Dealing with a certain polarity of thought, negation is, perhaps, the most crucial among the logical connectives. It has been studied since antiquity and has been subject to thorough investigations in the development of philosophical logic, linguistics, artificial intelligence and logic programming. This development shows that bringing into play various types of negation may produce highly fruitful and promising results in many areas, such as paraconsistent logic, non-monotonic reasoning, the theory of data bases and logic programming.
The properties of negation - in combination with those of other logical operations and structural features of the deductibility relation - serve as gateways among logical systems. Moreover, a difference between various logical systems can often be reconstructed as a difference of certain features of negation operators used in these systems.
Notwithstanding the importance of negation, the immense literature on negation is full of disagreements concerning at least necessary conditions under which a unary connective ought to be regarded as a negation operation, the syntactical type to which a negation operator should belong , etc. We hope that this session will contribute to comparing different kinds of negation, developing a general theory of negation, and investigating the scope and validity of principles about negation.
Topics suitable for this Special Session include, but are not limited to, the following ones:
● proof-theoretical versus semantical treatments of negation
● negation, consistency, and inconsistency; interrelations between these notions
● negation and Galois connections; correspondence theory for negation
● negation in the light of modal logic
● negation in relevant and substructural logics
● constructive treatments of negation
● negation in belief revision
● negation in logic programming and non-monotonic reasoning
● negation in adaptive logics
● negation in paraconsistent logics
● negation in categorical grammar
● negation in concept analysis
Special Session
Organized by Sergei Odintsov
(Sobolev Institute of Mathematics, Russia)
and
Heinrich Wansing
(Dresden University of Technology , Germany)
Invited talk
Giulia Battilotti, Department of Pure and Applied Mathematics, University of Padua, Italy, "Negation as a Primitive Duality in a Model for Quantum Computation"
Accepted contributed talks
1. Ofer Arieli, Scool of Computer Science, The Academic College of Tel-Aviv, Israel, Arnon Avron, Scool of Computer Science, Tel-Aviv University, Israel and Anna Zamansky, Dept of Software Engineering, Jerusalem College of Engineering, Israel, "All Natural Three-valued Paraconsistent Logics are Maximal"
2. Diderik Batens, Centre for Logic and Philosophy of Science, Gent University, Belgium, "Negations with a Contextual Meaning"
3. Jose Martinez Fernandez, Dept. of Logic, History and Philosophy of Science, University of Barcelona, Spain, "Negation and the Fixed-point Property"
4. Reinhard Kahle, Universidade Nova de Lisboa, Portugal, "Negation: Default is Explicit + Update"
5. Hitoshi Omori, Toshiharu Waragai, Tokio Institute of Technology, "Some Modal Logics Seen as Subsystems of Classical Propositional Calculus"
6. Andreas Pietz, Logic, Language and Cognition Research Group, University of Barcelona, Spain, "Negation in Dual Intuitionistic Logic"
7. Dave Ripley, Institut Jean-Nicod, France, "Weak Negations and Neighborhood Semantics"
8. Sebastian Sequoiah-Grayson, Centre for Logic, Institute of Philosophy University of Leuven, Belgium, "Negation as Test-failure DPL and Negation as Process Exclusion in Categorical Grammar"
9. Luca Tranchini, Philosophy and Social Sciences Department Siena University, Italy and Wilhelm-Schickard-Institute for Computer Science Tuebingen University, Germany, Negation and Refutation in Proof-theoretic Semantics
10. Susumu Yamasaki, Department of Computer Science, Okayama University, Japan, "Nonmonotonic Functions Caused by Distributive Negatives"
