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Books by jean-yves beziau

Conceptual Clarifications: Tributes to Patrick Suppes (1922-2014)

This is a collection of papers written by people who have worked with Patrick Suppes or have been... more This is a collection of papers written by people who have worked with Patrick Suppes or have been influenced by his ideas. It is a tribute to the friend and professor, draw before his death.

Papers by jean-yves beziau

We develop a theory of psychic dispositions inspired by color theory, using the latest developmen... more We develop a theory of psychic dispositions inspired by color theory, using
the latest developments of this theory using the hexagon of opposition.

In a first part we discuss what can be considered as a game or not, examining some typical games,... more In a first part we discuss what can be considered as a game
or not, examining some typical games, giving a formula characterizing
games, differentiating games from science, art, religion, sport and business.
In a second part we discuss a central game notion, the notion of
rule. We distinguish four categories of rules for a game: framework rules,
deontic rules, strategic rules and teleological rules. Our discussion is illustrated
by many examples ranging from chess to soccer via frescobol
and doll’s tea party

Review of I. H. Anellis, Van Heijenoort -- Logic and its History in the Work and Writings of Jean van Heijenoort

Square of Opposition: A Diagram and a Theory in Historical Perspective

History and Philosophy of Logic, 2014

The New Rising of the Square of Opposition

Around and Beyond the Square of Opposition, 2012

The mathematical structure of logical syntax

Contemporary Mathematics, 1999

Logica Universalis, 2014

In view of the speedy and huge expansion of the universe of logics, the question of the scope of ... more In view of the speedy and huge expansion of the universe of logics, the question of the scope of validity and the domain of application of fundamental logic theorems is more than ever crucial. What is true for classical logic and theories based on it, does not necessarily hold for non-classical logics.

Yaroslav Shramko and Heinrich Wansing, Truth and Falsehood - An Inquiry into Generalized Logical Values

Studia Logica, 2014

Idempotent Full Paraconsistent Negations are not Algebraizable

Notre Dame Journal of Formal Logic, 1998

... It is easy to prove that the class of ABS for a given logic is not empty. This justifies the ... more ... It is easy to prove that the class of ABS for a given logic is not empty. This justifies the study of a logic from the point of view of its class of ABS, called the theory of valuation and developed by da Costa (for an overview on the subject see [6] and [7]). ...

From Consequence Operator to Universal Logic: A Survey of General Abstract Logic

Logica Universalis, 2007

We present an overview of the different frameworks and structures that have been proposed during ... more We present an overview of the different frameworks and structures that have been proposed during the last century in order to develop a general theory of logics. This includes Tarski’s consequence operator, logical matrices, Hertz’s Satzsysteme, Gentzen’s sequent calculus, Suszko’s abstract logic, algebraic logic, da Costa’s theory of valuation and universal logic itself.

Around and Beyond the Square of Opposition

The theory of oppositions based on Aristotelian foundations of logic has been pictured in a strik... more The theory of oppositions based on Aristotelian foundations of logic has been pictured in a striking square diagram which can be understood and applied in many different ways having repercussions in various fields: epistemology, linguistics, mathematics, sociology, physics. The square can also be generalized in other two-dimensional or multi-dimensional objects extending in breadth and depth the original Aristotelian theory. The square of opposition from its origin in antiquity to the present day continues to exert a profound impact on the development of deductive logic. Since 10 years there is a new growing interest for the square due to recent discoveries and challenging interpretations. This book presents a collection of previously unpublished papers by high level specialists on the square from all over the world.

Many-Valued and Kripke Semantics

The Age of Alternative Logics, 2006

Round Squares Are No Contradictions (Tutorial on Negation Contradiction and Opposition)

Springer Proceedings in Mathematics & Statistics, 2015

Studies in Universal Logic

Two Genuine 3-Valued Paraconsistent Logics

Intelligent Systems Reference Library, 2016

In this paper we examine up to which point Modern logic can be qualified as non-Aristotelian. Aft... more In this paper we examine up to which point Modern logic can be qualified as non-Aristotelian. After clarifying the difference between logic as reasoning and logic as a theory of reasoning, we compare syllogistic with propositional and first-order logic. We touch the question of formal validity, variable and mathematization and we point out that Gentzen's cut-elimination theorem can be seen as the rejection of the central mechanism of syllogistic -the cut-rule has been first conceived as a modus Barbara by Hertz. We then examine the non-Aristotelian aspect of some non-classical logics, in particular paraconsistent logic. We argue that a paraconsistent negation can be seen as neo-Aristotelian since it corresponds to the notion of subcontrary in Boethius' square of opposition. We end by examining if the comparison promoted by Vasiliev between non-Aristotelian logic and non-Euclidian geometry makes sense.

Panorama de l’Identite

المخاطبات, 2015