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Propositional Logic

 Summary Propositional logic is the simpler of the two modern classical logics.  It ignores entirely the structure within propositions.  In classical propositional logic, molecular or compound propositions are built up from atomic propositions by means of the connectives, whose meaning is given by their truth tables.  The principle by which the meaning or truth conditions of compound propositions can be recovered by this "building up" process is known as compositionality. This leaf node is a sub-category of classical logic.  As such, non-standard propositional logics are not normally classified in this category—unless a comparison between classical logic and another logic is being drawn or one is reduced to the other—although restrictions of propositional logic in which nothing not a theorem in ordinary propositional logic is a theorem in the restriction do fit here.  Also appropriate here are modest extensions of propositional logic, provided that Boole's three laws of thought are not violated, viz. a proposition is either true or false, not neither, and not both. Meta-theoretical results for propositional logic are also generally classified as "proof theory," "model theory," "mathematical logic," etc.
 Key works See below.
 Introductions Because of the age of propositional logic there are literally hundreds of introductions to logic which cover this subject reasonably well.   Instructors will have their own favorites. In selecting a book for classroom use, I recommend checking one thing: how much meta-theory is included, so that the book is neither below nor above the level students can handle.
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1. I give an account of proof terms for derivations in a sequent calculus for classical propositional logic. The term for a derivation δ of a sequent Σ≻Δ encodes how the premises Σ and conclusions Δ are related in δ. This encoding is many–to–one in the sense that different derivations can have the same proof term, since different derivations may be different ways of representing the same underlying connection between premises and conclusions. However, not all proof terms for a sequent Σ≻Δ (...)

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2. Logic: A Primer.Erich Rast - manuscript
This text is a short introduction to logic that was primarily used for accompanying an introductory course in Logic for Linguists held at the New University of Lisbon (UNL) in fall 2010. The main idea of this course was to give students the formal background and skills in order to later assess literature in logic, semantics, and related fields and perhaps even use logic on their own for the purpose of doing truth-conditional semantics. This course in logic does not replace (...)
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3. In this article I define a strong conditional for classical sentential logic, and then extend it to three non-classical sentential logics. It is stronger than the material conditional and is not subject to the standard paradoxes of material implication, nor is it subject to some of the standard paradoxes of C. I. Lewis’s strict implication. My conditional has some counterintuitive consequences of its own, but I think its pros outweigh its cons. In any case, one can always augment one’s language (...)

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4. The Truth Table Formulation of Propositional Logic.Tristan Grøtvedt Haze - forthcoming - Teorema: International Journal of Philosophy.
Developing a suggestion of Wittgenstein, I provide an account of truth tables as formulas of a formal language. I define the syntax and semantics of TPL (the language of Tabular Propositional Logic), and develop its proof theory. Single formulas of TPL, and finite groups of formulas with the same top row and TF matrix (depiction of possible valuations), are able to serve as their own proofs with respect to metalogical properties of interest. The situation is different, however, for groups of (...)

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5. Solving the Ross and Prior Paradoxes. Classical Modal Calculus..Pociej Jan - 2024 - Https://Doi.Org/10.6084/M9.Figshare.25257277.V1.
Resolving the Ross and Prior paradoxes proved to be a difficult task. Its first two stages, involving the identification of the true natures of the implication and truth values, are described in the articles "Solving the Paradox of Material Implication – 2024" and "Solving Jörgensen's Dilemma – 2024". This article describes the third stage, which involves the discovery of missing modal operators and the Classical Modal Calculus. Finally, procedures for solving both paradoxes are provided.

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6. LK is much more difficult than NK, and to make matters worse, Gentzen's intention is still unclear when it comes to that system (LK). -/- The second and third volumes of the series titled What is LK? conduct the detailed survey of each inference-figure in a toe-to-toe way, as it were, which most mathematicians looked through. -/- The present volume, Vol.2, looks deeper into structural inference-figures, which is never an easy task.

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7. LK is much more difficult than NK, and to make matters worse, Gentzen's intention is still unclear when it comes to that system (LK). -/- The second and third volumes of the series titled What is LK? conduct the detailed survey of each inference-figure in a toe-to-toe way, as it were, which most mathematicians looked through. -/- The present volume, Vol.3, looks deeper into those operational inference-figures which concerns propositional logic.

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8. A fundamental question asked in modal logic is whether a given theory is consistent. But consistent with what? A typical way to address this question identifies a choice of background knowledge axioms (say, S4, D, etc.) and then shows the assumptions codified by the theory in question to be consistent with those background axioms. But determining the specific choice and division of background axioms is, at least sometimes, little more than tradition. This paper introduces generic theories for propositional modal logic (...)

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9. What is LK? Vol.1. Sequent (Textbook Series in Symbolic Logic).Yusuke Kaneko - 2023 - Amazon Kindle.
LK is much more difficult than NK, and to make matters worse, Gentzen's intention is still unclear when it comes to that system (LK). -/- This book, Vol.1 of the series titled What is LK?, tackles this issue, focusing on the sequent, the most enigmatic notion we find in LK. The dependence-relation we find in NK shall play a crucial role in that investigation. -/- The style is typically textbook-like, so readers can learn the system of LK, using this series (...)

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10. As a result of trying to distinguish between what we do not know as humans and what we do know, concepts such as dialectic were formed. On this basis, logic was developed to monitor arguments' validity and provide methods for creating valid complex arguments. This work provides a brief overview of such topics and studies the development of formal logic and its semantics. In doing so, we enter the territory of propositional logic and predicate logic. In the next edition, we (...)

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11. Fichte’s Formal Logic.Jens Lemanski & Andrew Schumann - 2023 - Synthese 202 (1):1-27.
Fichte’s Foundations of the Entire Wissenschaftslehre 1794 is one of the most fundamental books in classical German philosophy. The use of laws of thought to establish foundational principles of transcendental philosophy was groundbreaking in the late eighteenth and early nineteenth century and is still crucial for many areas of theoretical philosophy and logic in general today. Nevertheless, contemporaries have already noted that Fichte’s derivation of foundational principles from the law of identity is problematic, since Fichte lacked the tools to correctly (...)

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12. Symbolic Logic.Rebeka Ferreira - 2022 - Gig Φ Philosophy.
Basic Concepts in Logic Identifying & Evaluating Arguments Valid Argument Forms Complex Arguments Propositional Logic: Symbols & Translation Truth Tables: Statements Classifying & Comparing Statements.

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13. Compatibility and accessibility: lattice representations for semantics of non-classical and modal logics.Wesley Holliday - 2022 - In David Fernández Duque & Alessandra Palmigiano (eds.), Advances in Modal Logic, Vol. 14. College Publications. pp. 507-529.
In this paper, we study three representations of lattices by means of a set with a binary relation of compatibility in the tradition of Ploščica. The standard representations of complete ortholattices and complete perfect Heyting algebras drop out as special cases of the first representation, while the second covers arbitrary complete lattices, as well as complete lattices equipped with a negation we call a protocomplementation. The third topological representation is a variant of that of Craig, Haviar, and Priestley. We then (...)

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14. Prof. Kingfisher’s beautiful logic of problem-solving.Nine-Dollar Kingfisher - 2022 - Mindsponge Portal.
*Special Note: This piece presents a paradox artificially created by Prof. Kingfisher for pondering. It must not be regarded as a given truth.

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15. A Pocket Guide to Formal Logic.Karl Laderoute - 2022 - Peterborough, CA: Broadview Press.
_A Pocket Guide to Formal Logic_ is a succinct primer meant especially for those without any prior background in logic. Its brevity makes it well-suited to introductory courses in critical thinking or introductory philosophy with a formal logic component, and its friendly tone offers a welcoming introduction to this often-intimidating subject. The book provides a focused presentation of common methods used in statement logic, including translations, truth tables, and proofs. Supplemental materials—including more detailed treatments of select methods and concepts as (...)

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16. On the Logic of Belief and Propositional Quantification.Yifeng Ding - 2021 - Journal of Philosophical Logic 50 (5):1143-1198.
We consider extending the modal logic KD45, commonly taken as the baseline system for belief, with propositional quantifiers that can be used to formalize natural language sentences such as “everything I believe is true” or “there is something that I neither believe nor disbelieve.” Our main results are axiomatizations of the logics with propositional quantifiers of natural classes of complete Boolean algebras with an operator validating KD45. Among them is the class of complete, atomic, and completely multiplicative BAOs validating KD45. (...)

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17. Possibility Semantics.Wesley H. Holliday - 2021 - In Melvin Fitting (ed.), Selected Topics from Contemporary Logics. London: College Publications. pp. 363-476.
In traditional semantics for classical logic and its extensions, such as modal logic, propositions are interpreted as subsets of a set, as in discrete duality, or as clopen sets of a Stone space, as in topological duality. A point in such a set can be viewed as a "possible world," with the key property of a world being primeness—a world makes a disjunction true only if it makes one of the disjuncts true—which classically implies totality—for each proposition, a world either (...)

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18. This textbook is a logic manual which includes an elementary course and an advanced course. It covers more than most introductory logic textbooks, while maintaining a comfortable pace that students can follow. The technical exposition is clear, precise and follows a paced increase in complexity, allowing the reader to get comfortable with previous definitions and procedures before facing more difficult material. The book also presents an interesting overall balance between formal and philosophical discussion, making it suitable for both philosophy and (...)

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19. Normalisation and subformula property for a system of classical logic with Tarski’s rule.Nils Kürbis - 2021 - Archive for Mathematical Logic 61 (1):105-129.
This paper considers a formalisation of classical logic using general introduction rules and general elimination rules. It proposes a definition of ‘maximal formula’, ‘segment’ and ‘maximal segment’ suitable to the system, and gives reduction procedures for them. It is then shown that deductions in the system convert into normal form, i.e. deductions that contain neither maximal formulas nor maximal segments, and that deductions in normal form satisfy the subformula property. Tarski’s Rule is treated as a general introduction rule for implication. (...)

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20. Normalisation for Bilateral Classical Logic with some Philosophical Remarks.Nils Kürbis - 2021 - Journal of Applied Logics 2 (8):531-556.
Bilateralists hold that the meanings of the connectives are determined by rules of inference for their use in deductive reasoning with asserted and denied formulas. This paper presents two bilateral connectives comparable to Prior's tonk, for which, unlike for tonk, there are reduction steps for the removal of maximal formulas arising from introducing and eliminating formulas with those connectives as main operators. Adding either of them to bilateral classical logic results in an incoherent system. One way around this problem is (...)

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21. Note on 'Normalisation for Bilateral Classical Logic with some Philosophical Remarks'.Nils Kürbis - 2021 - Journal of Applied Logics 7 (8):2259-2261.
This brief note corrects an error in one of the reduction steps in my paper 'Normalisation for Bilateral Classical Logic with some Philosophical Remarks' published in the Journal of Applied Logics 8/2 (2021): 531-556.

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22. The Significance of Evidence-based Reasoning in Mathematics, Mathematics Education, Philosophy, and the Natural Sciences.Bhupinder Singh Anand - 2020 - Mumbai: DBA Publishing (First Edition).
In this multi-disciplinary investigation we show how an evidence-based perspective of quantification---in terms of algorithmic verifiability and algorithmic computability---admits evidence-based definitions of well-definedness and effective computability, which yield two unarguably constructive interpretations of the first-order Peano Arithmetic PA---over the structure N of the natural numbers---that are complementary, not contradictory. The first yields the weak, standard, interpretation of PA over N, which is well-defined with respect to assignments of algorithmically verifiable Tarskian truth values to the formulas of PA under the interpretation. (...)

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23. Constrained Pseudo-Propositional Logic.Ahmad-Saher Azizi-Sultan - 2020 - Logica Universalis 14 (4):523-535.
Propositional logic, with the aid of SAT solvers, has become capable of solving a range of important and complicated problems. Expanding this range, to contain additional varieties of problems, is subject to the complexity resulting from encoding counting constraints in conjunctive normal form. Due to the limitation of the expressive power of propositional logic, generally, such an encoding increases the numbers of variables and clauses excessively. This work eliminates the indicated drawback by interpolating constraint symbols and the set of natural (...)

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24. Choice-free stone duality.Nick Bezhanishvili & Wesley H. Holliday - 2020 - Journal of Symbolic Logic 85 (1):109-148.
The standard topological representation of a Boolean algebra via the clopen sets of a Stone space requires a nonconstructive choice principle, equivalent to the Boolean Prime Ideal Theorem. In this article, we describe a choice-free topological representation of Boolean algebras. This representation uses a subclass of the spectral spaces that Stone used in his representation of distributive lattices via compact open sets. It also takes advantage of Tarski’s observation that the regular open sets of any topological space form a Boolean (...)

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25. Traits essentiels d'une formalisation adéquate.Gheorghe-Ilie Farte - 2020 - Argumentum. Journal of the Seminar of Discursive Logic, Argumentation Theory and Rhetoric 18 (1):163-174.
In order to decide whether a discursive product of human reason corresponds or not to the logical order, one must analyze it in terms of syntactic correctness, consistency, and validity. The first step in logical analysis is formalization, that is, the process by which logical forms of thoughts are represented in different formal languages or logical systems. Although each thought can be properly formalized in different ways, the formalization variants are not equally adequate. The adequacy of formalization seems to depend (...)

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26. The accident of logical constants.Tristan Grøtvedt Haze - 2020 - Thought: A Journal of Philosophy 9 (1):34-42.
Work on the nature and scope of formal logic has focused unduly on the distinction between logical and extra-logical vocabulary; which argument forms a logical theory countenances depends not only on its stock of logical terms, but also on its range of grammatical categories and modes of composition. Furthermore, there is a sense in which logical terms are unnecessary. Alexandra Zinke has recently pointed out that propositional logic can be done without logical terms. By defining a logical-term-free language with the (...)

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27. The Power of Logic, 6th edition.Daniel Howard-Snyder, Frances Howard-Snyder & Ryan Wasserman - 2020 - New York: McGraw-Hill. Edited by Daniel Howard-Snyder & Ryan Wasserman.
This is a basic logic text for first-time logic students. Custom-made texts from the chapters is an option as well. And there is a website to go with text too.

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28. Calculus CL as a Formal System.Jens Lemanski & Ludger Jansen - 2020 - In Ahti Veikko Pietarinen, Peter Chapman, Leonie Bosveld-de Smet, Valeria Giardino, James Corter & Sven Linker (eds.), Diagrammatic Representation and Inference. Diagrams 2020. Lecture Notes in Computer Science, vol 12169. 2020. 93413 Cham, Deutschland: pp. 445-460.
In recent years CL diagrams inspired by Lange’s Cubus Logicus have been used in various contexts of diagrammatic reasoning. However, whether CL diagrams can also be used as a formal system seemed questionable. We present a CL diagram as a formal system, which is a fragment of propositional logic. Syntax and semantics are presented separately and a variant of bitstring semantics is applied to prove soundness and completeness of the system.

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29. Dynamic Non-Classicality.Matthew Mandelkern - 2020 - Australasian Journal of Philosophy 98 (2):382-392.
I show that standard dynamic approaches to the semantics of epistemic modals invalidate the classical laws of excluded middle and non-contradiction, as well as the law of epistemic non-contradiction. I argue that these facts pose a serious challenge.

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30. A Different Approach for Clique and Household Analysis in Synthetic Telecom Data Using Propositional Logic.Sandro Skansi, Kristina Šekrst & Marko Kardum - 2020 - In Marko Koričić (ed.), 2020 43rd International Convention on Information, Communication and Electronic Technology (MIPRO). IEEE Explore. pp. 1286-1289.
In this paper we propose an non-machine learning artificial intelligence (AI) based approach for telecom data analysis, with a special focus on clique detection. Clique detection can be used to identify households, which is a major challenge in telecom data analysis and predictive analytics. Our approach does not use any form of machine learning, but another type of algorithm: satisfiability for propositional logic. This is a neglected approach in modern AI, and we aim to demonstrate that for certain tasks, it (...)

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31. Form and Content: An Introduction to Formal Logic.Derek D. Turner - 2020 - Digital Commons @ Connecticut College.
Derek Turner, Professor of Philosophy, has written an introductory logic textbook that students at Connecticut College, or anywhere, can access for free. The book differs from other standard logic textbooks in its reliance on fun, low-stakes examples involving dinosaurs, a dog and his friends, etc. This work is published in 2020 under a Creative Commons AttributionNonCommercial-NoDerivatives 4.0 International License. You may share this text in any format or medium. You may not use it for commercial purposes. If you share it, (...)

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32. Algebraic and topological semantics for inquisitive logic via choice-free duality.Nick Bezhanishvili, Gianluca Grilletti & Wesley H. Holliday - 2019 - In Rosalie Iemhoff, Michael Moortgat & Ruy de Queiroz (eds.), Logic, Language, Information, and Computation. WoLLIC 2019. Lecture Notes in Computer Science, Vol. 11541. Springer. pp. 35-52.
We introduce new algebraic and topological semantics for inquisitive logic. The algebraic semantics is based on special Heyting algebras, which we call inquisitive algebras, with propositional valuations ranging over only the ¬¬-fixpoints of the algebra. We show how inquisitive algebras arise from Boolean algebras: for a given Boolean algebra B, we define its inquisitive extension H(B) and prove that H(B) is the unique inquisitive algebra having B as its algebra of ¬¬-fixpoints. We also show that inquisitive algebras determine Medvedev’s logic (...)

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33. Stoic Sequent Logic and Proof Theory.Susanne Bobzien - 2019 - History and Philosophy of Logic 40 (3):234-265.
This paper contends that Stoic logic (i.e. Stoic analysis) deserves more attention from contemporary logicians. It sets out how, compared with contemporary propositional calculi, Stoic analysis is closest to methods of backward proof search for Gentzen-inspired substructural sequent logics, as they have been developed in logic programming and structural proof theory, and produces its proof search calculus in tree form. It shows how multiple similarities to Gentzen sequent systems combine with intriguing dissimilarities that may enrich contemporary discussion. Much of Stoic (...)

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34. Question-Begging Arguments as Ones That Do Not Extend Knowledge.Rainer Ebert - 2019 - Philosophy and Progress 65 (1):125-144.
In this article, I propose a formal criterion that distinguishes between deductively valid arguments that do and do not beg the question. I define the concept of a Never-failing Minimally Competent Knower (NMCK) and suggest that an argument begs the question just in case it cannot possibly assist an NMCK in extending his or her knowledge.

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35. Two-Sided Trees for Sentential Logic, Predicate Logic, and Sentential Modal Logic.Jesse Fitts & David Beisecker - 2019 - Teaching Philosophy 42 (1):41-56.
This paper will present two contributions to teaching introductory logic. The first contribution is an alternative tree proof method that differs from the traditional one-sided tree method. The second contribution combines this tree system with an index system to produce a user-friendly tree method for sentential modal logic.

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36. A Note on Carnap’s Result and the Connectives.Tristan Haze - 2019 - Axiomathes 29 (3):285-288.
Carnap’s result about classical proof-theories not ruling out non-normal valuations of propositional logic formulae has seen renewed philosophical interest in recent years. In this note I contribute some considerations which may be helpful in its philosophical assessment. I suggest a vantage point from which to see the way in which classical proof-theories do, at least to a considerable extent, encode the meanings of the connectives (not by determining a range of admissible valuations, but in their own way), and I demonstrate (...)

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37. Oskari Kuusela, Wittgenstein on Logic as the Method of Philosophy: Re‐examining the Roots and Development of Analytic Philosophy . xi + 297, £55.00 hb. [REVIEW]Alessio Persichetti - 2019 - Philosophical Investigations 42 (4):424-427.

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38. Bilateralism, Independence and Coordination.Gonçalo Santos - 2018 - Teorema: International Journal of Philosophy 37 (1):23-27.
Bilateralism is a theory of meaning according to which assertion and denial are independent speech acts. Bilateralism also proposes two coordination principles for assertion and denial. I argue that if assertion and denial are independent speech acts, they cannot be coordinated by the bilateralist principles.

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39. Wordmorph!: A Word Game to Introduce Natural Deduction.Ian Stoner - 2018 - Teaching Philosophy 41 (2):199-204.
Some logic students falter at the transition from the mechanical method of truth tables to the less-mechanical method of natural deduction. This short paper introduces a word game intended to ease that transition.

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40. How May the Propositional Calculus Represent?Tristan Haze - 2017 - South American Journal of Logic 3 (1):173-184.
This paper is a conceptual study in the philosophy of logic. The question considered is 'How may formulae of the propositional calculus be brought into a representational relation to the world?'. Four approaches are distinguished: (1) the denotational approach, (2) the abbreviational approach, (3) the truth-conditional approach, and (4) the modelling approach. (2) and (3) are very familiar, so I do not discuss them. (1), which is now largely obsolete, led to some interesting twists and turns in early analytic philosophy (...)

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41. On the Concept of a Notational Variant.Alexander W. Kocurek - 2017 - In Alexandru Baltag, Jeremy Seligman & Tomoyuki Yamada (eds.), Logic, Rationality, and Interaction (LORI 2017, Sapporo, Japan). Springer. pp. 284-298.
In the study of modal and nonclassical logics, translations have frequently been employed as a way of measuring the inferential capabilities of a logic. It is sometimes claimed that two logics are “notational variants” if they are translationally equivalent. However, we will show that this cannot be quite right, since first-order logic and propositional logic are translationally equivalent. Others have claimed that for two logics to be notational variants, they must at least be compositionally intertranslatable. The definition of compositionality these (...)

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42. Bilateralist Detours: From Intuitionist to Classical Logic and Back.Nils Kürbis - 2017 - Logique Et Analyse 60 (239):301-316.
There is widespread agreement that while on a Dummettian theory of meaning the justified logic is intuitionist, as its constants are governed by harmonious rules of inference, the situation is reversed on Huw Price's bilateralist account, where meanings are specified in terms of primitive speech acts assertion and denial. In bilateral logics, the rules for classical negation are in harmony. However, as it is possible to construct an intuitionist bilateral logic with harmonious rules, there is no formal argument against intuitionism (...)

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43. Logika.Srećko Kovač - 2016 - Zagreb: Hrvatska sveučilišna naklada, 15th edition, corrected and revised.
The book contains an introduction to basic logical concepts and methods. It covers traditional logic of categorical judgment and syllogism, modern propositional logic, and introductory elements of predicate logic with corresponding methods (truth tables, natural deduction, truth trees).

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44. An Arithmetization of Logical Oppositions.Fabien Schang - 2016 - In Jean-Yves Béziau & Gianfranco Basti (eds.), The Square of Opposition: A Cornerstone of Thought. Basel, Switzerland: Birkhäuser. pp. 215-237.
An arithmetic theory of oppositions is devised by comparing expressions, Boolean bitstrings, and integers. This leads to a set of correspondences between three domains of investigation, namely: logic, geometry, and arithmetic. The structural properties of each area are investigated in turn, before justifying the procedure as a whole. Io finish, I show how this helps to improve the logical calculus of oppositions, through the consideration of corresponding operations between integers.

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45. Logical Squares for Classical Logic Sentences.Urszula Wybraniec-Skardowska - 2016 - Logica Universalis 10 (2-3):293-312.
In this paper, with reference to relationships of the traditional square of opposition, we establish all the relations of the square of opposition between complex sentences built from the 16 binary and four unary propositional connectives of the classical propositional calculus. We illustrate them by means of many squares of opposition and, corresponding to them—octagons, hexagons or other geometrical objects.

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46. The Logic Game: A Two-Player Game of Propositional Logic.Daniel J. Hicks & John Milanese - 2015 - Teaching Philosophy 38 (1):77-93.
This paper introduces The Logic Game, a two-player strategy game designed to help students in introductory logic classes learn the truth conditions for the logical operators. The game materials can be printed using an ordinary printer on ordinary paper, takes 10-15 minutes to play, and the rules are fairly easy to learn. This paper includes a complete set of rules, a URL for a website hosting all of the game materials, and the results of a study of the effectiveness of (...)

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47. What is wrong with classical negation?Nils Kürbis - 2015 - Grazer Philosophische Studien 92 (1):51-86.
The focus of this paper are Dummett's meaning-theoretical arguments against classical logic based on consideration about the meaning of negation. Using Dummettian principles, I shall outline three such arguments, of increasing strength, and show that they are unsuccessful by giving responses to each argument on behalf of the classical logician. What is crucial is that in responding to these arguments a classicist need not challenge any of the basic assumptions of Dummett's outlook on the theory of meaning. In particular, I (...)

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48. On Hilbert's Axiomatics of Propositional Logic.V. Michele Abrusci - 2014 - Perspectives on Science 22 (1):115-132.
Hilbert's conference lectures during the year 1922, Neuebegründung der Mathematik. Erste Mitteilung and Die logischen Grundlagen der Mathematik (both are published in (Hilbert [1935] 1965) pp. 157-195), contain his first public presentation of an axiom system for propositional logic, or at least for a fragment of propositional logic, which is largely influenced by the study on logical woks of Frege and Russell during the previous years.The year 1922 is at the beginning of Hilbert's foundational program in its definitive form. The (...)

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49. Inférences traditionelles comme n-lemmes.Gheorghe-Ilie Farte - 2014 - Argumentum. Journal of the Seminar of Discursive Logic, Argumentation Theory and Rhetoric 12 (2):136-140.
In this paper we propose to present from a new perspective some loci comunes of traditional logic. More exactly, we intend to show that some hypothetico-disjunctive inferences (i.e. the complex constructive dilemma, the complex destructive dilemma, the simple constructive dilemma, the simple destructive dilemma) and two hypothetico-categorical inferences (namely modus ponendo-ponens and modus tollendo-tollens) particularize two more abstract inferential structures: the constructive n-lemma and the destructive nlemma.

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50. Łukasiewicz Negation and Many-Valued Extensions of Constructive Logics.Thomas Macaulay Ferguson - 2014 - In Proc. 44th International Symposium on Multiple-Valued Logic. IEEE Computer Society Press. pp. 121-127.
This paper examines the relationships between the many-valued logics G~ and Gn~ of Esteva, Godo, Hajek, and Navara, i.e., Godel logic G enriched with Łukasiewicz negation, and neighbors of intuitionistic logic. The popular fragments of Rauszer's Heyting-Brouwer logic HB admit many-valued extensions similar to G which may likewise be enriched with Łukasiewicz negation; the fuzzy extensions of these logics, including HB, are equivalent to G ~, as are their n-valued extensions equivalent to Gn~ for any n ≥ 2. These enriched (...)

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