllogistic is a system of formal logic that relies on two types of argumental rules: (i) 5 rules (the accounts of the indemonstrables) which determine whether any given argument is an indemonstrable argument, i.e. an elementary syllogism the validity of which is not in need of further demonstration; (ii) one unary and three binary argumental rules which establish the formal validity of non-indemonstrable arguments by analysing them in one or more steps into one or more indemonstrable arguments (cut type rules and antilogism). The function of these rules is to reduce given non-indemonstrable arguments to indemonstrable syllogisms. Moreover, the Stoic method of deduction differs from standard modern ones in that the direction is reversed (similar to tableau methods). The Stoic system may hence be called an argumental reductive system of deduction. In this paper, a reconstruction of this system of logic is presented, and similarities to relevance logic are pointed out.

Comment: This paper can be used as specialised/further reading for an advanced undergrad or postgraduate course on ancient logic or as a primary reading in an advanced undergrad or postgraduate course on Stoic logic. Alternatively, given that the text argues that there are important parallels between Stoic logic and Relevance logic, it could be used in a course on Relevance logic as well. It requires prior knowledge of logic (in particular, proof theory).

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Kouri Kissel, Teresa, , Stewart Shapiro. Classical Logic
2018, The Stanford Encyclopedia of Philosophy, Edward N. Zalta (ed.)
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Summary: This article provides the basics of a typical logic, sometimes called ‘classical elementary logic’ or ‘classical first-order logic’, in a rigorous yet accessible manner. Section 2 develops a formal language, with a syntax and grammar. Section 3 sets up a deductive system for the language, in the spirit of natural deduction. Section 4 provides a model-theoretic semantics. Section 5 turns to the relationships between the deductive system and the semantics, and in particular, the relationship between derivability and validity. The authors show that an argument is derivable only if it is valid (soundness). Then they establish a converse: that an argument is valid only if it is derivable (completeness). They also briefly indicate other features of the logic, some of which are corollaries to soundness and completeness. The final section, Section 6, is devoted to a brief examination of the philosophical position that classical logic is ‘the one right logic’.

Comment: This article introduces all the necessary tools in order to understand both the proof-theoretic and the model-theoretic aspects of first-order classical logical consequence. As such it can be used as a main reading in an introductory logic course covering classical first-order logic (assuming the students will have already looked at classical propositional logic). Moreover, the article covers some metatheoretic results (soundness, completeness, compactness, upward and downward Löwenheim-Skolem), which makes it suitable as a reading for a slightly more advanced course in logic. Finally, the article includes a brief incursion into the topic of logical pluralism. This makes it suitable to be used in a course on non-classical logics with an introduction module on classical logic.

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Rošker, Jana S., , . Classical Chinese Logic
2015, Philosophy Compass, 10(5): 301-309.
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Abstract: The present article provides an introduction to classical Chinese logic, a term which refers to ancient discourses that were developed before the arrival of significant external influences and which flourished in China until the first unification of China, during the Qin Dynasty. Taking as its premise that logic implies both universal and culturally conditioned elements, the author describes the historical background of Chinese logic, the main schools of Chinese logical thought, the current state of research in this area and the crucial concepts and methods applied in classical Chinese logic. The close link between Chinese logic and the Chinese language is also stressed

Comment: Presupposes some familiarity with Aristotelian and Fregean logic, as well as ideas in analytic philosophy of language (e.g., theories of reference). This would be a good piece for countering the prejudice that nothing worthy of being called logic was done in the classical Chinese tradition. It is also a good piece for expanding students’ imaginative horizons and showing them how their ideas of what logic is have been culturally shaped.

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