Alternative Logics. Do Sciences Need Them?
Paul A. Weingartner
Springer Science & Business Media, Mar 9, 2013 - Computers - 368 pages
Initially proposed as rivals of classical logic, alternative logics have become increasingly important in sciences such as quantum physics, computer science, and artificial intelligence. The contributions collected in this volume address and explore the question whether the usage of logic in the sciences, especially in modern physics, requires a deviation from classical mathematical logic. The articles in the first part of the book set the scene by describing the context and the dilemma when applying logic in science. In part II the authors offer several logics that deviate in different ways from classical logics. The twelve papers in part III investigate in detail specific aspects such as quantum logic, quantum computation, computer-science considerations, praxic logic, and quantum probability. Most of the contributions are revised and partially extended versions of papers presented at a conference of the same title of the Académie Internationale de Philosophie des Sciences held at the Internationales Forschungszentrum Salzburg in May 1999. Others have been added to complete the picture of recent research in alternative logics as they have been developed for applications in the sciences.
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The Relevance of the Referents for Logic
Does Metaphysics Need a NonClassical Logic?
Nature of and Contrasts Between the Two Programs
Some Examples Concerning Stochastic Learning Procedures
Variant SecondOrder Logics
Commensurability and Distributivity in Quantum Logic
The Language of Interpretation in Quantum Physics
The General Structure of Models
Remarks on Criteria of Truth and Models in Science
Significant? Not Significant?
Outline of a Paraconsistent Category Theory
The Paraconsistent Theory OB1
Combinatory Logic as an Applicative Language
Operators in Combinatory Logic
Meaningless and Types
Using Logic for Program and Invariant Construction
The Search for an Empirical Logic
The Quantum Physical Reality
Experimental Approach to QuantumLogical Connectives
A Normed Quantum Logic of Observables
Quantum Logic and Quantum Probability
Von Neumann Lattices as Logics