Logica Universalis: Towards a General Theory of Logic

(ed.)
Boston: Birkhäuser Verlog (2005)
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Abstract

Universal Logic is not a new logic, but a general theory of logics, considered as mathematical structures. The name was introduced about ten years ago, but the subject is as old as the beginning of modern logic: Alfred Tarski and other Polish logicians such as Adolf Lindenbaum developed a general theory of logics at the end of the 1920s based on consequence operations and logical matrices. The subject was revived after the flowering of thousands of new logics during the last thirty years: there was a need for a systematic theory of logics to put some order in this chaotic multiplicity. This book contains recent works on universal logic by first-class researchers from all around the world. The book is full of new and challenging ideas that will guide the future of this exciting subject. It will be of interest for people who want to better understand what logic is. Tools and concepts are provided here for those who want to study classes of already existing logics or want to design and build new ones

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2007

Call number

QA9.2.L64 2005

ISBN(s)

0817672591   9780817672591   3764383534   9783764383534   3764372591

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Chapters

A global glance on categories in logic.Peter Arndt, Rodrigo Alvarenga Freirdee, Odilon Otavio Luciano & Hugo Luiz Mariano
Islamic Contradictory Theology . . . Is there any such Thing?Abbas Ahsan
Logica Universalis: Towards a General Theory of Logic.Jean-Yves Béziau (ed.)
1st World Logic Day: 14 January 2019.  (pages 1-20)Jean-Yves Beziau
A Buchholz Rule for Modal Fixed Point Logics.  (pages 1-19)Gerhard Jäger & Thomas Studer
Composition of Deductions within the Propositions-As-Types Paradigm.  (pages 1-13)Ivo Pezlar
Existence of Finite Total Equivalence Systems for Certain Closed Classes of 3-Valued Logic Functions.  (pages 1-26)Ilya Makarov
Games and Lindström Theorems.  (pages 1-21)Cheng Liao
Logic and Religion.  (pages 1-12)Jean-Yves Beziau & Ricardo Silvestre
New dimensions on translations between logics.  (pages 1-18)Walter A. Carnielli, Marcelo E. Coniglio & Itala M. L. D’Ottaviano
Preface.  (pages 1-1)Jean-Yves Beziau & Gillman Payette
Preface.  (pages 1-2)Jean-Yves Béziau
Quantified Temporal Alethic Boulesic Doxastic Logic.  (pages 1-65)Daniel Rönnedal
Some general results about proof normalization.  (pages 1-29)Marc Aiguier & Delphine Longuet
Special Issue on Multimodal Logics: A Preface. [REVIEW]  (pages 1-5)Walter Carnielli & Claudio Pizzi
The Classical Constraint on Relevance.  (pages 1-15)Arnon Avron
The Cretan Square.  (pages 1-5)Jean-Yves Beziau & Jens Lemanski
The Future of Logic: Foundation-Independence.  (pages 1-20)Florian Rabe
The power of the hexagon.  (pages 1-43)Jean-Yves Béziau
Universal Logic: Evolution of a Project.  (pages 1-8)Jean-Yves Beziau
A global glance on categories in logic.  (pages 3-39)Peter Arndt, Rodrigo de Alvarenga Freire, Odilon Otavio Luciano & Hugo Luiz Mariano
From consequence operator to universal logic: a survey of general abstract logic.  (pages 3--17)Jean-Yves Beziau
Things that are right with the traditional square of opposition.  (pages 3-11)Terence Parsons
On the Historical Transformations of the Square of Opposition as Semiotic Object.  (pages 7-26)Ioannis M. Vandoulakis & Tatiana Yu Denisova
Quantified Multimodal Logics in Simple Type Theory.  (pages 7-20)Christoph Benzmüller & Lawrence C. Paulson
Aristotle’s Prototype Rule-Based Underlying Logic.  (pages 9-35)John Corcoran
Kneale’s Natural Deductions as a Notational Variant of Beth’s Tableaus.  (pages 11-26)Zvonimir Šikić
Applications of squares of oppositions and their generalizations in philosophical analysis.  (pages 13-29)Jan Woleński
Thinking Negation in Early Hinduism and Classical Indian Philosophy.  (pages 13-33)Purushottama Bilimoria
Universal Properties of Łukasiewicz Consequence.  (pages 17-24)Daniele Mundici
The geometry of standard deontic logic.  (pages 19-57)Alessio Moretti
A Bunch of Diagrammatic Methods for Syllogistic.  (pages 21-36)Frank Thomas Sautter
Multimodal Incompleteness Under Weak Negations.  (pages 21-31)Juliana Bueno-Soler
N.A. Vasil’ev’s Logical Ideas and the Categorical Semantics of Many-Valued Logic.  (pages 21-43)D. Y. Maximov
Omnipresence, Multipresence and Ubiquity: Kinds of Generality in and Around Mathematics and Logics. [REVIEW]  (pages 21-73)I. Grattan-Guinness
Abstract Categorical Logic.  (pages 23-67)Marc Aiguier & Isabelle Bloch
Proofs and Countermodels in Non-Classical Logics.  (pages 25-60)Sara Negri
A Formalism to Specify Unambiguous Instructions Inspired by Mīmāṁsā in Computational Settings.  (pages 27-55)Bama Srinivasan & Ranjani Parthasarathi
Characteristic Inference Rules.  (pages 27-46)Alex Citkin
Swyneshed, Aristotle and the Rule of Contradictory Pairs.  (pages 27-50)Stephen Read
Diagonalization in double frames.  (pages 31-39)Andrzej Wiśniewski & Jerzy Pogonowski
Visualizations of the square of opposition.  (pages 31-41)Peter Bernhard
On the Mosaic Method for Many-Dimensional Modal Logics: A Case Study Combining Tense and Modal Operators. [REVIEW]  (pages 33-69)Carlos Caleiro, Luca Viganò & Marco Volpe
Karma Theory, Determinism, Fatalism and Freedom of Will.  (pages 35-60)Ricardo Sousa Silvestre
Gentzen-Type Sequent Calculi for Extended Belnap–Dunn Logics with Classical Negation: A General Framework.  (pages 37-63)Norihiro Kamide
Two Early Arabic Applications of Model-Theoretic Consequence.  (pages 37-54)Wilfrid Hodges
Cut-free ordinary sequent calculi for logics having generalized finite-valued semantics.  (pages 41-70)Arnon Avron, Jonathan Ben-Naim & Beata Konikowska
Many-place sequent calculi for finitely-valued logics.  (pages 41-66)Alexej P. Pynko
Ploucquet’s “Refutation” of the Traditional Square of Opposition.  (pages 43-58)Wolfgang Lenzen
A Unified Semantics for a Family of Modal Logics with Propositional Constants.  (pages 45-66)Matteo Pascucci
From the Logical Square to Blanché’s Hexagon: Formalization, Applicability and the Idea of the Normative Structure of Thought. [REVIEW]  (pages 45-67)Aimable-André Dufatanye
Contrary-to-Duty Reasoning: A Categorical Approach.  (pages 47-92)Clayton Peterson
Kant’s Antinomies of Pure Reason and the ‘Hexagon of Predicate Negation’.  (pages 51-67)Peter McLaughlin & Oliver Schlaudt
Is the Principle of Contradiction a Consequence of $$x^{2}=x$$ x 2 = x?  (pages 55-81)Jean-Yves Beziau
Completeness: From Husserl to Carnap.  (pages 57-83)Víctor Aranda
Distributive-lattice semantics of sequent calculi with structural rules.  (pages 59-94)Alexej P. Pynko
John Buridan on the bearer of logical relations.  (pages 59-70)Ernesto Perini-Santos
From Logic in Islam to Islamic Logic.  (pages 61-83)Musa Akrami
Towards a More General Concept of Inference.  (pages 61-81)Ivo Pezlar
Structural Rules for Multi-valued Logics.  (pages 65-75)Nissim Francez & Michael Kaminski
Correspondence Analysis for Some Fragments of Classical Propositional Logic.  (pages 67-85)Yaroslav Petrukhin & Vasilyi Shangin
Structuring Co-constructive Logic for Proofs and Refutations.  (pages 67-97)James Trafford
The concept of relevance and the logic diagram tradition.  (pages 67-135)Jan Dejnožka
Existential Import, Aristotelian Logic, and its Generalizations.  (pages 69-102)Corina Strößner
Lindenbaum-Type Logical Structures.  (pages 69-102)Sayantan Roy, Sankha S. Basu & Mihir K. Chakraborty
Why the Logical Hexagon?  (pages 69-107)Alessio Moretti
From fibring to cryptofibring. A solution to the collapsing problem.  (pages 71-92)Carlos Caleiro & Jaime Ramos
Modal Extensions of Sub-classical Logics for Recovering Classical Logic.  (pages 71-86)Marcelo E. Coniglio & Newton M. Peron
Non-Classical Stems from Classical: N. A. Vasiliev’s Approach to Logic and his Reassessment of the Square of Opposition. [REVIEW]  (pages 71-76)Valentin A. Bazhanov
Logic of Determination of Objects (LDO): How to Articulate “Extension” with “Intension” and “Objects” with “Concepts”. [REVIEW]  (pages 75-89)Jean-Pierre Desclés & Anca Pascu
Duality Results for (Co)Residuated Lattices.  (pages 77-99)Chrysafis Hartonas
Non-traditional squares of predication and quantification.  (pages 77-85)Mireille Staschok
Beyond Rasiowan Systems: Unital Deductive Systems.  (pages 83-102)Alexei Y. Muravitsky
Natural Deduction for Post’s Logics and their Duals.  (pages 83-100)Yaroslav Petrukhin
Philosophical Significance of Universal Logic---On Second Revolution of Mathematical Logic.  (pages 83-100)H. C. He, Zhitao He, Yingcang Ma & Lirong Ai
An Unexpected Boolean Connective.  (pages 85-103)Sérgio Marcelino
Leibniz’s Ontological Proof of the Existence of God and the Problem of »Impossible Objects«.  (pages 85-104)Wolfgang Lenzen
Axiomatisations of the Genuine Three-Valued Paraconsistent Logics $$mathbf {L3AG}$$ L 3 A G and $$mathbf {L3BG}$$ L 3 B G.  (pages 87-121)Alejandro Hernández-Tello, Miguel Pérez-Gaspar & Verónica Borja Macías
Axiomatising the Prior Future in Predicate Logic.  (pages 87-101)Max Cresswell
The square of opposition and the paradoxes.  (pages 87-105)Teresa Marques
Curry’s Formalism as Structuralism.  (pages 91-100)Jonathan P. Seldin
Inference Rules in Nelson’s Logics, Admissibility and Weak Admissibility.  (pages 93-120)Sergei Odintsov & Vladimir Rybakov
Modelling inference in argumentation through labelled deduction: Formalization and logical properties. [REVIEW]  (pages 93-124)Carlos Iván Chesñevar & Guillermo Ricardo Simari
What is a logic translation?  (pages 95-124)Till Mossakowski, Răzvan Diaconescu & Andrzej Tarlecki
Inconsistency-Adaptive Dialogical Logic.  (pages 99-134)Mathieu Beirlaen & Matthieu Fontaine
Logical Consequence in Avicenna’s Theory.  (pages 101-133)Saloua Chatti
On a New Idiom in the Study of Entailment.  (pages 101-113)R. E. Jennings, Y. Chen & J. Sahasrabudhe
Positive Jonsson Theories.  (pages 101-127)Bruno Poizat & Aibat Yeshkeyev
A Cube of Opposition for Predicate Logic.  (pages 103-114)Jørgen Fischer Nilsson
A Short Note on Essentially Σ1 Sentences.  (pages 103-111)Franco Montagna & Duccio Pianigiani
Hypothetical Logic of Proofs.  (pages 103-140)Eduardo Bonelli & Gabriela Steren
Negative Predication and Distinctness.  (pages 103-138)Bartosz Więckowski
A Logical Analysis of the Anselm’s Unum Argumentum.  (pages 105-119)Jean-Pierre Desclés
On Induction Principles for Partial Orders.  (pages 105-147)Ievgen Ivanov
Aristotle’s Non-Logical Works and the Square of Oppositions in Semiotics.  (pages 107-126)Stefania Bonfiglioli
Approaching the alethic modal hexagon of opposition.  (pages 109-118)Peter Simons
Relative Contingency and Bimodality.  (pages 113-123)Claudio Pizzi
On the Meaning of Connectives (Apropos of a Non-Necessitarianist Challenge).  (pages 115-126)Luis Estrada-González
Structures of Opposition and Comparisons: Boolean and Gradual Cases.  (pages 115-149)Didier Dubois, Henri Prade & Agnès Rico
A Hexagonal Framework of the Field $${\mathbb{F}_4}$$ and the Associated Borromean Logic.  (pages 119-147)René Guitart
Monotonic and Non-monotonic Embeddings of Anselm’s Proof.  (pages 121-138)Jacob Archambault
On a Distinction of Two Facets of Meaning and its Role in Proof-theoretic Semantics.  (pages 121-127)Nissim Francez
Bimodal Logic with Contingency and Accident: Bisimulation and Axiomatizations.  (pages 123-147)Jie Fan
A Shared Framework for Consequence Operations and Abstract Model Theory.  (pages 125-145)Christian Wallmann
A new modal lindström theorem.  (pages 125-138)Johan van Benthem
Symmetric generalized galois logics.  (pages 125-152)Katalin Bimbó & J. Michael Dunn
The Method of Scientific Discovery in Peirce’s Philosophy: Deduction, Induction, and Abduction. [REVIEW]  (pages 127-164)Cassiano Terra Rodrigues
The square of opposition and the four fundamental choices.  (pages 127-141)Antonino Drago
On a Generalization of Equilogical Spaces.  (pages 129-140)Fabio Pasquali
Preface: Medieval Logic.  (pages 129-131)Rodrigo Guerizoli & Guy Hamelin
The Meanings of ‘Logic’ in the Thirteenth Century.  (pages 133-154)Alfredo Storck
Correction to: Sequent Systems for Negative Modalities.  (pages 135-135)Ori Lahav, João Marcos & Yoni Zohar
The Vatican Square.  (pages 135-141)Jean-Yves Beziau & Raffaela Giovagnoli
Hintikka Memorial Issue: Introduction and Remarks on Jaakko Hintikka’s Logical Philosophy.  (pages 137-145)Ahti-Veikko Pietarinen
Two semantical approaches to paraconsistent modalities.  (pages 137-160)Juliana Bueno-Soler
An Intensional Formalization of Generic Statements.  (pages 139-160)Hugolin Bergier
Computer-Assisted Analysis of the Anderson-Hájek Controversy.  (pages 139-151)Benzmüller Christoph, Weber Leon & Woltzenlogel Paleo Bruno
Computer-Assisted Analysis of the Anderson–Hájek Ontological Controversy.  (pages 139-151)C. Benzmüller, L. Weber & B. Woltzenlogel Paleo
Information algebras and consequence operators.  (pages 139-165)Jürg Kohlas & Robert F. Stärk
Extracting BB′IW Inhabitants of Simple Types From Proofs in the Sequent Calculus $${LT_\to^{t}}$$ L T → t for Implicational Ticket Entailment.  (pages 141-164)Katalin Bimbó & J. Michael Dunn
Venn Diagram with Names of Individuals and Their Absence: A Non-classical Diagram Logic.  (pages 141-206)Reetu Bhattacharjee, Mihir Kr Chakraborty & Lopamudra Choudhury
Aristotle’s Cubes and Consequential Implication.  (pages 143-153)Claudio Pizzi
Platonic Contrariety : Ancestor of the Aristotelian Notion of Contradiction ?  (pages 143-156)Geneviève Lachance
From Single Agent to Multi-Agent via Hypersequents.  (pages 147-166)Francesca Poggiolesi
Super Models.  (pages 147-150)Jaakko Hintikka
A Note on Logicality of Generalized Quantifiers.  (pages 149-152)Tin Perkov
A Pragmatic Dissolution of Curry’s Paradox.  (pages 149-175)Rafael Félix Mora Ramirez
From Blanché’s Hexagonal Organization of Concepts to Formal Concept Analysis and Possibility Theory.  (pages 149-169)Didier Dubois & Henri Prade
Beyond Logical Pluralism and Logical Monism.  (pages 151-174)Pavel Arazim
Perspectives on the Logical Study of Language.  (pages 151-163)Jaakko Hintikka
Russell and his sources for non-classical logics.  (pages 153-218)Irving H. Anellis
Topological Representation of Intuitionistic and Distributive Abstract Logics.  (pages 153-175)Andreas Bernhard Michael Brunner & Steffen Lewitzka
What is Identical?  (pages 153-170)Marta Vlasáková
Nominalism and Semantics in Abelard and Ockham.  (pages 155-180)Guy Hamelin & Danilo Luiz Silva Maia
Weakened semantics and the traditional square of opposition.  (pages 155-165)Luis Estrada-González
Disentangling Contradiction from Contrariety via Incompatibility.  (pages 157-170)Jean-Yves Beziau
Preface: Is logic universal? [REVIEW]  (pages 161-162)Jean-Yves Beziau
The Decision Problem for Effective Procedures.  (pages 161-174)Nathan Salmón
Human Rationality Challenges Universal Logic.  (pages 163-205)Brian R. Gaines
Negation and Paraconsistent Logics.  (pages 165-176)Soma Dutta & Mihir K. Chakraborty
On Non-Deterministic Quantification.  (pages 165-191)Thomas Macaulay Ferguson
On TAE Machines and Their Computational Power.  (pages 165-170)Apostolos Syropoulos
Characteristic Formulas of Partial Heyting Algebras.  (pages 167-193)Alex Citkin
Logical Extensions of Aristotle’s Square.  (pages 167-187)Dominique Luzeaux, Jean Sallantin & Christopher Dartnell
Structuralist logic: Implications, inferences, and consequences. [REVIEW]  (pages 167-181)Arnold Koslow
Two's Company: The humbug of many logical values.  (pages 169-189)Carlos Caleiro, Walter Carnielli, Marcelo Coniglio & João Marcos
A Reinterpretation of the Semilattice Semantics with Applications.  (pages 171-191)Yale Weiss
Hintikka on the “Kant–Frege View”: A Critical Assessment.  (pages 171-178)Giovanni Mion
Leibniz’s Logic and the “Cube of Opposition”.  (pages 171-189)Wolfgang Lenzen
The Classical Aristotelian Hexagon Versus the Modern Duality Hexagon.  (pages 171-199)Hans Smessaert
Eigenlogic in the Spirit of George Boole.  (pages 175-207)Zeno Toffano
Probability Logics for Reasoning About Quantum Observations.  (pages 175-219)Angelina Ilić Stepić, Zoran Ognjanović & Aleksandar Perović
Modal Definability: Two Commuting Equivalence Relations.  (pages 177-194)Yana Rumenova & Tinko Tinchev
On Pairs of Dual Consequence Operations.  (pages 177-203)Urszula Wybraniec-Skardowska & Jacek Waldmajer
The Semiotics of Spider Diagrams.  (pages 177-204)James Burton & John Howse
Hintikka, Free Logician.  (pages 179-201)Matthieu Fontaine
Ockham’s Calculus of Strict Implication.  (pages 181-191)Wolfgang Lenzen
Some restricted lindenbaum theorems equivalent to the axiom of choice.  (pages 183-199)David W. Miller
Strong Normalizability of Typed Lambda-Calculi for Substructural Logics.  (pages 189-207)Motohiko Mouri & Norihiro Kamide
Friendliness and sympathy in logic.  (pages 191-206)Jean-Yves Beziau
Friendliness and sympathy in logic.  (pages 191-206)David C. Makinson
Logical Friendliness and Sympathy in Logic.  (pages 191--205)David C. Makinson
Subalternation and existence presuppositions in an unconventionally formalized canonical square of opposition.  (pages 191-213)Dale Jacquette
Boethius of Dacia and Radulphus Brito on the Universal Sign ‘Every’.  (pages 193-211)Ana María Mora-Márquez
Calculi for Many-Valued Logics.  (pages 193-226)Michael Kaminski & Nissim Francez
Toward a Clarity of the Extreme Value Theorem.  (pages 193-214)Karin U. Katz, Mikhail G. Katz & Taras Kudryk
A Universal Approach to Guarantee Data Privacy.  (pages 195-209)Thomas Studer
Tableaux for Logics of Content Relationship and Set-Assignment Semantics.  (pages 195-219)Tomasz Jarmużek & Mateusz Klonowski
Deontological Square, Hexagon, and Decagon: A Deontic Framework for Supererogation.  (pages 201-216)Jan C. Joerden
General logic-systems and finite consequence operators.  (pages 201-208)Robert A. Herrmann
Hintikka and the Functions of Logic.  (pages 203-217)Montgomery Link
On Combined Connectives.  (pages 205-224)A. Sernadas, C. Sernadas & J. Rasga
Translating Non-classical Logics into Classical Logic by Using Hidden Variables.  (pages 205-224)Juan C. Agudelo-Agudelo
A Characterisation of Some $$\mathbf {Z}$$ Z -Like Logics.  (pages 207-219)Krystyna Mruczek-Nasieniewska & Marek Nasieniewski
Logic and Natural Selection.  (pages 207-223)Jaroslav Peregrin
A galois connection.  (pages 209-219)Stan J. Surma
Abelian Logic and the Logics of Pointed Lattice-Ordered Varieties.  (pages 209-233)Francesco Paoli, Matthew Spinks & Robert Veroff
Essential Structure of Proofs as a Measure of Complexity.  (pages 209-242)Jaime Ramos, João Rasga & Cristina Sernadas
Beppo Levi’s Analysis of the Paradoxes.  (pages 211-231)Riccardo Bruni
When the World is Not Enough: Medieval Ways to Deal with the Lack of Referents.  (pages 213-235)Frédéric Goubier & Ernesto Perini-Santos
Harmony in Multiple-Conclusion Natural-Deduction.  (pages 215-259)Nissim Francez
Singular Propositions, Negation and the Square of Opposition.  (pages 215-231)Lopamudra Choudhury & Mihir Kumar Chakraborty
How to take advantage of the blur between the finite and the infinite.  (pages 217-226)Pierre Cartier
Minimally generated abstract logics.  (pages 219-241)Steffen Lewitzka & Andreas B. M. Brunner
Varieties of Rigidity.  (pages 219-240)Tuukka Tanninen
A Dialectic Contra-Classical Logic.  (pages 221-229)Nissim Francez
A universal logic approach to adaptive logics.  (pages 221-242)Diderik Batens
Composition-Nominative Logics as Institutions.  (pages 221-238)Alexey Chentsov & Mykola Nikitchenko
From Truth Degree Comparison Games to Sequents-of-Relations Calculi for Gödel Logic.  (pages 221-235)Christian Fermüller, Timo Lang & Alexandra Pavlova
Is ‘No’ a Force-Indicator? Yes, Sooner or Later!  (pages 225-251)Fabien Schang & James Trafford
Logical discrimination (2nd edition).  (pages 225–246)Lloyd Humberstone
Referential Opacity and Epistemic Logic.  (pages 225-247)Saloua Chatti
The Place of Logic in Reasoning.  (pages 225-239)Daniel Kayser
Logic and colour.  (pages 227-248)Dany Jaspers
On Nonmonotonic Consequence Relations.  (pages 227-249)Alexei Muravitsky
Revising the Elenchus via Belief Revision.  (pages 231-258)Ekaterina Kubyshkina & Mattia Petrolo
A General Lindström Theorem for Some Normal Modal Logics.  (pages 233-264)Sebastian Enqvist
Metalogical Decorations of Logical Diagrams.  (pages 233-292)Lorenz Demey & Hans Smessaert
“Setting” n-Opposition.  (pages 235-263)Régis Pellissier
Analytics vs. Elements.  (pages 237-252)Costas Dimitracopoulos
Paradox, Closure and Indirect Speech Reports.  (pages 237-251)Stephen Read
A Molecular Logic of Chords and Their Internal Harmony.  (pages 239-269)Ingolf Max
Is Logic Necessary?  (pages 241-254)Gregory McColm
To Peirce Hintikka’s Thoughts.  (pages 241-262)Ahti-Veikko Pietarinen
Abstract logics, logic maps, and logic homomorphisms.  (pages 243-276)Steffen Lewitzka
Positive Amalgamation.  (pages 243-258)Mohammed Belkasmi
Theory of completeness for logical spaces.  (pages 243-291)Kensaku Gomi
Guest Editor’s Introduction: JvH100. [REVIEW]  (pages 249-267)Irving H. Anellis
On Refutation Rules.  (pages 249-254)Tomasz Skura
Mathematical Perspectives on Liar Paradoxes.  (pages 251-269)José-Luis Usó-Doménech, Josué-Antonio Nescolarde-Selva, Lorena Segura-Abad, Kristian Alonso-Stenberg & Hugh Gash
A Universal Algebraic Set Theory Built on Mereology with Applications.  (pages 253-283)Ioachim Drugus
Interconnection of the Lattices of Extensions of Four Logics.  (pages 253-281)Alexei Y. Muravitsky
Universal Logic and Aristotelian Logic: Formality and Essence of Logic.  (pages 253-278)Julie Brumberg-Chaumont
Carnap, Goguen, and the hyperontologies: Logical pluralism and heterogeneous structuring in ontology design. [REVIEW]  (pages 255-333)Dominik Lücke
Dung’s Argumentation is Essentially Equivalent to Classical Propositional Logic with the Peirce–Quine Dagger.  (pages 255-318)Dov M. Gabbay
Introducing H, an Institution-Based Formal Specification and Verification Language.  (pages 259-277)Răzvan Diaconescu
Ultravaluations and their Applications in $$\textsf{CPL}$$.  (pages 259-267)Krzysztof A. Krawczyk & Bożena Piȩta
Fraïssé’s Construction from a Topos-Theoretic Perspective.  (pages 261-281)Olivia Caramello
Innovation and Application of Logic: An Interview with Jaakko Hintikka.  (pages 263-271)Lu Wang
Elements of Categorical Logic: Fifty Years Later. [REVIEW]  (pages 265-273)Valeria de Paiva & Andrei Rodin
Perfect IFG-Formulas.  (pages 265-275)Allen L. Mann
Rooted Hypersequent Calculus for Modal Logic S5.  (pages 269-295)Hamzeh Mohammadi & Mojtaba Aghaei
Logic Prizes et Cætera.  (pages 271-296)Jean-Yves Beziau
Paraconsistent Orbits of Logics.  (pages 271-289)Edelcio G. de Souza, Alexandre Costa-Leite & Diogo H. B. Dias
Labelled Tableau Systems for Some Subintuitionistic Logics.  (pages 273-288)Minghui Ma
Deduction as Reduction, from a Categorical Point of View.  (pages 275-289)Dominique Duval
Birkhoff Completeness in Institutions.  (pages 277-309)Mihai Codescu & Daniel Găină
Jean van Heijenoort: Kaleidoscope. [REVIEW]  (pages 277-291)Anita Burdman Feferman
Structuring the universe of universal logic.  (pages 277-294)Vladimir L. Vasyukov
Correction to: Some Restricted Lindenbaum Theorems Equivalent to the Axiom of Choice.  (pages 279-279)David W. Miller
Erratum to: Universal Logic and Aristotelian Logic: Formality and Essence of Logic.  (pages 279-279)Julie Brumberg-Chaumont
First-Order Logic and First-Order Functions.  (pages 281-329)Rodrigo A. Freire
The Normal and Self-extensional Extension of Dunn–Belnap Logic.  (pages 281-296)Arnon Avron
Compositional Meaning in Logic.  (pages 283-295)Carlos Caleiro & Luca Viganò
Preface: Scope of Logic Theorems In Memoriam Adolf Lindenbaum.  (pages 283-284)Jean-Yves Beziau
Adolf Lindenbaum: Notes on his Life, with Bibliography and Selected References.  (pages 285-320)Jan Zygmunt & Robert Purdy
On the Universality of Atomic and Molecular Logics via Protologics.  (pages 285-322)Guillaume Aucher
$$hbox {Venn}{i{o1}}$$ Venn i o 1 : A Diagram System for Universe Without Boundary.  (pages 289-346)Reetu Bhattacharjee, Mihir Kr Chakraborty & Lopamudra Choudhury
Internal Diagrams and Archetypal Reasoning in Category Theory.  (pages 291-321)Eduardo Ochs
A refutation theory.  (pages 293-302)Tomasz Skura
Jean van Heijenoort and the Gödel Editorial Project.  (pages 293-299)John W. Dawson
Logical Squares for Classical Logic Sentences.  (pages 293-312)Urszula Wybraniec-Skardowska
On preserving.  (pages 295-310)Gillman Payette & Peter K. Schotch
A Note on a Description Logic of Concept and Role Typicality for Defeasible Reasoning Over Ontologies.  (pages 297-325)Ivan Varzinczak
Epistemic Logics with Quantification Over Epistemic Operators: Decidability and Expressiveness.  (pages 297-330)Gennady Shtakser
Farewell to Suppression-Freedom.  (pages 297-330)Tore Fjetland Øgaard
Self-Extensional Three-Valued Paraconsistent Logics.  (pages 297-315)Arnon Avron
Editor’s Introduction to Jean van Heijenoort, Historical Development of Modern Logic.  (pages 301-326)Irving H. Anellis
On the 3d visualisation of logical relations.  (pages 303-332)Hans Smessaert
Functorial duality for ortholattices and de Morgan lattices.  (pages 311-333)Katalin Bimbó
Generalization and Composition of Modal Squares of Oppositions.  (pages 313-325)Claudio Pizzi
Modal Multilattice Logic.  (pages 317-343)Norihiro Kamide & Yaroslav Shramko
The Logic with Truth and Falsehood Operators from a Point of View of Universal Logic.  (pages 319-325)Sergey Pavlov
Direct Proofs of Lindenbaum Conditionals.  (pages 321-343)René Gazzari
A Probabilistic Logic Between $$LPP1$$ L P P 1 and $$LPP2$$ L P P 2.  (pages 323-333)Šejla Dautović
A Reduction Theorem for the Kripke–Joyal Semantics: Forcing Over an Arbitrary Category can Always be Replaced by Forcing Over a Complete Heyting Algebra. [REVIEW]  (pages 323-334)Imants Barušs & Robert Woodrow
A Square of Oppositions in Intuitionistic Logic with Strong Negation.  (pages 327-338)François Lepage
Constrained Consequence.  (pages 327-350)Katarina Britz, Johannes Heidema & Ivan Varzinczak
Dualities for Płonka Sums.  (pages 327-339)Stefano Bonzio
Historical Development of Modern Logic.  (pages 327-337)Jean van Heijenoort
Measuring Inconsistency in Generalized Propositional Logic.  (pages 331-356)John Grant
On Rearrangement Inequalities for Triangular Norms and Co-norms in Multi-valued Logic.  (pages 331-346)Chai Wah Wu
On the Origin of Logical Determinism in Babylonia.  (pages 331-357)Andrew Schumann
Sound Reasoning : Prospects and Challenges of Current Acoustic Logics.  (pages 331-343)Marc Champagne
A Methodological Shift in Favor of (Some) Paraconsistency in the Sciences.  (pages 335-354)María del Rosario Martínez-Ordaz
Some multi-conclusion modal paralogics.  (pages 335-353)Casey McGinnis
What do Freyd’s Toposes Classify?  (pages 335-340)Peter Johnstone
Jean van Heijenoort’s Conception of Modern Logic, in Historical Perspective.  (pages 339-409)Irving H. Anellis
Syllogisms and 5-Square of Opposition with Intermediate Quantifiers in Fuzzy Natural Logic.  (pages 339-357)Petra Murinová & Vilém Novák
Abstract Logical Constants.  (pages 341-350)Tin Perkov
Dagger Categories of Tame Relations.  (pages 341-370)Bart Jacobs
On Transferring Model Theoretic Theorems of $${\mathcal{L}_{{\infty},\omega}}$$ L ∞, ω in the Category of Sets to a Fixed Grothendieck Topos.  (pages 345-391)Nathanael Leedom Ackerman
Probabilistic Argumentation: An Equational Approach.  (pages 345-382)D. M. Gabbay & O. Rodrigues
Sequent Systems for Negative Modalities.  (pages 345-382)Ori Lahav, João Marcos & Yoni Zohar
A Study of the Metatheory of Assertoric Syllogistic.  (pages 347-371)Maristela Rocha
On the Origin of Indian Logic from the Viewpoint of the Pāli Canon.  (pages 347-393)Andrew Schumann
On the Modal Logic of Jeffrey Conditionalization.  (pages 351-374)Zalán Gyenis
Coproduct and Amalgamation of Deductive Systems by Means of Ordered Algebras.  (pages 355-380)Ciro Russo
Generalized definitional reflection and the inversion principle.  (pages 355-376)Peter Schroeder-Heister
Bases for Structures and Theories I.  (pages 357-381)Jeffrey Ketland
Violence Hexagon.  (pages 359-371)Lorenzo Magnani
Why Make Things Simple When You Can Make Them Complicated? An Appreciation of Lewis Carroll’s Symbolic Logic.  (pages 359-379)Amirouche Moktefi
Quotient Completion for the Foundation of Constructive Mathematics.  (pages 371-402)Maria Emilia Maietti & Giuseppe Rosolini
Cubes and Hypercubes of Opposition, with Ethical Ruminations on Inviolability.  (pages 373-376)Frode Bjørdal
Measuring Inconsistency in Generalized Propositional Logic Extended with Nonunary Operators.  (pages 373-404)John Grant
New Logics for Quantum Non-individuals?  (pages 375-395)Jonas R. Becker Arenhart
Recovering a logic from its fragments by meta-fibring.  (pages 377-416)Marcelo Esteban Coniglio
The Klein Group, Squares of Opposition and the Explanation of Fallacies in Reasoning.  (pages 377-392)Serge Robert & Janie Brisson
Frege’s Ontological Diagram Completed.  (pages 381-387)David Makinson
Unification in Pretabular Extensions of S4.  (pages 381-397)Stepan I. Bashmakov
Locally Tabular $$ne $$ Locally Finite.  (pages 383-400)Sérgio Marcelino & Umberto Rivieccio
Numerical Existence Property and Categories with an Internal Copy.  (pages 383-394)Samuele Maschio
Weakening and Extending {mathbb{Z}}.  (pages 383-409)Mauricio Osorio, J. L. Carballido, C. Zepeda & J. A. Castellanos
An Extended Paradefinite Logic Combining Conflation, Paraconsistent Negation, Classical Negation, and Classical Implication: How to Construct Nice Gentzen-type Sequent Calculi.  (pages 389-417)Norihiro Kamide
A Non-Standard Analysis of a Cultural Icon: The Case of Paul Halmos.  (pages 393-405)Piotr Błaszczyk, Alexandre Borovik, Vladimir Kanovei, Mikhail G. Katz, Taras Kudryk, Semen S. Kutateladze & David Sherry
The Institution-Theoretic Scope of Logic Theorems.  (pages 393-406)Răzvan Diaconescu, Till Mossakowski & Andrzej Tarlecki
Logical Rules as Fractions and Logics as Sketches.  (pages 395-405)Dominique Duval
The Sphere Model of Consciousness: From Geometrical to Neuro-Psycho-Educational Perspectives.  (pages 395-415)P. Paoletti & T. Dotan Ben Soussan
The Sphere Model of Consciousness: From Geometrical to Neuro-Psycho-Educational Perspectives.  (pages 395-415)P. Paoletti & T. Dotan Ben Soussan
Canonical Extensions and Kripke–Galois Semantics for Non-distributive Logics.  (pages 397-422)Chrysafis Hartonas
The Role of the Common in Cognitive Prosperity: Our Command of the Unspeakable and Unwriteable.  (pages 399-433)John Woods
A Note on Two’s Company: “The Humbug of Many Logical Values”.  (pages 401-407)Daniel Skurt
Probabilization of Logics: Completeness and Decidability. [REVIEW]  (pages 403-440)Pedro Baltazar
A Categorical Interpretation of the Intuitionistic, Typed, First Order Logic with Hilbert’s $${\varepsilon}$$ ε -Terms.  (pages 407-418)Fabio Pasquali
Dugundji’s Theorem Revisited.  (pages 407-422)Marcelo E. Coniglio & Newton M. Peron
Tree-Like Proof Systems for Finitely-Many Valued Non-deterministic Consequence Relations.  (pages 407-420)Pawel Pawlowski
Expressivist Perspective on Logicality.  (pages 409-419)Pavel Arazim
Complementary Proof Nets for Classical Logic.  (pages 411-432)Gabriele Pulcini & Achille C. Varzi
Equilibrium States in Numerical Argumentation Networks.  (pages 411-473)D. M. Gabbay & O. Rodrigues
Jean van Heijenoort’s Contributions to Proof Theory and Its History.  (pages 411-458)Irving H. Anellis
Theological Discourse and Logic.  (pages 417-423)Stanisław Krajewski & Marcin Trepczyński
First-order Logics of Evidence and Truth with Constant and Variable Domains.  (pages 419-449)Abilio Rodrigues & Henrique Antunes
Widersinn in Husserl’s Pure Logic.  (pages 419-430)Manuel Gustavo Isaac
Admissibility in Positive Logics.  (pages 421-437)Alex Citkin
Encoding Complete Metric Structures by Classical Structures.  (pages 421-459)Nathanael Leedom Ackerman
Craig Interpolation in the Presence of Unreliable Connectives.  (pages 423-446)João Rasga, Cristina Sernadas & Amlcar Sernadas
Generalized Correspondence Analysis for Three-Valued Logics.  (pages 423-460)Yaroslav Petrukhin
The Talmudic Logic Project, Ongoing Since 2008.  (pages 425-442)Dov M. Gabbay, Uri Schild & Esther David
Theory of Semi-Instantiation in Abstract Argumentation.  (pages 431-516)D. M. Gabbay
Finite Tree-Countermodels via Refutation Systems in Extensions of Positive Logic with Strong Negation.  (pages 433-441)Tomasz Skura
Implicational Tonoid Logics: Algebraic and Relational Semantics.  (pages 435-456)Eunsuk Yang & J. Michael Dunn
An Alternative Definition of Quantifiers on Four-Valued Łukasiewicz Algebras.  (pages 439-463)L. J. González, M. B. Lattanzi & A. G. Petrovich
From Analogical Proportion to Logical Proportions.  (pages 441-505)Henri Prade & Gilles Richard
Counterpossibles and Normal Defaults in the Filioque Controversy.  (pages 443-455)Jacob Archambault
On Consequence and Rejection as Operators.  (pages 443-460)Alexei Muravitsky
There is No Paradox of Logical Validity.  (pages 447-467)Roy T. Cook
A Modern Rigorous Approach to Stratification in NF/NFU.  (pages 451-468)Tin Adlešić & Vedran Čačić
Implicational Partial Galois Logics: Relational Semantics.  (pages 457-476)Eunsuk Yang & J. Michael Dunn
Non-monotonic Logic and the Compatibility of Science and Religion.  (pages 457-466)Marcin Trepczyński
Which Mathematical Logic is the Logic of Mathematics?  (pages 459-475)Jaakko Hintikka
Bases for Structures and Theories II.  (pages 461-479)Jeffrey Ketland
Developing Metalogic to Formalize Ontological Disputes of the Systems in Metaphysics by Introducing the Notion of Functionally Isomorphic Quantifiers.  (pages 461-492)Jolly Thomas
Rejection: A Historico-Epistemological View.  (pages 461-482)Alexei Muravitsky
Classical Negation Strikes Back: Why Priest’s Attack on Classical Negation Can’t Succeed.  (pages 465-487)Jonas R. Becker Arenhart & Ederson Safra Melo
Thomas Manlevelt: God in Logic.  (pages 467-476)Alfred van der Helm
Forcing, Downward Löwenheim-Skolem and Omitting Types Theorems, Institutionally.  (pages 469-498)Daniel Găină
Natural Deduction for Quantum Logic.  (pages 469-497)K. Tokuo
The Universal Theory of First Order Algebras and Various Reducts.  (pages 475-500)Lawrence Valby
Frege’s Ancestral and Its Circularities.  (pages 477-483)Ignacio Angelelli
Mathematics and Theology in the Thought of Nicholas of Cusa.  (pages 477-485)Roman Murawski
k-Provability in $$\hbox {PA}$$ PA.  (pages 477-516)Paulo Guilherme Santos & Reinhard Kahle
Herbrand’s fundamental theorem in the eyes of Jean Van heijenoort.  (pages 485-520)Claus-Peter Wirth
Iterated Mixed Strategies and Pascal’s Wager.  (pages 487-494)Emil Badici
A Proof-Theoretic Semantics for Exclusion.  (pages 489-505)Nissim Francez & Michael Kaminski
Pecularities of Some Three- and Four-Valued Second Order Logics.  (pages 493-509)Allen P. Hazen & Francis Jeffry Pelletier
Graded Structures of Opposition in Fuzzy Natural Logic.  (pages 495-522)Petra Murinová
Logic Diagrams, Sacred Geometry and Neural Networks.  (pages 495-513)Jens Lemanski
Maximum Segments as Natural Deduction Images of Some Cuts.  (pages 499-533)Mirjana Borisavljević
The Scope of Gödel’s First Incompleteness Theorem.  (pages 499-552)Bernd Buldt
A Strong and Rich 4-Valued Modal Logic Without Łukasiewicz-Type Paradoxes.  (pages 501-522)José M. Méndez & Gemma Robles
A Routley–Meyer Semantics for Gödel 3-Valued Logic and Its Paraconsistent Counterpart.  (pages 507-532)Gemma Robles
The Pursuit of an Implication for the Logics L3A and L3B.  (pages 507-524)Alejandro Hernández-Tello, José Arrazola Ramírez & Mauricio Osorio Galindo
Pavel Florensky’s Theory of Religious Antinomies.  (pages 515-540)Paweł Rojek
Axiomatization of Some Basic and Modal Boolean Connexive Logics.  (pages 517-536)Mateusz Klonowski
Canonical Syllogistic Moods in Traditional Aristotelian Logic.  (pages 517-531)Enrique Alvarez-Fontecilla
Toward A Visual Proof System: Lewis Carroll’s Method of Trees.  (pages 521-534)Francine F. Abeles
Constrained Pseudo-Propositional Logic.  (pages 523-535)Ahmad-Saher Azizi-Sultan
Liberating Paraconsistency from Contradiction.  (pages 523-544)Jonas R. Becker Arenhart
Natural Deduction for Fitting’s Four-Valued Generalizations of Kleene’s Logics.  (pages 525-532)Yaroslav I. Petrukhin
The Grammar of Platonism.  (pages 533-541)Hartley Slater
Logic, Spatial Algorithms and Visual Reasoning.  (pages 535-543)Andrew Schumann & Jens Lemanski
On Rereading van Heijenoort’s Selected Essays.  (pages 535-552)Solomon Feferman
An Intuitionist Reasoning Upon Formal Intuitionist Logic: Logical Analysis of Kolmogorov’s 1932 Paper.  (pages 537-552)Antonino Drago
Gödel’s Second Theorem and the Provability of God’s Existence.  (pages 541-549)Meir Buzaglo
Two Squares of Opposition in Two Arabic Treatises: al-Suhrawardī and al-Sanūsī.  (pages 545-580)Saloua Chatti
Metalanguage and Revelation: Rethinking Theology’s Language and Relevance.  (pages 551-575)Andrea Vestrucci
In Defense of Logical Universalism: Taking Issue with Jean van Heijenoort. [REVIEW]  (pages 553-586)Philippe de Rouilhan
In Defense of Logical Universalism: Taking Issue with Jean van Heijenoort.  (pages 553-586)Philippe Rouilhan
Knowability and Other Onto-theological Paradoxes.  (pages 577-586)Franca D’Agostini
On the Logical Geometry of Geometric Angles.  (pages 581-601)Hans Smessaert & Lorenz Demey
Logic as Calculus Versus Logic as Language, Language as Calculus Versus Language as Universal Medium, and Syntax Versus Semantics.  (pages 587-596)Jan Woleński
Logic as a Science and Logic as a Theory: Remarks on Frege, Russell and the Logocentric Predicament.  (pages 597-613)Anssi Korhonen
Three-Dimensional Affine Spatial Logics.  (pages 603-620)Adam Trybus
Things May Not Be Simple: On Wittgenstein’s Internal Relations.  (pages 621-641)Fabien Schang
Observation of Autonomous Behavioral Selection in Physarum Plasmodium.  (pages 643-653)Tomohiro Shirakawa, Hiroshi Sato & Kazuki Ishimaru
Logics in Fungal Mycelium Networks.  (pages 655-669)Andrew Adamatzky, Phil Ayres, Alexander E. Beasley, Nic Roberts & Han A. B. Wösten
Brain and Its Universal Logical Model of Multi-Agent Biological Systems.  (pages 671-687)Jerzy Król, Andrew Schumann & Krzysztof Bielas

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Jean-Yves Beziau
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Citations of this work

Taking Degrees of Truth Seriously.Josep Maria Font - 2009 - Studia Logica 91 (3):383-406.
Human Rationality Challenges Universal Logic.Brian R. Gaines - 2010 - Logica Universalis 4 (2):163-205.

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