## Alternative Logics. Do Sciences Need Them?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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### Contents

3 | |

The Relevance of the Referents for Logic | 21 |

Does Metaphysics Need a NonClassical Logic? | 27 |

Noneism | 33 |

Noneist Logic | 37 |

Nature of and Contrasts Between the Two Programs | 47 |

References | 53 |

Inaccessible Cardinals | 59 |

Some Examples Concerning Stochastic Learning Procedures | 208 |

Praxic Logics | 215 |

Variant Epistemologies | 221 |

Variant SecondOrder Logics | 227 |

Commensurability and Distributivity in Quantum Logic | 236 |

References | 247 |

The Language of Interpretation in Quantum Physics | 249 |

Wider Issues | 255 |

NonEuclidean Geometry | 66 |

The General Structure of Models | 72 |

Remarks on Criteria of Truth and Models in Science | 79 |

Significant? Not Significant? | 87 |

Outline of a Paraconsistent Category Theory | 95 |

The Paraconsistent Theory OB1 | 104 |

References | 113 |

Combinatory Logic as an Applicative Language | 121 |

Operators in Combinatory Logic | 130 |

Meaningless and Types | 136 |

Conclusion | 142 |

InconsistencyAdaptive Logics | 156 |

In Conclusion | 162 |

References | 172 |

Using Logic for Program and Invariant Construction | 184 |

Conclusion | 201 |

The Search for an Empirical Logic | 261 |

Conclusion | 267 |

The Quantum Physical Reality | 275 |

Conclusion | 283 |

Experimental Approach to QuantumLogical Connectives | 285 |

Conclusion | 297 |

A Syntax | 303 |

A Normed Quantum Logic of Observables | 312 |

Final Remarks | 319 |

QuantumLogical Gates | 327 |

QuantumComputational Semantics | 333 |

Quantum Logic and Quantum Probability | 339 |

346 | |

Von Neumann Lattices as Logics | 354 |

361 | |